What separates a vector quantity from a scalar quantity?

A vector has magnitude and direction; a scalar has magnitude only. Velocity is a vector, while speed is a scalar.

When is the point-object model useful in kinematics?

When an object's size and rotation do not matter for the motion being studied. Its position can then represent the whole object.

When may the constant-acceleration kinematic equations be used?

Only over an interval with constant acceleration. They are not general formulas for changing acceleration.

Why must a velocity statement name or imply a reference frame?

Velocity depends on the observer's frame. The same object can be at rest in one frame and moving in another.

Why can horizontal and vertical projectile motion be analyzed separately?

Perpendicular components evolve independently. With negligible air resistance, gravity changes only the vertical component.

Can an object have zero velocity and nonzero acceleration at one instant?

Yes. At the top of a vertical toss, velocity is momentarily zero while gravitational acceleration still points downward.

A runner completes one lap and returns to the start. How do distance and displacement compare?

The distance is one lap, while the displacement is zero. Displacement depends only on the change from initial to final position.

What makes a reference frame convenient for a motion problem?

It makes the relevant positions or velocities simple. A good frame reduces bookkeeping without changing physical predictions.

How are the components of a launch velocity v at angle θ found?

v_x = v cos θ and v_y = v sin θ. The angle is measured from the positive horizontal axis.

What does average velocity measure?

Displacement per elapsed time. In one dimension, v_avg = Δx/Δt; direction comes from the sign of Δx.

Do a vector's magnitude and its component use different SI units?

No. A vector and each of its components use the same unit; for example, velocity and its x-component both use m/s.

A velocity-versus-time graph curves upward and becomes progressively steeper while staying above zero. What does that show?

The object moves in the positive direction and speeds up with increasing positive acceleration. The graph's slope is acceleration; because that slope changes, the acceleration is nonuniform.

What are a projectile's horizontal and vertical accelerations when air resistance is negligible and up is positive?

a_x = 0 and a_y = -g. Horizontal velocity stays constant while vertical velocity changes.

What does average acceleration measure?

Change in velocity per elapsed time. In one dimension, a_avg = Δv/Δt.

What does a negative one-dimensional vector component mean?

It points opposite the chosen positive direction. The minus sign describes direction, not a negative physical size.

For constant acceleration, what does v = v₀ + at retrieve?

Velocity after elapsed time t. Use it when initial velocity, constant acceleration, and time are known or related.

How are a vector's magnitude and direction reconstructed from perpendicular components v_x and v_y?

v = √(v_x² + v_y²). When v_x ≠ 0, use θ = tan⁻¹(v_y/v_x) and the component signs to choose the quadrant. If v_x = 0 and v_y ≠ 0, the vector points along +y or -y; if both components are zero, its direction is undefined.

At an instant when velocity is nonzero, how do velocity and acceleration signs show whether a one-dimensional object is speeding up?

It speeds up when velocity and acceleration have the same sign. Opposite signs mean speed is decreasing at that instant.

What does the slope of a position-versus-time graph represent?

Velocity. A steeper slope means a larger speed, and the slope's sign gives direction.

Two observers use inertial frames, where an object with zero net force has constant velocity. If the observers move at constant velocity relative to each other, do they agree on an object's acceleration?

Yes, in a Galilean inertial-frame model. Subtracting a constant frame velocity changes velocity but not acceleration. This definition distinguishes an inertial frame from an accelerating, noninertial frame.

A projectile lands at its launch height with negligible air resistance. How do its launch and landing speeds compare?

They are equal. The horizontal component is unchanged, and the vertical component returns with equal magnitude and opposite sign.

A car's velocity changes from -2 m/s to +6 m/s in 2 s. What is its average acceleration?

+4 m/s². Δv = 8 m/s, and 8 m/s ÷ 2 s = 4 m/s².

If the positive axis is reversed, what happens to a one-dimensional vector component and its magnitude?

The component changes sign, while the magnitude stays the same. A coordinate choice changes the signed description, not the physical vector.

For constant acceleration, what does Δx = v₀t + ½at² retrieve?

Displacement over time t. It includes both initial-velocity motion and the displacement added by constant acceleration.

For a horizontal launch from height h in uniform gravity with negligible air resistance, what sets the time to reach the ground?

The vertical drop alone. Starting with v_y = 0, the time follows h = ½gt² and does not depend on horizontal speed.

Why can average speed differ from the magnitude of average velocity?

Average speed uses total distance, while average velocity uses displacement. Reversing direction increases distance without necessarily increasing displacement.

What does the slope of a velocity-versus-time graph represent?

Acceleration. The slope's units are (m/s)/s = m/s².

A passenger walks forward at 2 m/s inside a train moving forward at 18 m/s. What is the passenger's ground velocity?

20 m/s forward. Add the passenger's train-relative velocity to the train's ground velocity.

Does projectile mass affect the ideal trajectory when air resistance is negligible?

No. All projectiles have the same gravitational acceleration, so equal initial conditions give equal trajectories.

Can an object have nonzero velocity and zero acceleration?

Yes. Constant-velocity motion has nonzero velocity while the velocity change, and therefore acceleration, is zero.

A cart starts from rest with constant acceleration. Which graph should be linear if x = x₀ + ½at² applies?

Position x versus t². Its slope is ½a when the initial velocity is zero.

What does signed area under a velocity-versus-time graph represent?

Displacement. Area below the time axis contributes negative displacement.

At the highest point of a projectile's path, what are its vertical velocity and vertical acceleration?

v_y = 0, but a_y = -g. The vertical velocity pauses before reversing; gravity does not switch off.

How can a motion sensor test whether a cart moves at constant velocity?

Record position at equal time intervals and graph position versus time. A straight line with nearly constant slope supports constant velocity.

A car passes a parked observer at 12 m/s. What is the parked observer's velocity in the car's frame?

-12 m/s. In the car's frame, the ground and observer move backward at the car's speed.

Which constant-acceleration equation connects speed and displacement without using time?

v² = v₀² + 2aΔx. Use signed one-dimensional quantities and constant acceleration.

How could video data test the independence of projectile components?

Track x and y at equal times. A linear x-versus-t graph and a quadratic vertical trend support constant horizontal velocity and vertical acceleration.

A velocity-versus-time graph stays below zero but slopes upward toward zero. What is happening?

The object moves in the negative direction while slowing down. Velocity is negative and acceleration is positive.

How can average velocity over a very short interval approximate instantaneous velocity?

Shrink the time interval around the instant. The displacement divided by that short interval approaches the local position–time graph slope.

A walker moves 7 m east, then 3 m west. What is the one-dimensional displacement if east is positive?

+4 m. Add signed displacements: +7 m + (-3 m) = +4 m.

What shape is the path of a projectile with a nonzero horizontal velocity component in a uniform gravitational field when air resistance is negligible?

A parabola. Constant horizontal velocity and constant vertical acceleration produce the curve. A purely vertical launch is the special case: its spatial path is a vertical line.

In a motion diagram with dots at equal time intervals and velocity arrows, what do wider dot spacing and longer arrows show?

Greater speed. Wider spacing means more distance is covered during each equal time interval, while longer velocity arrows represent a larger velocity magnitude. Each arrow points in the direction of motion.

What does signed area under an acceleration-versus-time graph represent?

Change in velocity. Add that signed area to the initial velocity to find the final velocity.

How is one-dimensional relative velocity calculated for two objects A and B?

v_A relative to B = v_A - v_B. Both velocities must be measured in the same frame before subtracting.

When its speed is nonzero, what direction does a projectile's instantaneous velocity point?

Tangent to its path. Its horizontal and vertical velocity components combine to set that direction.

What does choosing a system boundary decide in a mechanics problem?

It decides which objects belong to the system and which forces count as external. Internal interactions occur between objects inside the boundary.

What belongs on a free-body diagram for one chosen object?

Only forces exerted on that object by other objects. Do not draw velocity, acceleration, or forces the chosen object exerts elsewhere.

What assumptions define the ideal-string model used in introductory algebra-based physics?

The string is massless, inextensible, and flexible. It pulls along its length, doesn't stretch, and can redirect around an ideal pulley.

What does translational equilibrium require?

Zero net force. The object may be at rest or move with constant velocity.

In an inertial frame, how does Newton's second law connect force and motion?

ΣF = ma. The net external force on the chosen object or system causes its acceleration; mass sets how strongly the velocity responds.

How do mass and weight differ?

Mass measures inertia in kilograms; weight is gravitational force in newtons. Near a surface, F_g = mg.

Algebra-Based Physics 1 Flashcards: Complete 8-Unit Course Review

A 400-card review of concepts, formulas, graphs, experiments, and reasoning across eight units of algebra-based physics.

Por el autor Flashcards Open Source App

Sobre este mazo

This 400-card deck reviews concepts, formulas, graphs, experiments, and reasoning across eight units of algebra-based physics. It moves through Kinematics; Force and Translational Dynamics; Work, Energy, and Power; Linear Momentum; Torque and Rotational Dynamics; Energy and Momentum of Rotating Systems; Oscillations; and Fluids.

What you'll retrieve

Choose the governing principle for a situation or claim, then explain the prediction in plain language.
Recall what a quantity or equation means, when it applies, how it scales, and which SI unit it uses.
Read slopes, signed areas, extrema, signs, and shapes across motion, force, energy, momentum, rotation, oscillation, and fluid graphs.
Plan a small experiment by naming useful variables, measurements, controls, linearized graphs, slope meanings, and uncertainty checks.
Solve one focused original algebra-based setup with units and a short reason.
Use selected reverse and contrast prompts to recognize conditions and separate common confusion pairs. The deck doesn't mechanically reverse every fact.

Bare formula-to-symbol lists, long multipart calculations, and imitation exam questions are excluded. The deck also stays outside calculus-based mechanics, three-dimensional angular-momentum analysis, electricity and magnetism, circuits, thermodynamics, waves and optics, modern physics, viscous-flow effects and nonideal viscosity corrections, turbulence, surface tension, and other topics beyond this algebra-based scope.

The order is deliberate: Units 1–4 establish motion, forces, energy, and momentum; Units 5–6 reuse those ideas for rotation and orbits; Unit 7 applies them to oscillations; Unit 8 closes with static and moving ideal fluids. Its release-direction cards ask only for the immediate acceleration in a static, uniform ideal fluid when weight and buoyancy are the only forces. Definitions appear before dependent uses. The sequence interleaves closely related formula, graph, condition, calculation, and contrast prompts with unrelated retrievals. Short prerequisite steps stay closer only when each card introduces a genuinely different idea.

Every prompt, answer, numerical setup, explanation, ordering choice, and metadata field was independently written from common physics knowledge and checked with compatible or authoritative fact sources. The CC0 label applies to that original expression and organization to the extent applicable rights exist; it does not claim ownership of common physics facts or third-party material.

This is an independently authored, unofficial educational deck by Flashcards Open Source App. It is not affiliated with or endorsed by any course or exam provider. No exam questions, mark schemes, curriculum prose, commercial deck text, source prose, logos, figures, or trade dress were copied.

Tarjetas de este mazo

Tarjeta 1
Pregunta
What separates a vector quantity from a scalar quantity?
Respuesta
A vector has magnitude and direction; a scalar has magnitude only. Velocity is a vector, while speed is a scalar.
Tarjeta 2
Pregunta
When is the point-object model useful in kinematics?
Respuesta
When an object's size and rotation do not matter for the motion being studied. Its position can then represent the whole object.
Tarjeta 3
Pregunta
When may the constant-acceleration kinematic equations be used?
Respuesta
Only over an interval with constant acceleration. They are not general formulas for changing acceleration.
Tarjeta 4
Pregunta
Why must a velocity statement name or imply a reference frame?
Respuesta
Velocity depends on the observer's frame. The same object can be at rest in one frame and moving in another.
Tarjeta 5
Pregunta
Why can horizontal and vertical projectile motion be analyzed separately?
Respuesta
Perpendicular components evolve independently. With negligible air resistance, gravity changes only the vertical component.
Tarjeta 6
Pregunta
Can an object have zero velocity and nonzero acceleration at one instant?
Respuesta
Yes. At the top of a vertical toss, velocity is momentarily zero while gravitational acceleration still points downward.
Tarjeta 7
Pregunta
A runner completes one lap and returns to the start. How do distance and displacement compare?
Respuesta
The distance is one lap, while the displacement is zero. Displacement depends only on the change from initial to final position.
Tarjeta 8
Pregunta
What makes a reference frame convenient for a motion problem?
Respuesta
It makes the relevant positions or velocities simple. A good frame reduces bookkeeping without changing physical predictions.
Tarjeta 9
Pregunta
How are the components of a launch velocity v at angle θ found?
Respuesta
v_x = v cos θ and v_y = v sin θ. The angle is measured from the positive horizontal axis.
Tarjeta 10
Pregunta
What does average velocity measure?
Respuesta
Displacement per elapsed time. In one dimension, v_avg = Δx/Δt; direction comes from the sign of Δx.
Tarjeta 11
Pregunta
Do a vector's magnitude and its component use different SI units?
Respuesta
No. A vector and each of its components use the same unit; for example, velocity and its x-component both use m/s.
Tarjeta 12
Pregunta
A velocity-versus-time graph curves upward and becomes progressively steeper while staying above zero. What does that show?
Respuesta
The object moves in the positive direction and speeds up with increasing positive acceleration. The graph's slope is acceleration; because that slope changes, the acceleration is nonuniform.
Tarjeta 13
Pregunta
What are a projectile's horizontal and vertical accelerations when air resistance is negligible and up is positive?
Respuesta
a_x = 0 and a_y = -g. Horizontal velocity stays constant while vertical velocity changes.
Tarjeta 14
Pregunta
What does average acceleration measure?
Respuesta
Change in velocity per elapsed time. In one dimension, a_avg = Δv/Δt.
Tarjeta 15
Pregunta
What does a negative one-dimensional vector component mean?
Respuesta
It points opposite the chosen positive direction. The minus sign describes direction, not a negative physical size.
Tarjeta 16
Pregunta
For constant acceleration, what does v = v₀ + at retrieve?
Respuesta
Velocity after elapsed time t. Use it when initial velocity, constant acceleration, and time are known or related.
Tarjeta 17
Pregunta
How are a vector's magnitude and direction reconstructed from perpendicular components v_x and v_y?
Respuesta
v = √(v_x² + v_y²). When v_x ≠ 0, use θ = tan⁻¹(v_y/v_x) and the component signs to choose the quadrant. If v_x = 0 and v_y ≠ 0, the vector points along +y or -y; if both components are zero, its direction is undefined.
Tarjeta 18
Pregunta
At an instant when velocity is nonzero, how do velocity and acceleration signs show whether a one-dimensional object is speeding up?
Respuesta
It speeds up when velocity and acceleration have the same sign. Opposite signs mean speed is decreasing at that instant.
Tarjeta 19
Pregunta
What does the slope of a position-versus-time graph represent?
Respuesta
Velocity. A steeper slope means a larger speed, and the slope's sign gives direction.
Tarjeta 20
Pregunta
Two observers use inertial frames, where an object with zero net force has constant velocity. If the observers move at constant velocity relative to each other, do they agree on an object's acceleration?
Respuesta
Yes, in a Galilean inertial-frame model. Subtracting a constant frame velocity changes velocity but not acceleration. This definition distinguishes an inertial frame from an accelerating, noninertial frame.
Tarjeta 21
Pregunta
A projectile lands at its launch height with negligible air resistance. How do its launch and landing speeds compare?
Respuesta
They are equal. The horizontal component is unchanged, and the vertical component returns with equal magnitude and opposite sign.
Tarjeta 22
Pregunta
A car's velocity changes from -2 m/s to +6 m/s in 2 s. What is its average acceleration?
Respuesta
+4 m/s². Δv = 8 m/s, and 8 m/s ÷ 2 s = 4 m/s².
Tarjeta 23
Pregunta
If the positive axis is reversed, what happens to a one-dimensional vector component and its magnitude?
Respuesta
The component changes sign, while the magnitude stays the same. A coordinate choice changes the signed description, not the physical vector.
Tarjeta 24
Pregunta
For constant acceleration, what does Δx = v₀t + ½at² retrieve?
Respuesta
Displacement over time t. It includes both initial-velocity motion and the displacement added by constant acceleration.
Tarjeta 25
Pregunta
For a horizontal launch from height h in uniform gravity with negligible air resistance, what sets the time to reach the ground?
Respuesta
The vertical drop alone. Starting with v_y = 0, the time follows h = ½gt² and does not depend on horizontal speed.
Tarjeta 26
Pregunta
Why can average speed differ from the magnitude of average velocity?
Respuesta
Average speed uses total distance, while average velocity uses displacement. Reversing direction increases distance without necessarily increasing displacement.
Tarjeta 27
Pregunta
What does the slope of a velocity-versus-time graph represent?
Respuesta
Acceleration. The slope's units are (m/s)/s = m/s².
Tarjeta 28
Pregunta
A passenger walks forward at 2 m/s inside a train moving forward at 18 m/s. What is the passenger's ground velocity?
Respuesta
20 m/s forward. Add the passenger's train-relative velocity to the train's ground velocity.
Tarjeta 29
Pregunta
Does projectile mass affect the ideal trajectory when air resistance is negligible?
Respuesta
No. All projectiles have the same gravitational acceleration, so equal initial conditions give equal trajectories.
Tarjeta 30
Pregunta
Can an object have nonzero velocity and zero acceleration?
Respuesta
Yes. Constant-velocity motion has nonzero velocity while the velocity change, and therefore acceleration, is zero.
Tarjeta 31
Pregunta
A cart starts from rest with constant acceleration. Which graph should be linear if x = x₀ + ½at² applies?
Respuesta
Position x versus t². Its slope is ½a when the initial velocity is zero.
Tarjeta 32
Pregunta
What does signed area under a velocity-versus-time graph represent?
Respuesta
Displacement. Area below the time axis contributes negative displacement.
Tarjeta 33
Pregunta
At the highest point of a projectile's path, what are its vertical velocity and vertical acceleration?
Respuesta
v_y = 0, but a_y = -g. The vertical velocity pauses before reversing; gravity does not switch off.
Tarjeta 34
Pregunta
How can a motion sensor test whether a cart moves at constant velocity?
Respuesta
Record position at equal time intervals and graph position versus time. A straight line with nearly constant slope supports constant velocity.
Tarjeta 35
Pregunta
A car passes a parked observer at 12 m/s. What is the parked observer's velocity in the car's frame?
Respuesta
-12 m/s. In the car's frame, the ground and observer move backward at the car's speed.
Tarjeta 36
Pregunta
Which constant-acceleration equation connects speed and displacement without using time?
Respuesta
v² = v₀² + 2aΔx. Use signed one-dimensional quantities and constant acceleration.
Tarjeta 37
Pregunta
How could video data test the independence of projectile components?
Respuesta
Track x and y at equal times. A linear x-versus-t graph and a quadratic vertical trend support constant horizontal velocity and vertical acceleration.
Tarjeta 38
Pregunta
A velocity-versus-time graph stays below zero but slopes upward toward zero. What is happening?
Respuesta
The object moves in the negative direction while slowing down. Velocity is negative and acceleration is positive.
Tarjeta 39
Pregunta
How can average velocity over a very short interval approximate instantaneous velocity?
Respuesta
Shrink the time interval around the instant. The displacement divided by that short interval approaches the local position–time graph slope.
Tarjeta 40
Pregunta
A walker moves 7 m east, then 3 m west. What is the one-dimensional displacement if east is positive?
Respuesta
+4 m. Add signed displacements: +7 m + (-3 m) = +4 m.
Tarjeta 41
Pregunta
What shape is the path of a projectile with a nonzero horizontal velocity component in a uniform gravitational field when air resistance is negligible?
Respuesta
A parabola. Constant horizontal velocity and constant vertical acceleration produce the curve. A purely vertical launch is the special case: its spatial path is a vertical line.
Tarjeta 42
Pregunta
In a motion diagram with dots at equal time intervals and velocity arrows, what do wider dot spacing and longer arrows show?
Respuesta
Greater speed. Wider spacing means more distance is covered during each equal time interval, while longer velocity arrows represent a larger velocity magnitude. Each arrow points in the direction of motion.
Tarjeta 43
Pregunta
What does signed area under an acceleration-versus-time graph represent?
Respuesta
Change in velocity. Add that signed area to the initial velocity to find the final velocity.
Tarjeta 44
Pregunta
How is one-dimensional relative velocity calculated for two objects A and B?
Respuesta
v_A relative to B = v_A - v_B. Both velocities must be measured in the same frame before subtracting.
Tarjeta 45
Pregunta
When its speed is nonzero, what direction does a projectile's instantaneous velocity point?
Respuesta
Tangent to its path. Its horizontal and vertical velocity components combine to set that direction.
Tarjeta 46
Pregunta
What does choosing a system boundary decide in a mechanics problem?
Respuesta
It decides which objects belong to the system and which forces count as external. Internal interactions occur between objects inside the boundary.
Tarjeta 47
Pregunta
What belongs on a free-body diagram for one chosen object?
Respuesta
Only forces exerted on that object by other objects. Do not draw velocity, acceleration, or forces the chosen object exerts elsewhere.
Tarjeta 48
Pregunta
What assumptions define the ideal-string model used in introductory algebra-based physics?
Respuesta
The string is massless, inextensible, and flexible. It pulls along its length, doesn't stretch, and can redirect around an ideal pulley.
Tarjeta 49
Pregunta
What does translational equilibrium require?
Respuesta
Zero net force. The object may be at rest or move with constant velocity.
Tarjeta 50
Pregunta
In an inertial frame, how does Newton's second law connect force and motion?
Respuesta
ΣF = ma. The net external force on the chosen object or system causes its acceleration; mass sets how strongly the velocity responds.
Tarjeta 51
Pregunta
How do mass and weight differ?
Respuesta
Mass measures inertia in kilograms; weight is gravitational force in newtons. Near a surface, F_g = mg.
Tarjeta 52
Pregunta
How does static friction choose its magnitude before slipping begins?
Respuesta
It matches the needed tangential contact force up to a maximum. In general, f_s ≤ μ_sN.
Tarjeta 53
Pregunta
For an ideal spring in its linear range, what is the spring force when its end is displaced by a signed amount x from the relaxed or natural length?
Respuesta
F_s = -kx. The sign shows that the spring force opposes the signed extension or compression and points toward the relaxed or natural length.
Tarjeta 54
Pregunta
What direction does centripetal acceleration point in circular motion?
Respuesta
Toward the circle's center. It changes the velocity's direction even when speed is constant.
Tarjeta 55
Pregunta
What is the gravitational force magnitude between two point masses?
Respuesta
F_g = Gm₁m₂/r². Here r is the center-to-center separation.
Tarjeta 56
Pregunta
Why isn't the normal force always equal to an object's weight?
Respuesta
It adjusts to the contact and acceleration conditions. Other vertical forces or vertical acceleration can change its magnitude.
Tarjeta 57
Pregunta
What determines a friction coefficient in the simple model?
Respuesta
The pair of contacting materials and their surface condition. It isn't a universal property of either material alone.
Tarjeta 58
Pregunta
What is the centripetal-acceleration magnitude for speed v and radius r?
Respuesta
a_c = v²/r. It is a kinematic requirement, not a separate force.
Tarjeta 59
Pregunta
An elevator accelerates upward. How does the scale reading compare with a rider's weight?
Respuesta
It is greater than the weight. Upward net force requires N - mg > 0.
Tarjeta 60
Pregunta
What does a spring constant k measure, and what is its SI unit?
Respuesta
It measures stiffness in N/m. A larger k means more force is needed for the same displacement in the linear range.
Tarjeta 61
Pregunta
Three equal point masses are at (0,0), (3 m,0), and (0,3 m). Where is their center of mass?
Respuesta
At (1 m,1 m). Average the x-coordinates and y-coordinates separately for equal masses.
Tarjeta 62
Pregunta
What provides centripetal force?
Respuesta
The inward component of real forces such as tension, gravity, friction, or a normal force. 'Centripetal force' names their net inward result.
Tarjeta 63
Pregunta
How is near-surface gravitational field strength related to weight?
Respuesta
F_g = mg. The local field strength g has units N/kg, equivalent to m/s².
Tarjeta 64
Pregunta
How is weight resolved on an incline of angle θ measured from horizontal?
Respuesta
mg sin θ points down the slope and mg cos θ points into the slope. These are components of one gravitational force.
Tarjeta 65
Pregunta
What does Newton's third law say about an interaction between objects A and B?
Respuesta
The force of A on B and the force of B on A have equal magnitude and opposite direction. They act on different objects.
Tarjeta 66
Pregunta
What does signed tangential acceleration describe during circular motion?
Respuesta
It describes how quickly speed changes and which way the tangential acceleration points along the chosen tangent. Its magnitude is the absolute value of the instantaneous rate of change of speed. If it points with the velocity, speed increases; if it points against the velocity, speed decreases. Its sign follows the chosen tangent.
Tarjeta 67
Pregunta
What happens to gravitational force if the separation between two point masses doubles?
Respuesta
It becomes one-fourth as large. The force follows an inverse-square dependence on distance.
Tarjeta 68
Pregunta
How can an adjustable incline estimate a block's coefficient of static friction when no other applied force acts?
Respuesta
Raise the incline slowly until the block just begins to slide. At that threshold, the simple block model gives μ_s = tan θ.
Tarjeta 69
Pregunta
In an inertial frame, what determines the acceleration of a fixed-mass system's center of mass?
Respuesta
The net external force divided by the system's total mass. Internal force pairs cannot change the center-of-mass motion of the whole system.
Tarjeta 70
Pregunta
Which tension components act for a conical pendulum?
Respuesta
The vertical component balances weight, and the horizontal component supplies centripetal force. The bob moves in a horizontal circle.
Tarjeta 71
Pregunta
What does apparent weight measure for an object supported by one surface?
Respuesta
The normal-force magnitude exerted by that support. It can differ from gravitational force when the object accelerates.
Tarjeta 72
Pregunta
How are several forces combined to find net force?
Respuesta
Add them as vectors, component by component. Opposing components subtract according to the chosen signs.
Tarjeta 73
Pregunta
Why is tension uniform along one continuous ideal string?
Respuesta
Every massless segment must have zero net force in the ideal model. Without frictional contact or a massive pulley changing it, the tension magnitude stays the same throughout the string.
Tarjeta 74
Pregunta
A 0.5 kg object moves at 4 m/s in a circle of radius 2 m. What inward net force is required?
Respuesta
4 N. F_in = mv²/r = 0.5 × 16 / 2.
Tarjeta 75
Pregunta
What local equivalence links a uniform gravitational field with a uniformly accelerating reference frame?
Respuesta
A uniform gravitational field and a uniformly accelerating reference frame can produce the same local mechanical effects. Local observations alone may not distinguish them.
Tarjeta 76
Pregunta
For the same net force, what happens to acceleration if mass doubles?
Respuesta
Acceleration is halved. From a = ΣF/m, acceleration is inversely proportional to mass.
Tarjeta 77
Pregunta
How do static and kinetic friction coefficients usually compare for the same pair of surfaces?
Respuesta
Typically μ_s > μ_k. Starting sliding usually requires a larger friction threshold than maintaining it.
Tarjeta 78
Pregunta
How are radial and tangential acceleration combined when circular speed changes?
Respuesta
Add the perpendicular components as vectors. The total magnitude is √(a_c² + a_t²).
Tarjeta 79
Pregunta
A spherically symmetric planet has twice Earth's mass and the same radius. How does its surface g compare with Earth's?
Respuesta
It is twice as large. Surface field strength follows g = GM/R².
Tarjeta 80
Pregunta
Does a force have to point in the direction of motion?
Respuesta
No. A force points in the direction of the interaction; it may speed up, slow down, or turn the object.
Tarjeta 81
Pregunta
Where is the center of mass of a uniform object with a symmetric mass distribution?
Respuesta
At its geometric center of symmetry. Symmetry lets opposite mass elements balance without a detailed sum.
Tarjeta 82
Pregunta
How are speed, period, and frequency related in uniform circular motion?
Respuesta
v = 2πr/T = 2πrf, with T = 1/f. One cycle covers one circumference.
Tarjeta 83
Pregunta
Why is an object apparently weightless in free fall?
Respuesta
Its support force is zero while it and its surroundings accelerate together under gravity. Gravity still acts.
Tarjeta 84
Pregunta
Can forces balance along one axis while an object accelerates along another?
Respuesta
Yes. Zero net force in one component gives zero acceleration only in that direction; another component can remain unbalanced.
Tarjeta 85
Pregunta
Why don't Newton's third-law forces cancel on one object's free-body diagram?
Respuesta
Only one force in the pair acts on that object. The partner force belongs on the other object's diagram.
Tarjeta 86
Pregunta
On a frictionless banked curve, which force components create vertical balance and inward acceleration?
Respuesta
The normal force's vertical component balances weight, while its horizontal component supplies the inward net force.
Tarjeta 87
Pregunta
What motion results when the net force on an object is zero in an inertial frame?
Respuesta
Constant velocity. Rest is the special case with constant velocity equal to zero.
Tarjeta 88
Pregunta
A 3 kg cart has a net horizontal force of 12 N. What is its acceleration?
Respuesta
4 m/s². Use a = ΣF/m = 12/3.
Tarjeta 89
Pregunta
What does the observed equivalence of inertial and gravitational mass imply for free fall?
Respuesta
Free-fall acceleration is independent of the falling object's mass. Inertial and gravitational mass are proportional and conventionally assigned equal numerical values.
Tarjeta 90
Pregunta
Does friction in the simple dry-friction model depend on apparent contact area?
Respuesta
No. For a fixed normal force and the same contacting materials, the model treats friction magnitude as independent of apparent contact area.
Tarjeta 91
Pregunta
When should Hooke's-law predictions be treated cautiously?
Respuesta
When deformation leaves the spring's linear elastic range. Force may no longer be proportional to displacement.
Tarjeta 92
Pregunta
What bank angle θ supports speed v on an ideal frictionless curve of radius r?
Respuesta
tan θ = v²/(rg). The result assumes no vertical acceleration and no friction.
Tarjeta 93
Pregunta
Why do internal forces cancel when finding the net force on a complete system?
Respuesta
They occur in equal-and-opposite pairs between system parts. Each pair sums to zero in the system's force total.
Tarjeta 94
Pregunta
An elevator moves downward at constant speed. How does the scale reading compare with weight?
Respuesta
It equals the weight. Constant velocity means zero acceleration and N - mg = 0.
Tarjeta 95
Pregunta
What assumptions let an ideal pulley redirect a string without changing its tension magnitude?
Respuesta
The pulley is massless and frictionless, and the string is ideal. It changes the tension's direction while the magnitude stays the same on both sides.
Tarjeta 96
Pregunta
What does inertia describe?
Respuesta
An object's resistance to changes in velocity. Mass measures translational inertia.
Tarjeta 97
Pregunta
For the same fixed-mass object or system across all measurements, what does the slope of a net-force-versus-acceleration graph represent?
Respuesta
Its mass. Written as ΣF = ma, the graph has slope m when the object or system and its mass stay fixed.
Tarjeta 98
Pregunta
Does zero net force mean no forces act?
Respuesta
No. Several forces can act and cancel vectorially.
Tarjeta 99
Pregunta
What is the common model for kinetic-friction magnitude?
Respuesta
f_k = μ_kN. It applies while the surfaces slide under the model's assumptions.
Tarjeta 100
Pregunta
How could hanging masses measure the spring constant of one ideal spring?
Respuesta
At static equilibrium, record the spring's extension for several known weights and graph mg versus extension. Keep the same spring in its linear range; the slope is k.
Tarjeta 101
Pregunta
For the same object at the same circular radius, how does required inward net force change if speed doubles?
Respuesta
It becomes four times as large. F_in = mv²/r depends on speed squared.
Tarjeta 102
Pregunta
Where is the center of mass of two point masses on an x-axis?
Respuesta
At x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂). It lies closer to the larger mass.
Tarjeta 103
Pregunta
Why must net force, rather than one selected force, be used in ΣF = ma?
Respuesta
All external forces contribute to acceleration. Ignoring a force changes the vector sum and the prediction.
Tarjeta 104
Pregunta
Why can tension vary along a hanging chain with nonnegligible mass?
Respuesta
Higher sections must support and accelerate more chain below them. Newton's third law still applies locally to each interaction; it does not make tension uniform everywhere.
Tarjeta 105
Pregunta
What makes a reference frame inertial?
Respuesta
An object with zero net force has constant velocity in that frame. A frame accelerating relative to an inertial frame is noninertial.
Tarjeta 106
Pregunta
How could carts test the proportionality between acceleration and net force?
Respuesta
Keep total mass constant, vary the applied net force, and graph acceleration versus force. A line through the origin supports a ∝ ΣF.
Tarjeta 107
Pregunta
How does Kepler's third-law scaling compare two satellites in circular orbits at center-to-center radii r when their masses are negligible relative to the same fixed central mass?
Respuesta
T² ∝ r³. The circular orbit with the larger center-to-center radius has the longer period.
Tarjeta 108
Pregunta
Which direction does kinetic friction act?
Respuesta
Opposite the relative sliding of the contacting surfaces. It is not automatically opposite the object's velocity in every frame.
Tarjeta 109
Pregunta
What does the slope of a spring-force-versus-displacement graph give?
Respuesta
-k when signed force is graphed against signed displacement. The slope magnitude is the spring constant.
Tarjeta 110
Pregunta
What is the minimum speed at the top of an ideal vertical loop of radius r when gravity alone supplies the inward force?
Respuesta
v_min = √(gr). At the threshold, the support force or tension is zero.
Tarjeta 111
Pregunta
What is translational kinetic energy?
Respuesta
Energy associated with an object's translational motion. For a point-like object, K = ½mv².
Tarjeta 112
Pregunta
How is work by a constant force calculated when its point of application undergoes a straight displacement?
Respuesta
W = Fd cos θ. Here d is the displacement of the force's point of application, and θ is the angle between the force and that displacement.
Tarjeta 113
Pregunta
What does power measure?
Respuesta
The rate of energy transfer or conversion. P_avg = ΔE_transferred/Δt; when work is the relevant transfer, P_avg = W/Δt.
Tarjeta 114
Pregunta
What does conservation of energy say for an isolated system?
Respuesta
The system's total energy stays constant. Energy may change form or move among system parts, but it is not created or destroyed.
Tarjeta 115
Pregunta
Can translational kinetic energy be negative?
Respuesta
No. Mass is positive and speed is squared, so translational kinetic energy is zero or positive.
Tarjeta 116
Pregunta
What does negative work by a force mean?
Respuesta
The force makes a negative contribution to the system's kinetic-energy change. Its component opposes the displacement of its point of application; potential energy may rise while total mechanical energy stays constant.
Tarjeta 117
Pregunta
What is the near-surface change in gravitational potential energy?
Respuesta
ΔU_g = mgΔy. It applies when g can be treated as constant.
Tarjeta 118
Pregunta
When is a chosen system's mechanical energy K + U conserved?
Respuesta
When no net energy crosses the system boundary and no internal process converts energy in either direction between mechanical and nonmechanical forms. If either condition fails, K + U can change even though total energy still balances for the system plus surroundings.
Tarjeta 119
Pregunta
What is the SI unit of power?
Respuesta
The watt, W. One watt equals one joule per second.
Tarjeta 120
Pregunta
For an object modeled as a particle, what connects net work by all forces to its change in translational kinetic energy?
Respuesta
The work–energy theorem: W_net = ΔK. Under the particle model, positive net work raises translational kinetic energy and negative net work lowers it. A rotating rigid system requires total kinetic energy and work at the forces' points of application.
Tarjeta 121
Pregunta
A ball falls from rest through height h near a planet's surface. For the ball–planet system, g is constant and air resistance is negligible. What speed does energy conservation predict?
Respuesta
v = √(2gh). The system's mgh decrease in gravitational potential energy becomes ½mv².
Tarjeta 122
Pregunta
Does choosing a different zero level for potential energy change physical predictions?
Respuesta
No. Only potential-energy differences enter measurable energy changes.
Tarjeta 123
Pregunta
Can an engine do the same work with different average power?
Respuesta
Yes. Doing the same work in less time requires greater average power.
Tarjeta 124
Pregunta
When does a constant nonzero force do zero work over an interval?
Respuesta
When its point of application has zero displacement or its displacement is perpendicular to the force. Then W = Fd cos θ is zero.
Tarjeta 125
Pregunta
A particle-modeled block slides down a fixed frictionless track. Does the path shape affect its final speed at a given lower height?
Respuesta
No. With only gravity doing work, the potential-energy change depends on height, not path.
Tarjeta 126
Pregunta
How does translational kinetic energy change if speed doubles at constant mass?
Respuesta
It becomes four times as large. Kinetic energy depends on v².
Tarjeta 127
Pregunta
What is the elastic potential energy of an ideal spring displaced by a signed amount x from its relaxed or natural length, with U_s = 0 there?
Respuesta
U_s = ½kx². Choosing zero energy at the relaxed length gives the same stored energy for equal-magnitude extension or compression.
Tarjeta 128
Pregunta
What does signed area under a force-component-versus-position graph represent when position tracks that force's point of application?
Respuesta
Work done by that force along the measured coordinate. Area below the position axis counts as negative work under the graph's sign convention.
Tarjeta 129
Pregunta
A chosen system starts with 20 J of mechanical energy and converts 6 J of it into thermal energy, with no energy crossing the boundary. How much mechanical energy remains?
Respuesta
14 J. The 6 J thermal-energy increase matches the mechanical-energy decrease.
Tarjeta 130
Pregunta
What shape does a translational-kinetic-energy-versus-speed graph have for fixed mass?
Respuesta
The right-hand half of an upward-opening parabola through the origin. Speed is nonnegative, and K is proportional to v², not v.
Tarjeta 131
Pregunta
A machine transfers 600 J in 3 s. What is its average power?
Respuesta
200 W. Divide energy transferred by elapsed time.
Tarjeta 132
Pregunta
Why does the normal force do no work on a nonrotating block sliding across a fixed horizontal floor?
Respuesta
The force is perpendicular to the horizontal displacement of its points of application. Their dot product is zero in this pure-translation model.
Tarjeta 133
Pregunta
A coaster modeled as a particle moves on a fixed frictionless track. Where is its speed greatest?
Respuesta
At the lowest accessible position. Gravitational potential energy is smallest there, so kinetic energy is largest.
Tarjeta 134
Pregunta
Two objects have equal mass and velocities of equal magnitude but opposite direction. How do their translational kinetic energies compare?
Respuesta
They are equal. Kinetic energy uses speed and has no direction.
Tarjeta 135
Pregunta
What makes work by a conservative force path independent?
Respuesta
It depends only on the initial and final configurations. Any two paths between the same endpoints give the same conservative-force work.
Tarjeta 136
Pregunta
A 10 N force acts while its point of application moves 3 m in the force direction. How much work does the force do?
Respuesta
30 J. Here θ = 0, so W = Fd = 10×3.
Tarjeta 137
Pregunta
How is total potential energy built for a system with several interacting pairs?
Respuesta
Add the potential energy assigned to each relevant pair. Count each interaction pair once and use one consistent reference choice.
Tarjeta 138
Pregunta
How should external work appear in an energy equation?
Respuesta
As energy transferred across the system boundary. A useful form is ΔE_system = W_external + other transfers.
Tarjeta 139
Pregunta
How does a spring launch problem combine energy forms?
Respuesta
Initial elastic energy becomes kinetic energy and possibly gravitational or thermal energy. Write only the forms present in the chosen initial and final states.
Tarjeta 140
Pregunta
For a constant force parallel to the velocity of its point of application, how is instantaneous mechanical power calculated?
Respuesta
P = Fv. More generally, P = F·v_point, so only the force component along that point's velocity contributes.
Tarjeta 141
Pregunta
How does translational kinetic energy change if mass triples at constant speed?
Respuesta
It triples. Kinetic energy is directly proportional to mass.
Tarjeta 142
Pregunta
How much net work does a conservative force do around a path that returns to the initial configuration?
Respuesta
Zero. The initial and final potential energies are the same.
Tarjeta 143
Pregunta
Where is stable equilibrium on a potential-energy-versus-position graph?
Respuesta
At a local minimum. Small displacements produce forces that point back toward the minimum.
Tarjeta 144
Pregunta
Which displacement belongs in the work done by a force on a rigid object?
Respuesta
The displacement of that force's point of application. Using the center-of-mass displacement can be wrong when the object also rotates.
Tarjeta 145
Pregunta
What happens to mechanical energy when kinetic friction acts inside the chosen system?
Respuesta
Some mechanical energy becomes thermal energy. The broader system's total energy still balances.
Tarjeta 146
Pregunta
A nonrotating particle falls from rest through vertical drop h under constant g. If its gravitational-potential decrease becomes only translational kinetic energy, with no other energy changes, what graph linearizes final speed?
Respuesta
Graph v² versus drop height h. Under those conditions, v² = 2gh, so the slope should be 2g.
Tarjeta 147
Pregunta
If two students start and finish a stair climb at the same speeds, how could data compare their average mechanical output power against gravity?
Respuesta
Measure each student's mass, vertical rise, and climb time, then calculate mgh/t. Equal initial and final speeds make ΔK = 0; if ΔK is negligible, the result is an approximation. This is mechanical output power against gravity, not metabolic input power.
Tarjeta 148
Pregunta
How can force-sensor data measure work when force changes as its point of application moves?
Respuesta
Graph the force component along the motion against the point-of-application position and find the signed area. A rectangle formula isn't enough for a varying force.
Tarjeta 149
Pregunta
Why is potential energy assigned to a system rather than one isolated object?
Respuesta
It belongs to an interaction between system parts. Gravitational potential energy, for example, belongs to the object–Earth system.
Tarjeta 150
Pregunta
How can work by a nonconservative force depend on path?
Respuesta
Different routes can have different force histories or path lengths. Kinetic-friction work, for example, can change with distance traveled.
Tarjeta 151
Pregunta
A 2 kg cart moves at 3 m/s. What is its translational kinetic energy?
Respuesta
9 J. K = ½(2)(3²) = 9 J.
Tarjeta 152
Pregunta
A block slides distance d across a stationary surface while constant kinetic friction f_k opposes its displacement. What work does friction do on the block?
Respuesta
W_f = -f_k d. The negative sign follows from friction pointing opposite the block's displacement in this stated setup.
Tarjeta 153
Pregunta
A 2 kg object rises 5 m where g = 10 m/s². What is ΔU_g?
Respuesta
+100 J. ΔU_g = mgΔy = 2 × 10 × 5.
Tarjeta 154
Pregunta
Why are energy bar charts useful?
Respuesta
They make initial energy, final energy, and transfers explicit. A correct chart respects the chosen system and reference levels.
Tarjeta 155
Pregunta
A motor lifts the same load through the same height twice as fast. Both lifts begin and end at the same speeds and have equal or negligible dissipative losses. How do the motor's mechanical output work and average power compare?
Respuesta
The mechanical output work is unchanged, while average power doubles. The two lifts have the same ΔU_g, the same ΔK, and the same losses, so the same output energy is delivered in half the time.
Tarjeta 156
Pregunta
A nonrotating 1 kg block starts from rest and receives 18 J of net work. What speed does it reach?
Respuesta
6 m/s. For this pure-translation model, ΔK = 18 J = ½(1)v².
Tarjeta 157
Pregunta
Why is gravitational potential energy lower when two attracting point masses—or nonoverlapping spherical bodies—are closer in the inverse-square model?
Respuesta
Energy must be supplied to separate them. With zero chosen at infinite center-to-center separation, U_g = -GMm/r.
Tarjeta 158
Pregunta
What does a steep potential-energy graph imply about force magnitude in one dimension?
Respuesta
A large force magnitude. Force points toward decreasing potential energy and corresponds to the negative slope of U(x).
Tarjeta 159
Pregunta
An ideal spring with k = 80 N/m is compressed 0.50 m from its relaxed length. With U_s = 0 at that length, what elastic energy is stored?
Respuesta
10 J. U_s = ½(80)(0.50²).
Tarjeta 160
Pregunta
A constant 50 N force acts while its point of application moves at 4 m/s in the force direction. What mechanical power is delivered?
Respuesta
200 W. P = Fv_point = 50 × 4.
Tarjeta 161
Pregunta
If potential energy decreases by 30 J and no energy crosses the system boundary, what happens to the other energy forms?
Respuesta
They increase by a total of 30 J. Often kinetic energy rises, but thermal or other forms may share the increase.
Tarjeta 162
Pregunta
Does an object's translational kinetic energy depend on the reference frame?
Respuesta
Yes. Different inertial observers can measure different speeds and therefore different K = ½mv² for the same object.
Tarjeta 163
Pregunta
Why can work depend on the system boundary?
Respuesta
Changing the system can reclassify energy transfer. For example, friction may be external work on one system but internal thermal-energy conversion in a larger system.
Tarjeta 164
Pregunta
A force-component-versus-position graph for the force's point of application forms a triangle of base 4 m and height 6 N above the axis. What work does it show?
Respuesta
12 J. The signed area is ½×4×6.
Tarjeta 165
Pregunta
A motor transfers 50 J into a chosen system while another device transfers 12 J out. What is the net system-energy change?
Respuesta
+38 J. Add the signed transfers across the boundary: 50 J - 12 J.
Tarjeta 166
Pregunta
What is the clearest first step in an energy-conservation problem?
Respuesta
Choose the system and the initial and final states. That choice determines which energies and transfers belong in the equation.
Tarjeta 167
Pregunta
Why can energy methods solve some problems without finding time?
Respuesta
Energy connects states through position, speed, and transfers. Time is absent unless power or a time-dependent process matters.
Tarjeta 168
Pregunta
Why can a force's instantaneous mechanical power be zero while the force is nonzero?
Respuesta
Its point of application may be instantaneously at rest, or the force may be perpendicular to that point's velocity. In either case F·v_point = 0.
Tarjeta 169
Pregunta
What is the SI unit of kinetic energy?
Respuesta
The joule, J. One joule equals 1 kg·m²/s².
Tarjeta 170
Pregunta
How is work by a conservative force related to potential-energy change?
Respuesta
W_conservative = -ΔU. When the conservative force does positive work, potential energy falls.
Tarjeta 171
Pregunta
Where is unstable equilibrium on a potential-energy-versus-position graph?
Respuesta
At a local maximum. A small displacement produces a force that pushes the system farther away.
Tarjeta 172
Pregunta
For a particle moving in a circle at constant speed, does the inward net force change its translational kinetic energy?
Respuesta
No. The inward net force is perpendicular to the particle's instantaneous velocity, so its net work is zero and it changes the velocity's direction rather than its magnitude.
Tarjeta 173
Pregunta
Why should thermal energy not be written as a force?
Respuesta
Thermal energy is an energy store, not an interaction force. Friction is the interaction that converts or transfers energy.
Tarjeta 174
Pregunta
How could a ramp experiment test mechanical-energy conservation for a cart–Earth system when the cart is modeled as a particle?
Respuesta
Measure speed and height at several points, calculate K + U_g with one consistent zero level, and compare within uncertainty. Systematic drift suggests unmodeled energy transfer or conversion.
Tarjeta 175
Pregunta
According to the plotted power's definition and sign convention, what does signed area under a power-versus-time graph represent?
Respuesta
Energy transferred or converted over the interval. Interpret positive and negative areas using the graph's stated sign convention and what its power represents.
Tarjeta 176
Pregunta
What is linear momentum?
Respuesta
p = mv. Momentum is a vector in the direction of velocity and uses SI units kg·m/s.
Tarjeta 177
Pregunta
How is a multi-object system's total momentum found?
Respuesta
Add every object's momentum as a vector. In one dimension, add signed values.
Tarjeta 178
Pregunta
For a chosen object or system, what is external impulse?
Respuesta
The change in its momentum: J_external = Δp. For constant net external force, J_external = F_net,external Δt.
Tarjeta 179
Pregunta
What experimental uncertainty matters strongly when comparing collision kinetic energies?
Respuesta
Velocity uncertainty. Because K depends on v², small speed errors can produce larger relative energy errors.
Tarjeta 180
Pregunta
Why can two objects bounce apart yet still collide inelastically?
Respuesta
Bouncing does not guarantee kinetic-energy conservation. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.
Tarjeta 181
Pregunta
A 3 kg cart moves right at 4 m/s. What is its momentum if right is positive?
Respuesta
+12 kg·m/s. p = mv = 3 × 4.
Tarjeta 182
Pregunta
Why can momentum be negative while kinetic energy cannot?
Respuesta
Momentum carries direction through velocity's sign. Kinetic energy depends on speed squared.
Tarjeta 183
Pregunta
When is a system's total linear momentum conserved?
Respuesta
When the net external impulse is zero or negligible during the interval. Internal impulses cancel in the system total.
Tarjeta 184
Pregunta
Two equal masses collide elastically in one dimension; one is initially at rest. What commonly happens?
Respuesta
They exchange velocities. The incoming mass stops and the other leaves with its speed under the ideal conditions.
Tarjeta 185
Pregunta
Can total kinetic energy increase in an explosion?
Respuesta
Yes. Stored internal energy can become kinetic energy. Total momentum is conserved for a defined system with zero or negligible net external impulse, while total energy remains conserved for the system plus surroundings.
Tarjeta 186
Pregunta
How is total momentum related to center-of-mass velocity?
Respuesta
p_total = Mv_cm. M is the system's total mass.
Tarjeta 187
Pregunta
How does a nonzero external impulse affect system momentum?
Respuesta
It changes total momentum by that impulse. J_external = Δp_system.
Tarjeta 188
Pregunta
Two carts start at rest and push apart with negligible external horizontal impulse. How do their final momenta compare?
Respuesta
They are equal in magnitude and opposite in direction. The system began with zero total momentum.
Tarjeta 189
Pregunta
What are equivalent SI units for impulse?
Respuesta
N·s and kg·m/s. Both represent a change in momentum.
Tarjeta 190
Pregunta
What defines an elastic collision?
Respuesta
Both total momentum and total kinetic energy are conserved for the chosen isolated system. Individual objects may exchange both quantities.
Tarjeta 191
Pregunta
How can a force sensor and motion detector test the impulse–momentum theorem for one cart?
Respuesta
Account for every external force component along the measured axis, compare the net-force–time area with m(v_f - v_i), and include uncertainty. Agreement supports J_external = Δp.
Tarjeta 192
Pregunta
A person jumps right from a stationary boat. Neglecting external horizontal impulse, which way does the boat move?
Respuesta
Left. The person and boat acquire opposite momenta so total momentum remains zero.
Tarjeta 193
Pregunta
Why must momentum signs be kept through an impulse calculation?
Respuesta
Impulse changes a vector quantity. Reversal can make Δp larger than either momentum magnitude alone.
Tarjeta 194
Pregunta
What defines a perfectly inelastic collision?
Respuesta
The objects stick together after impact. Momentum is conserved in an isolated system, but kinetic energy decreases as much as the constraints allow.
Tarjeta 195
Pregunta
Why can momentum be conserved during a collision even when large forces act?
Respuesta
For a defined system with zero or negligible net external impulse, the large collision forces are internal. Their equal-and-opposite impulses cancel within that system.
Tarjeta 196
Pregunta
Two objects have equal speed. Which has the larger momentum magnitude?
Respuesta
The object with larger mass. At equal speed, momentum is proportional to mass.
Tarjeta 197
Pregunta
How is momentum conservation written for a two-dimensional isolated interaction?
Respuesta
Conserve components separately: Σp_x,i = Σp_x,f and Σp_y,i = Σp_y,f. Both component equations must hold for the same interaction.
Tarjeta 198
Pregunta
For a chosen object or system, how is average net external force related to impulse?
Respuesta
F_avg,external = Δp/Δt. For the same momentum change, a longer interaction time gives a smaller average force.
Tarjeta 199
Pregunta
Which conservation law alone can determine the shared final velocity of a sticking collision?
Respuesta
Linear momentum conservation, if external impulse is negligible. Kinetic energy is not conserved in the sticking process.
Tarjeta 200
Pregunta
Two equal momentum vectors point along +x and +y. What direction does their total momentum point?
Respuesta
At 45° between the positive axes. Equal perpendicular components produce that resultant direction.
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Tarjeta 201
Pregunta
If external impulse during a collision is small but not zero, what should experimental data show?
Respuesta
Final total momentum should be close to, but not exactly equal to, initial total momentum. The difference estimates external impulse.
Tarjeta 202
Pregunta
A force–time pulse has the same area but twice the peak force and half the duration. How does its impulse change?
Respuesta
It does not change. Impulse depends on total signed area, not peak force alone.
Tarjeta 203
Pregunta
A 1 kg cart at 4 m/s sticks to an identical stationary cart. If external impulse is negligible, how does final kinetic energy compare with the initial 8 J?
Respuesta
It is 4 J, half the initial value. The 4 J decrease in translational kinetic energy becomes internal or thermal energy through deformation, and some energy may be carried by sound.
Tarjeta 204
Pregunta
How can a nearly frictionless cart track improve a momentum-conservation test?
Respuesta
It reduces external horizontal impulse during the collision. That makes the two-cart system closer to isolated.
Tarjeta 205
Pregunta
How does an object's momentum change if its speed doubles at constant mass?
Respuesta
Its momentum magnitude doubles. Momentum depends linearly on speed.
Tarjeta 206
Pregunta
For a chosen object or system, what does signed area under its net-external-force-versus-time graph represent?
Respuesta
External impulse, which equals the change in that object's or system's momentum. Area below the time axis contributes negative impulse under the graph's sign convention.
Tarjeta 207
Pregunta
A firework at rest explodes into two pieces with negligible external impulse. If one piece has twice the mass, how do the piece speeds compare?
Respuesta
The heavier piece moves at half the speed of the lighter piece. Their momentum magnitudes must match.
Tarjeta 208
Pregunta
Why is sticking evidence of an inelastic collision?
Respuesta
The objects share one final velocity, while some translational kinetic energy becomes internal or thermal energy through deformation. Translational kinetic energy is not conserved.
Tarjeta 209
Pregunta
Can a moving two-object system have zero total momentum?
Respuesta
Yes. Equal and opposite momenta cancel even though each object is moving.
Tarjeta 210
Pregunta
A constant 6 N net external force acts on a chosen object for 0.5 s. What impulse does it deliver?
Respuesta
3 N·s in the force direction. Multiply the net external force by the interaction time.
Tarjeta 211
Pregunta
What does a momentum-versus-velocity graph's slope represent for one object?
Respuesta
Its mass. The relationship p = mv is linear through the origin.
Tarjeta 212
Pregunta
A 2 kg cart at +3 m/s sticks to a 1 kg cart at rest. If external horizontal impulse is negligible, what is their final velocity?
Respuesta
+2 m/s. Momentum conservation gives (2×3 + 1×0)/(2+1).
Tarjeta 213
Pregunta
An isolated two-dimensional interaction has known initial total momentum p_total,i and known first outgoing momentum p₁,f. How is the second outgoing momentum found?
Respuesta
Subtract component by component: p₂,f = p_total,i - p₁,f. Thus p₂x,f = p_total,x,i - p₁x,f, with the same subtraction for y.
Tarjeta 214
Pregunta
A 2 kg ball changes velocity from +3 m/s to -1 m/s. What impulse acts on it?
Respuesta
-8 N·s. Δp = m(v_f - v_i) = 2(-1 - 3).
Tarjeta 215
Pregunta
What remains conserved in an isolated inelastic collision?
Respuesta
Total momentum. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.
Tarjeta 216
Pregunta
Why does choosing both colliding objects as the system simplify momentum analysis?
Respuesta
Their contact forces become internal. Only external impulse can change the system total.
Tarjeta 217
Pregunta
For a chosen object or system, what does the slope of its momentum-versus-time graph represent?
Respuesta
Net external force. A steeper slope means a larger force in the slope's signed direction.
Tarjeta 218
Pregunta
Why do airbags reduce injury force during a stop?
Respuesta
They increase the stopping time for roughly the same momentum change. That lowers the average force.
Tarjeta 219
Pregunta
A 1 kg cart at 4 m/s sticks to an identical stationary cart. If external impulse is negligible, what final speed do they share?
Respuesta
2 m/s. Momentum 4 kg·m/s is shared by 2 kg.
Tarjeta 220
Pregunta
For a defined collision system with zero or negligible net external impulse, how can before-and-after velocity measurements classify the collision?
Respuesta
First verify total momentum within uncertainty, then compare total kinetic energy. Unchanged kinetic energy supports elastic behavior; any change beyond uncertainty means the collision isn't elastic, with a decrease indicating an ordinary inelastic collision.
Tarjeta 221
Pregunta
What is angular displacement?
Respuesta
The signed angle through which a rigid body rotates. In calculations, radians make the linear–angular relationships direct.
Tarjeta 222
Pregunta
For a rigid body rotating about a chosen fixed axis, what does angular velocity measure?
Respuesta
Signed angular displacement per time about that axis. Average angular velocity is ω_avg = Δθ/Δt under one sign convention.
Tarjeta 223
Pregunta
For a rigid body rotating about a chosen fixed axis, what does angular acceleration measure?
Respuesta
Change in signed angular velocity per time about that axis. Average angular acceleration is α_avg = Δω/Δt.
Tarjeta 224
Pregunta
What does rotational inertia measure?
Respuesta
Resistance to angular acceleration about a specified axis. It depends on mass and how that mass is distributed relative to the axis.
Tarjeta 225
Pregunta
What is the lever arm in a torque calculation?
Respuesta
The perpendicular distance from the axis to the force's line of action. It is not always the full distance to the contact point.
Tarjeta 226
Pregunta
For a planar rigid object in an inertial frame, what two conditions give simultaneous translational and rotational equilibrium?
Respuesta
ΣF_external = 0 and Στ_external = 0 about a fixed axis. Static equilibrium also requires the object to be at rest.
Tarjeta 227
Pregunta
Two points lie on the same rotating rigid disk. Which rotational quantities are the same?
Respuesta
They share angular displacement, angular velocity, and angular acceleration. Their linear speeds and accelerations can differ with radius.
Tarjeta 228
Pregunta
How is rotational inertia found for a collection of point masses?
Respuesta
I_total = Σmᵢrᵢ². Each rᵢ is that mass's perpendicular distance from the chosen axis.
Tarjeta 229
Pregunta
What determines the magnitude of torque from one force about a chosen axis?
Respuesta
τ = rF sin θ = r_perp F. The radius vector r runs from the axis to the force's point of application, θ is the angle between r and the force, and r_perp is the lever arm.
Tarjeta 230
Pregunta
What is Newton's second law for a rigid system rotating about an axis fixed in an inertial frame?
Respuesta
Στ_external = Iα when rotational inertia I about that axis is constant. Net external torque and angular acceleration use the same signed-axis convention.
Tarjeta 231
Pregunta
For a point on a rigid body rotating about a fixed axis, how is signed arc displacement related to signed angular displacement in radians?
Respuesta
Δs = rΔθ. Here r is the point's perpendicular distance from the fixed axis, and both displacements use matching sign conventions along the circular path.
Tarjeta 232
Pregunta
In a planar rigid-body model, can an object with zero net external force and zero net external torque about its center of mass be moving?
Respuesta
Yes. Its center of mass may translate at constant velocity while it rotates at constant angular velocity; the stated zero net force and center-of-mass torque don't require rest.
Tarjeta 233
Pregunta
At an instant when ω ≠ 0, what do the signs of angular velocity and angular acceleration show about rotational speed?
Respuesta
Matching signs mean the rotation speeds up; opposite signs mean it slows down. The sign convention chooses which rotation direction is positive.
Tarjeta 234
Pregunta
How are clockwise and counterclockwise torques combined?
Respuesta
Choose one direction as positive and add signed torques. Net torque is the algebraic sum about the same axis.
Tarjeta 235
Pregunta
For the same rigid system with constant rotational inertia about the same axis fixed in an inertial frame, what happens if net-external-torque magnitude doubles?
Respuesta
Angular-acceleration magnitude doubles. Under those conditions, |α| is directly proportional to |Στ_external|.
Tarjeta 236
Pregunta
Why must an axis be named when stating rotational inertia?
Respuesta
The same object has different rotational inertia about different axes. Mass distribution relative to the chosen axis changes.
Tarjeta 237
Pregunta
For one rigid body rotating about a fixed axis, what does the slope of its angular-position-versus-time graph represent?
Respuesta
Signed angular velocity about that axis. A constant slope means constant angular velocity under the graph's sign convention.
Tarjeta 238
Pregunta
Why is torque's unit N·m not called a joule?
Respuesta
Torque and energy are different physical quantities despite matching unit dimensions. Torque describes rotational effectiveness of a force.
Tarjeta 239
Pregunta
A rigid wheel has constant I = 2 kg·m² about an axis fixed in an inertial frame and net external torque 8 N·m about that axis. What is its angular-acceleration magnitude?
Respuesta
4 rad/s². |α| = |Στ_external|/I = 8/2.
Tarjeta 240
Pregunta
Where can the weight of a rigid object be treated as acting in a uniform gravitational field?
Respuesta
At the object's center of mass. That single force gives the same net gravitational force and torque.
Tarjeta 241
Pregunta
For a point on a rigid body rotating about a fixed axis, how is tangential-speed magnitude related to angular velocity?
Respuesta
v_t = r|ω|. Here r is the perpendicular distance from the fixed axis. Points farther from the axis move faster even though the rigid body has one angular velocity.
Tarjeta 242
Pregunta
For constant angular acceleration about one fixed axis, what does ω = ω₀ + αt retrieve?
Respuesta
Angular velocity after elapsed time t. Use signed angular quantities about that axis over an interval with constant α.
Tarjeta 243
Pregunta
A free-body diagram for a rigid bar must support a torque calculation about a marked axis. What must it show besides each force's direction and magnitude?
Respuesta
Each force's point of application or line of action relative to the axis. That geometry sets the lever arm and torque sign; omitting it can preserve the net-force picture while losing the net torque.
Tarjeta 244
Pregunta
For the same rigid system about the same axis fixed in an inertial frame, what does the slope of a net-external-torque-versus-angular-acceleration graph represent?
Respuesta
Its constant rotational inertia I about that axis. The graph follows Στ_external = Iα.
Tarjeta 245
Pregunta
A thin hoop and solid disk have the same mass and radius and rotate about their central symmetry axes. With I_hoop = MR² and I_disk = ½MR², which has larger I?
Respuesta
The hoop. More of its mass lies far from the axis.
Tarjeta 246
Pregunta
Why can a rigid object have zero net external force but nonzero net external torque?
Respuesta
External forces can cancel as vectors while acting along different lines. The resulting couple can still change the object's rotation.
Tarjeta 247
Pregunta
Which constant-angular-acceleration equation connects angular velocity and angular displacement about one fixed axis without time?
Respuesta
ω² = ω₀² + 2αΔθ. Use signed quantities about that axis over an interval with constant α.
Tarjeta 248
Pregunta
A 10 N perpendicular force acts 0.40 m from a pivot. What torque magnitude does it produce?
Respuesta
4 N·m. τ = rF for a perpendicular force.
Tarjeta 249
Pregunta
For a rigid body rotating about a fixed axis, how is the signed tangential-acceleration component related to angular acceleration?
Respuesta
For a positive tangent consistent with the angular sign convention, a_t = rα. Its alignment or opposition with velocity determines whether speed increases or decreases.
Tarjeta 250
Pregunta
Why can two equal-mass rigid wheels have different angular-acceleration magnitudes under equal net-external-torque magnitudes about comparable axes fixed in an inertial frame?
Respuesta
Their rotational inertias about those axes can differ because their mass distributions differ. Mass alone doesn't set rotational response.
Tarjeta 251
Pregunta
For one rigid body rotating about a fixed axis, what does signed area under its angular-velocity-versus-time graph represent?
Respuesta
Signed angular displacement about that axis. Area below the time axis contributes negative angular displacement under the graph's sign convention.
Tarjeta 252
Pregunta
A rigid object rests on a support that is slowly tilted in uniform gravity. If gravity and support contact are its only external interactions, sufficient static friction prevents slipping, and the motion is quasistatic, what marks the onset of tipping?
Respuesta
The object's center-of-mass vertical line reaches the edge of its support region. Beyond that point, gravity produces an unbalanced tipping torque.
Tarjeta 253
Pregunta
A point is twice as far from a rigid wheel's fixed axis as another point. How do their tangential speeds compare?
Respuesta
The farther point moves twice as fast. v_t is proportional to radius for their common angular-speed magnitude |ω|.
Tarjeta 254
Pregunta
Does moving the chosen pivot change an individual force's torque?
Respuesta
Yes. Torque depends on the axis, though a correctly solved physical prediction stays consistent.
Tarjeta 255
Pregunta
How does the parallel-axis theorem relate rotational inertia to a parallel axis a distance d from the center of mass?
Respuesta
I = I_cm + Md². Shifting the axis away from the center of mass increases rotational inertia.
Tarjeta 256
Pregunta
How could an experiment determine a rigid wheel's constant rotational inertia about an axis fixed in an inertial frame?
Respuesta
Apply several known signed net external torques about that axis, measure signed angular acceleration, and graph torque versus α. The slope is I.
Tarjeta 257
Pregunta
For a point at perpendicular distance r > 0 from a rigid body's fixed rotation axis, what is the radial-acceleration magnitude?
Respuesta
a_r = v_t²/r = rω². The acceleration points toward the axis. At r = 0, use a_r = rω² = 0; the quotient form isn't defined there.
Tarjeta 258
Pregunta
How could a meterstick experiment test torque balance?
Respuesta
Hang known forces at measured lever arms and compare signed r_perp F values at equilibrium. Repeat with different pivot choices.
Tarjeta 259
Pregunta
For uniform rotation at frequency f, what is the angular-speed magnitude?
Respuesta
|ω| = 2πf. One revolution is 2π rad, and uniform rotation has the same angular-speed magnitude throughout the cycle.
Tarjeta 260
Pregunta
Why is choosing the pivot at an unknown support force often useful?
Respuesta
That force then has zero lever arm and drops out of the torque equation. The physical equilibrium does not depend on the calculation shortcut.
Tarjeta 261
Pregunta
Among parallel axes through or near a rigid object, which gives the minimum rotational inertia?
Respuesta
The parallel axis through the center of mass. Any offset adds the positive term Md².
Tarjeta 262
Pregunta
Compare rigid systems with constant rotational inertia about comparable axes fixed in an inertial frame. If net external torque is the same but I triples, what happens to angular acceleration?
Respuesta
It becomes one-third as large. For each stated system, α = Στ_external/I.
Tarjeta 263
Pregunta
A rigid wheel of radius 0.50 m has angular-speed magnitude 6 rad/s about its fixed axis. What is the rim speed?
Respuesta
3 m/s. v_t = r|ω| = 0.50 × 6.
Tarjeta 264
Pregunta
A 30 N child sits 2 m left of a seesaw pivot. If the seesaw's own weight acts through the pivot, where should a 20 N child sit on the right for balance?
Respuesta
3 m from the pivot. Balance torque magnitudes: 30×2 = 20×r.
Tarjeta 265
Pregunta
For constant angular acceleration about one fixed axis, what does Δθ = ω₀t + ½αt² retrieve?
Respuesta
Angular displacement over elapsed time t. Use signed angular quantities about that axis; the equation combines the initial angular-velocity contribution with the change caused by constant α.
Tarjeta 266
Pregunta
A 20 N force acts at 30° to a radius vector of magnitude 0.60 m from a chosen axis. What torque magnitude results?
Respuesta
6 N·m. |τ| = rF sin θ = 0.60 × 20 × sin 30°.
Tarjeta 267
Pregunta
How does moving mass farther from a rotation axis affect rotational inertia?
Respuesta
It increases rotational inertia strongly. For a point mass, I = mr².
Tarjeta 268
Pregunta
How can angular-acceleration data compare two rigid objects' constant rotational inertias about comparable axes fixed in an inertial frame?
Respuesta
Apply the same measured net-external-torque magnitude about each axis and compare |α|. The object with smaller angular-acceleration magnitude has larger I.
Tarjeta 269
Pregunta
Why must angular displacement be in radians for Δs = rΔθ?
Respuesta
Radians define angle as arc length divided by radius. Degree measure would require a conversion factor.
Tarjeta 270
Pregunta
When does a nonzero force produce zero torque about an axis?
Respuesta
When its line of action passes through the axis. The lever arm is then zero.
Tarjeta 271
Pregunta
What is angular momentum for a rigid object rotating about an axis fixed in an inertial frame?
Respuesta
L = Iω about that axis. Use one signed-axis convention consistently for L and ω.
Tarjeta 272
Pregunta
What magnitude relation holds for a planar, constant-radius rigid object whose center of mass lies on its rolling axis when it rolls without slipping on a stationary surface?
Respuesta
v_cm = R|ω|. Here R is the constant rolling radius; the contact point is instantaneously at rest relative to the surface.
Tarjeta 273
Pregunta
For a rigid system rotating about an axis fixed in an inertial frame, how is work by a constant torque about that axis related to angular displacement?
Respuesta
W = τΔθ when torque and angular displacement use the same signed axis. The angle must be in radians.
Tarjeta 274
Pregunta
For point masses—or nonoverlapping spherical bodies—M and m separated center to center by r, what is gravitational potential energy with zero at infinity?
Respuesta
U_g = -GMm/r. The negative sign reflects U_g = 0 at infinity and attraction. In an isolated gravity-only inverse-square system, total mechanical energy determines binding: E < 0 is bound, while E ≥ 0 is unbound.
Tarjeta 275
Pregunta
When is a chosen system's angular momentum about an axis fixed in an inertial frame conserved?
Respuesta
When net external torque on the system about that axis is zero or negligible over the interval. Internal torques cannot change the system total.
Tarjeta 276
Pregunta
What does kinetic friction do to mechanical energy while a wheel slips on a stationary surface?
Respuesta
It converts mechanical energy into internal or thermal energy while the surfaces slide. Use qualitative energy accounting here; no no-slip relation connects the magnitudes v_cm and R|ω| during the slip.
Tarjeta 277
Pregunta
What is the angular-momentum magnitude of a translating point object about a chosen fixed point in an inertial frame?
Respuesta
L = mvr sin θ = r_perp mv. Here r points from the chosen point to the object, v is its speed, and θ is the angle between them. The SI unit is kg·m²/s.
Tarjeta 278
Pregunta
For a satellite of negligible mass relative to a fixed central body, how do speed and energy change along one gravity-only elliptical orbit?
Respuesta
Speed and kinetic energy are greatest near the central body, while gravitational potential energy is greatest farther away. Total mechanical energy stays constant.
Tarjeta 279
Pregunta
What is a rigid body's rotational kinetic energy about a fixed axis?
Respuesta
K_rot = ½Iω². It depends on rotational inertia about that axis and angular speed.
Tarjeta 280
Pregunta
Two planar rigid objects with constant rolling radii and centers of mass on their rolling axes are released from rest on the same fixed incline. Each rolls without slipping under gravity and its contact forces, with no other applied force or torque and negligible dissipation. Which accelerates faster: the one with smaller or larger I_cm/(MR²)?
Respuesta
The one with smaller I_cm/(MR²). Here I_cm is rotational inertia about the center of mass, M is total mass, and R is that object's constant rolling radius. Under the stated model, a_cm = g sin θ/(1 + I_cm/(MR²)).
Tarjeta 281
Pregunta
How could a rotating-platform experiment test angular-momentum conservation about the platform's axis, treated as fixed in the lab's inertial frame?
Respuesta
Choose the platform, rider, and moved masses as one system. In both the initial and final arrangements, wait until the rider and moved masses are stationary relative to the platform and the whole system co-rotates with one common signed angular velocity; then measure I_i, ω_i, I_f, and ω_f and compare I_iω_i with I_fω_f. Keep net external torque about the axis negligible, reduce bearing friction, and include uncertainty.
Tarjeta 282
Pregunta
For a satellite of mass m negligible beside a fixed central mass M, how are K, U_g, and total mechanical energy E related in a gravity-only circular orbit at center-to-center radius r?
Respuesta
K = -U_g/2 and E = U_g/2 = -K. Since U_g = -GMm/r, this gives K = GMm/(2r) and E = -GMm/(2r).
Tarjeta 283
Pregunta
For a rigid system rotating about an axis fixed in an inertial frame, how is instantaneous mechanical power delivered by a torque about that axis related to angular velocity?
Respuesta
P = τω for signed torque and angular velocity about the same axis. It is the rotational counterpart of P = F·v_point.
Tarjeta 284
Pregunta
In a planar common-axis rigid-body model, what kinetic-energy expression applies to a body rolling without slipping, with I_cm and ω taken about the same axis through its center of mass?
Respuesta
K = ½Mv_cm² + ½I_cmω². In this model, the rigid body's motion combines center-of-mass translation with rotation about one axis through the center of mass. I_cm and ω must refer to that same axis.
Tarjeta 285
Pregunta
Does angular-momentum conservation require rotational kinetic-energy conservation?
Respuesta
No. Internal work can change rotational kinetic energy while angular momentum stays constant.
Tarjeta 286
Pregunta
Why do astronauts feel weightless in orbit even though gravity acts on them?
Respuesta
They and their spacecraft are in continuous free fall together. Apparent weight is small because support forces are small.
Tarjeta 287
Pregunta
Two wheels spin at the same angular speed. Which has more rotational kinetic energy?
Respuesta
The wheel with larger rotational inertia. At common ω, K_rot is proportional to I.
Tarjeta 288
Pregunta
For a chosen system, what does the slope of its angular-momentum-versus-time graph about an axis fixed in an inertial frame represent?
Respuesta
Net external torque on the system about that axis. A constant slope means constant signed net external torque there.
Tarjeta 289
Pregunta
A motor supplies 12 N·m of torque about a shaft axis fixed in the lab's inertial frame while the shaft turns in the torque direction at 10 rad/s. What mechanical power does it deliver?
Respuesta
120 W. Using signed quantities about the shaft axis, P = τω = 12×10.
Tarjeta 290
Pregunta
While a rigid wheel is slipping on a stationary surface, how are the magnitudes v_cm and R|ω| related?
Respuesta
No no-slip equality applies. Their values evolve separately until friction may bring the contact point to rest relative to the surface.
Tarjeta 291
Pregunta
A launched object has negligible mass relative to a fixed central mass M and starts at center-to-center radius r. What minimum speed lets it escape under gravity alone without further propulsion or drag?
Respuesta
v_escape = √(2GM/r). At that threshold, total mechanical energy is zero with the object reaching infinity at zero speed.
Tarjeta 292
Pregunta
In a planar common-axis rigid-body model, what kinetic-energy forms can a rigid body have when it translates and rotates about an axis through its center of mass?
Respuesta
Both translational and rotational kinetic energy. The total is K = ½Mv_cm² + ½I_cmω², where I_cm and ω refer to the same axis through the center of mass.
Tarjeta 293
Pregunta
For a chosen object or system, what is angular impulse about an axis fixed in an inertial frame?
Respuesta
The change in that object or system's angular momentum about the axis. For constant net external torque, ΔL = τ_net,external Δt. Use the same axis and sign convention throughout. Angular impulse has units N·m·s, equivalent to kg·m²/s.
Tarjeta 294
Pregunta
Two equal-mass planar rigid objects have constant rolling radii and centers of mass on their rolling axes. They start from rest at the same height and roll without slipping to the same lower endpoint with negligible dissipation. Why can their final speeds differ?
Respuesta
Their rotational inertias divide the same decrease in gravitational potential energy differently between translation and rotation. A larger I_cm/(MR²) leaves less energy for translational speed, where I_cm is rotational inertia about the center of mass and R is rolling radius.
Tarjeta 295
Pregunta
For a satellite of negligible mass relative to a fixed central body, how does angular momentum behave along one gravity-only elliptical orbit?
Respuesta
It stays constant because gravity exerts zero torque about the central body. The satellite moves faster when closer and slower when farther away.
Tarjeta 296
Pregunta
How does rotational kinetic energy change if angular speed doubles at fixed I?
Respuesta
It becomes four times as large. Rotational kinetic energy depends on ω².
Tarjeta 297
Pregunta
Why should external torque be evaluated about the same axis used for angular momentum?
Respuesta
Both quantities depend on the chosen axis. Mixing axes breaks the conservation statement.
Tarjeta 298
Pregunta
For a chosen object or system about an axis fixed in an inertial frame, what does signed area under its net-external-torque-versus-time graph represent?
Respuesta
Angular impulse, equal to that object or system's ΔL about the axis. Use the graph's signed-axis convention. The area has units N·m·s, equivalent to kg·m²/s.
Tarjeta 299
Pregunta
Why can static friction act on a rigid object rolling without slipping on a stationary rigid surface without necessarily dissipating mechanical energy?
Respuesta
The contact point is instantaneously at rest relative to the surface, so there is no sliding. Static friction can still supply the torque needed for rolling.
Tarjeta 300
Pregunta
For a satellite whose mass is negligible beside a fixed central mass M, what is its speed in a gravity-only circular orbit at center-to-center radius r?
Respuesta
v = √(GM/r). Gravity supplies the inward net force.
Tarjeta 301
Pregunta
A chosen system's included mass co-rotates with one common angular velocity before and after a change. If its rotational inertia about an axis fixed in an inertial frame doubles while net external torque about that axis is negligible, what happens to its angular speed?
Respuesta
It halves. Because all included mass shares one angular velocity in each state, L = Iω applies. With the same axis and sign convention, angular-momentum conservation gives I_iω_i = I_fω_f.
Tarjeta 302
Pregunta
For a rigid system rotating about an axis fixed in an inertial frame, what does signed area under its net-external-torque-versus-angular-position graph represent when angle is in radians?
Respuesta
Net rotational work, equal to the system's change in rotational kinetic energy. Torque and angular position must use the same signed axis.
Tarjeta 303
Pregunta
Why can't the rolling condition alone prove that friction points uphill or downhill?
Respuesta
Friction direction depends on the tendency to slip and the applied forces or torques. Solve the dynamics instead of guessing from motion.
Tarjeta 304
Pregunta
A satellite of mass m, negligible beside a fixed central mass M, follows a circular orbit at center-to-center radius r under gravity alone. What is its total mechanical energy?
Respuesta
E = -GMm/(2r). A larger circular orbit has greater, less-negative energy even though its speed is lower.
Tarjeta 305
Pregunta
A spinning student pulls masses closer to an axis fixed in the lab's inertial frame while net external torque about that axis is negligible. Why does angular speed increase?
Respuesta
Rotational inertia decreases while angular momentum stays constant. Therefore Iω remains constant by increasing ω.
Tarjeta 306
Pregunta
What makes simple harmonic motion a special kind of periodic motion?
Respuesta
Its restoring force or torque is proportional to displacement and points toward equilibrium. Periodic motion alone does not guarantee this relationship.
Tarjeta 307
Pregunta
What does the amplitude of an SHM displacement graph represent?
Respuesta
The maximum distance from equilibrium. It is nonnegative even though displacement alternates sign.
Tarjeta 308
Pregunta
How are period and frequency related?
Respuesta
T = 1/f. Period is seconds per cycle; frequency is cycles per second, measured in hertz.
Tarjeta 309
Pregunta
What is the period of a mass m on an ideal spring of constant k when spring mass and damping are negligible?
Respuesta
T = 2π√(m/k). The motion must stay in the spring's linear SHM range.
Tarjeta 310
Pregunta
For one-dimensional SHM, what is the equilibrium position?
Respuesta
The position where the restoring force or torque—and therefore acceleration along the SHM coordinate—is zero. A stable equilibrium produces a restoring response after a small displacement.
Tarjeta 311
Pregunta
How far apart in phase are displacement and velocity in SHM?
Respuesta
One-quarter cycle. Velocity reaches an extremum when displacement crosses zero.
Tarjeta 312
Pregunta
When can a simple pendulum be modeled as SHM?
Respuesta
For small angular displacements. Then the restoring torque is approximately proportional to angular displacement.
Tarjeta 313
Pregunta
An oscillator completes 12 cycles in 6 s. What are its frequency and period?
Respuesta
f = 2 Hz and T = 0.5 s. Frequency is cycles per time, and period is its reciprocal.
Tarjeta 314
Pregunta
For a horizontal ideal spring oscillator, what is potential energy at displacement x from its relaxed equilibrium length when U_s = 0 there?
Respuesta
U_s = ½kx². It has the same value at +x and -x.
Tarjeta 315
Pregunta
At the equilibrium position of SHM, is the oscillator necessarily at rest?
Respuesta
No. The restoring force or torque and acceleration along the SHM coordinate are zero there, but speed is usually greatest.
Tarjeta 316
Pregunta
How does a spring oscillator's period change if k becomes four times as large?
Respuesta
The period is halved. T is proportional to 1/√k.
Tarjeta 317
Pregunta
How are acceleration and displacement related along the SHM coordinate?
Respuesta
a = -ω²x, where ω = 2πf is the oscillation's angular frequency. Here ω describes the oscillator's phase rate, not a rigid body's rotational angular velocity. The acceleration component along the SHM coordinate points toward equilibrium.
Tarjeta 318
Pregunta
For a horizontal ideal spring oscillator with amplitude A, what is total mechanical energy when U_s = 0 at the relaxed equilibrium length?
Respuesta
E = ½kA². It stays constant when dissipative effects are negligible.
Tarjeta 319
Pregunta
In a small-angle pendulum, where are speed and gravitational potential energy greatest?
Respuesta
Speed is greatest at the bottom; gravitational potential energy is greatest at the turning points. Energy trades between those forms.
Tarjeta 320
Pregunta
How can frequency be read from an oscillation-versus-time graph?
Respuesta
Measure the time between repeating equivalent points to find T, then use f = 1/T. Adjacent peaks are one period apart.
Tarjeta 321
Pregunta
Why does an ideal mass–spring oscillator exhibit SHM?
Respuesta
Its net restoring force is F_net = -kx, where x is displacement from equilibrium. The force is proportional to displacement and points back toward equilibrium.
Tarjeta 322
Pregunta
A horizontal ideal spring has k = 50 N/m and amplitude 0.20 m. With U_s = 0 at equilibrium, what is the oscillator's total energy?
Respuesta
1 J. E = ½(50)(0.20²).
Tarjeta 323
Pregunta
At maximum positive displacement in SHM, what are velocity and acceleration?
Respuesta
Velocity is zero; acceleration has maximum magnitude toward equilibrium. With positive displacement, acceleration is negative.
Tarjeta 324
Pregunta
How does a spring oscillator's period change if its mass becomes four times as large?
Respuesta
The period doubles. T is proportional to √m.
Tarjeta 325
Pregunta
Why isn't uniform circular motion itself one-dimensional SHM?
Respuesta
The object travels around a circle, not back and forth along one line. Its projection onto a diameter does follow SHM.
Tarjeta 326
Pregunta
For the same ideal oscillator, how does total SHM energy change if amplitude doubles while k or mω² stays fixed?
Respuesta
It becomes four times as large. Under those fixed system parameters, total energy is proportional to A².
Tarjeta 327
Pregunta
In one-dimensional SHM, what are speed and acceleration along the SHM coordinate at equilibrium?
Respuesta
Speed is maximum, while acceleration along the SHM coordinate is zero. The restoring force or torque vanishes there.
Tarjeta 328
Pregunta
Does changing amplitude change the period of an ideal spring oscillator or small-angle pendulum?
Respuesta
No within the ideal SHM model. The period depends on system parameters, not amplitude.
Tarjeta 329
Pregunta
How is maximum speed related to amplitude and angular frequency in SHM?
Respuesta
v_max = ωA. Maximum speed occurs at equilibrium.
Tarjeta 330
Pregunta
For a horizontal ideal spring oscillator, how can kinetic energy at displacement x from equilibrium be found for amplitude A?
Respuesta
K = ½k(A² - x²). Subtract spring potential energy from the constant total.
Tarjeta 331
Pregunta
How far apart in phase are displacement and acceleration in SHM?
Respuesta
Half a cycle, or 180°. When displacement is nonzero, acceleration has the opposite sign; at equilibrium, both are zero.
Tarjeta 332
Pregunta
What is the period of a small-angle simple pendulum of length L when damping is negligible?
Respuesta
T = 2π√(L/g). The simple-pendulum model uses a point-like bob on a light, inextensible string with a fixed support; bob mass doesn't affect the period.
Tarjeta 333
Pregunta
If x(t) is at a positive maximum at t = 0, what qualitative pattern follows over one cycle?
Respuesta
It crosses equilibrium moving negative at T/4, reaches negative maximum at T/2, returns through equilibrium at 3T/4, and reaches maximum positive displacement at T.
Tarjeta 334
Pregunta
At equilibrium, how are a horizontal ideal spring oscillator's energies divided?
Respuesta
Kinetic energy is maximum and spring potential energy is minimum. With x measured from equilibrium, U_s = 0 at x = 0.
Tarjeta 335
Pregunta
An SHM object is at negative displacement and moving toward equilibrium. What signs do velocity and acceleration have if positive is right?
Respuesta
Both are positive. Motion and restoring acceleration point right toward equilibrium.
Tarjeta 336
Pregunta
How does a pendulum's period change if its length becomes nine times as large?
Respuesta
The period triples. T is proportional to √L.
Tarjeta 337
Pregunta
If SHM starts at maximum positive displacement, what equation gives its position?
Respuesta
x(t) = A cos(2πft). A is amplitude, f is frequency, and t is elapsed time.
Tarjeta 338
Pregunta
What feature would rule out ideal SHM in a force-versus-displacement-from-equilibrium graph?
Respuesta
A restoring-force relationship that is not a straight line through the origin over the motion's range. Ideal SHM needs F ∝ -x.
Tarjeta 339
Pregunta
At a horizontal ideal spring oscillator's turning points, how are kinetic and spring potential energy divided?
Respuesta
Kinetic energy is zero and spring potential energy is maximum. The object momentarily stops at |x| = A.
Tarjeta 340
Pregunta
For the same ideal spring with negligible damping and spring mass, which graph can determine k from measured periods and attached masses?
Respuesta
Graph T² versus m. For T = 2π√(m/k), the slope is 4π²/k.
Tarjeta 341
Pregunta
What makes a substance a fluid?
Respuesta
It deforms continuously under a shear force and takes the shape of its container. Liquids and gases are fluids.
Tarjeta 342
Pregunta
What is mass density?
Respuesta
Mass per volume: ρ = m/V. Its SI unit is kg/m³.
Tarjeta 343
Pregunta
For pressure that is uniform over a surface patch, how is it related to normal force and area?
Respuesta
P = F_perpendicular/A. Pressure is a scalar field even though the contact force has direction.
Tarjeta 344
Pregunta
What is volume flow rate?
Respuesta
Volume passing a cross-section per time: Q = ΔV/Δt. Its SI unit is m³/s.
Tarjeta 345
Pregunta
What is the buoyant-force magnitude on an object immersed in a static fluid whose density is uniform over the displaced volume?
Respuesta
The weight of the displaced fluid: F_B = ρ_fluid gV_displaced. Here ρ_fluid is the uniform density over that volume.
Tarjeta 346
Pregunta
What conditions support the basic Bernoulli model used here?
Respuesta
Steady, incompressible, nonviscous flow along the compared flow path, with a completely filled pipe unless stated otherwise. Incompressible means a moving fluid element's density stays effectively constant. Pumps or major dissipative effects require extra terms.
Tarjeta 347
Pregunta
Under the ideal model, how does average density predict whether a free object floats or sinks?
Respuesta
It floats if its average density is less than the fluid's and sinks if it is greater. Equal average density gives neutral buoyancy when fully submerged; assume no support or other external force.
Tarjeta 348
Pregunta
How are volume flow rate, cross-sectional area, and average fluid speed normal to that area related?
Respuesta
Q = Av. This gives the volume crossing a completely filled pipe section per time.
Tarjeta 349
Pregunta
How does a static fluid exert force on a surface?
Respuesta
Many particle–surface interactions produce a net force perpendicular to the surface. A static fluid does not exert a tangential shear force.
Tarjeta 350
Pregunta
How does pressure change with depth in a static uniform fluid?
Respuesta
It increases by ΔP = ρgΔh. Greater depth means more fluid weight above each unit area.
Tarjeta 351
Pregunta
What force balance holds for an object floating at rest when buoyancy and weight are its only vertical forces?
Respuesta
F_B = mg. The object's weight equals the weight of the fluid it displaces.
Tarjeta 352
Pregunta
What is the continuity equation for steady incompressible flow in one filled pipe?
Respuesta
A₁v₁ = A₂v₂. The same volume flow rate passes each cross-section.
Tarjeta 353
Pregunta
Why does a static fluid produce an upward buoyant force?
Respuesta
Pressure is greater on the object's lower surfaces than on its upper surfaces. The vertical pressure forces do not cancel.
Tarjeta 354
Pregunta
What is the absolute pressure at depth h below the open surface of a static, uniform liquid?
Respuesta
P_abs = P_atm + ρgh. ρgh is the gauge pressure from the liquid column.
Tarjeta 355
Pregunta
Immediately after a fully submerged object is released in a static, uniform ideal fluid, which way does it accelerate if its average density exceeds the fluid density and only weight and buoyancy act?
Respuesta
Downward. Weight exceeds buoyant force, so the initial net force and acceleration point downward.
Tarjeta 356
Pregunta
Water's average speed normal to a 0.020 m² pipe cross-section is 3 m/s. What is the volume flow rate?
Respuesta
0.060 m³/s. Q = Av = 0.020×3.
Tarjeta 357
Pregunta
What does the slope of a mass-versus-volume graph represent for one uniform material?
Respuesta
Density. Since m = ρV, the line's slope is ρ.
Tarjeta 358
Pregunta
How do gauge pressure and absolute pressure differ?
Respuesta
Gauge pressure is measured relative to atmospheric pressure; absolute pressure is measured relative to vacuum. P_abs = P_atm + P_gauge.
Tarjeta 359
Pregunta
For a fully submerged rigid object in a static, incompressible, uniform fluid, does buoyant force increase with depth?
Respuesta
No. Displaced volume, fluid density, and g stay constant, so F_B stays constant despite higher absolute pressure.
Tarjeta 360
Pregunta
For steady incompressible flow in a filled pipe, what happens to speed if cross-sectional area halves?
Respuesta
It doubles. Continuity keeps Av constant.
Tarjeta 361
Pregunta
When does a fluid element's velocity change?
Respuesta
Its velocity changes when a nonzero net force acts on it. Pressure forces and gravity can contribute to that net force.
Tarjeta 362
Pregunta
For steady, incompressible, nonviscous flow along the same flow path, what does Bernoulli's equation express?
Respuesta
Conservation of mechanical energy per unit volume. Along that flow path, P + ½ρv² + ρgy stays constant under the stated conditions.
Tarjeta 363
Pregunta
For a uniform object floating at rest in a uniform-density fluid with buoyancy and weight as its only vertical forces, what fraction of its volume is submerged?
Respuesta
V_sub/V_object = ρ_object/ρ_fluid. A less-dense object floats with a smaller fraction submerged.
Tarjeta 364
Pregunta
For steady incompressible flow in a filled pipe, what happens to speed if pipe radius halves?
Respuesta
It becomes four times as large. Area is proportional to radius squared.
Tarjeta 365
Pregunta
What does Pascal's principle say for a confined incompressible fluid at rest?
Respuesta
An applied pressure change is transmitted throughout the fluid. The same pressure change acts at every connected point.
Tarjeta 366
Pregunta
In a uniform static fluid, what does the slope of gauge pressure versus depth represent?
Respuesta
ρg. For known g, the slope can determine fluid density.
Tarjeta 367
Pregunta
Immediately after a fully submerged object is released in a static, uniform ideal fluid, which way does it accelerate if its average density is less than the fluid density and only weight and buoyancy act?
Respuesta
Upward. Buoyant force exceeds weight, so the initial net force and acceleration point upward.
Tarjeta 368
Pregunta
For steady incompressible flow in a filled pipe, area narrows from 0.040 m² to 0.010 m². If initial speed is 2 m/s, what is final speed?
Respuesta
8 m/s. Continuity gives v₂ = A₁v₁/A₂.
Tarjeta 369
Pregunta
What physical quantity does each term in P + ½ρv² + ρgy share?
Respuesta
Energy per unit volume, equivalent to pressure. Every term uses units of pascals.
Tarjeta 370
Pregunta
In one static fluid of uniform density, what experimental graph could test F_B = ρ_fluid gV_displaced?
Respuesta
Graph measured buoyant force versus displaced volume. A line with slope near ρ_fluid g supports the model.
Tarjeta 371
Pregunta
A uniform object of density 750 kg/m³ floats at rest in uniform-density water of density 1000 kg/m³, with buoyancy and weight as its only vertical forces. What fraction is submerged?
Respuesta
0.75, or 75%. Use the density ratio for floating equilibrium.
Tarjeta 372
Pregunta
A main pipe splits into two outlets during steady incompressible flow. What flow-rate relation holds?
Respuesta
Incoming flow rate equals the sum of outgoing flow rates. Q_in = Q_out,1 + Q_out,2.
Tarjeta 373
Pregunta
For steady, incompressible, nonviscous efflux with negligible losses, what is Torricelli's speed for an opening a vertical distance h below a large open surface?
Respuesta
v = √(2gh). Both locations are open to atmospheric pressure, and the large surface makes the upper-fluid speed negligible.
Tarjeta 374
Pregunta
Why does the same force create more pressure on a smaller area?
Respuesta
Pressure is inversely proportional to area for fixed perpendicular force. Concentrating the force raises F/A.
Tarjeta 375
Pregunta
A sample has mass 0.60 kg and volume 2.0×10⁻⁴ m³. What is its density?
Respuesta
3.0×10³ kg/m³. Divide mass by volume.
Tarjeta 376
Pregunta
What conservation law underlies the continuity equation for incompressible flow?
Respuesta
Conservation of mass. Constant density turns equal mass flow into equal volume flow.
Tarjeta 377
Pregunta
An immersed object rests on a scale that exerts an upward support force. If weight, buoyancy, and that support are its only vertical forces, with mg ≥ F_B, how is apparent weight related to buoyant force?
Respuesta
N = mg - F_B. Here N is the upward scale-force magnitude. The fluid supports part of the object's weight, so the scale reading is no greater than its weight under the stated condition.
Tarjeta 378
Pregunta
What is the SI unit of pressure?
Respuesta
The pascal, Pa. One pascal equals 1 N/m².
Tarjeta 379
Pregunta
How do pressures compare at the same horizontal level in one connected static fluid?
Respuesta
They are equal. Container shape does not change pressure at a fixed elevation.
Tarjeta 380
Pregunta
What does specific gravity compare?
Respuesta
A substance's density with water's density. It is a dimensionless ratio, commonly ρ_substance/ρ_water.
Tarjeta 381
Pregunta
How could collecting outflow test a volume flow rate predicted from area and average normal speed?
Respuesta
Measure collected volume over a timed interval and compare ΔV/Δt with Av. Repeat trials and include volume and timing uncertainty.
Tarjeta 382
Pregunta
How does the particle model distinguish a fluid from a rigid solid?
Respuesta
Fluid particles can rearrange and flow past one another. A rigid solid resists sustained shape change.
Tarjeta 383
Pregunta
At equal height along the same flow path in steady, incompressible, nonviscous flow, how are pressure and speed related?
Respuesta
The faster region has lower static pressure. Along that flow path at equal height, P + ½ρv² remains constant.
Tarjeta 384
Pregunta
A fully submerged object displaces 0.020 m³ of static water. Using ρ = 1000 kg/m³ and g = 10 m/s², what is F_B?
Respuesta
200 N. F_B = ρgV = 1000×10×0.020.
Tarjeta 385
Pregunta
Why can a steel ship float even though steel is denser than water?
Respuesta
Its hollow shape makes the ship's overall average density less than water. It displaces enough water for buoyant force to balance weight.
Tarjeta 386
Pregunta
How does an ideal hydraulic lift with a confined incompressible fluid at rest multiply force?
Respuesta
Equal pressure change gives F₁/A₁ = F₂/A₂. The larger-area piston produces the larger force.
Tarjeta 387
Pregunta
For steady, incompressible, nonviscous efflux with negligible losses, what graph can test Torricelli's relation while fluid head h varies?
Respuesta
Graph v² versus h. With both locations open to atmospheric pressure and upper-surface speed negligible, the model predicts slope 2g.
Tarjeta 388
Pregunta
What does incompressible mean in the introductory ideal-fluid model?
Respuesta
A fluid element's density stays effectively constant as it moves. Its volume does not appreciably shrink under pressure changes.
Tarjeta 389
Pregunta
At two points along the same flow path in steady, incompressible, nonviscous flow, how are pressure and height related when speed is equal?
Respuesta
Pressure is lower at the higher point. P + ρgy remains constant.
Tarjeta 390
Pregunta
How can water displacement measure an irregular solid's volume?
Respuesta
Submerge it fully and measure the increase in displaced-water volume. The volume change equals the submerged solid's volume if no water enters it.
Tarjeta 391
Pregunta
Two equal-volume samples have densities ρ and 3ρ. How do their masses compare?
Respuesta
The denser sample has three times the mass. From m = ρV, mass scales with density at fixed volume.
Tarjeta 392
Pregunta
How can scale readings in air and water determine buoyant force?
Respuesta
Subtract the immersed scale reading from the air reading. When the object is at rest and air buoyancy is negligible, the decrease equals the liquid's buoyant force.
Tarjeta 393
Pregunta
Static water has ρ = 1000 kg/m³. Using g = 10 m/s², what gauge pressure is 3 m below its open surface?
Respuesta
30,000 Pa. P_gauge = ρgh = 1000×10×3.
Tarjeta 394
Pregunta
During steady incompressible outflow, why can a large tank's top-surface speed be neglected compared with outlet speed?
Respuesta
The tank's surface area is much larger than the outlet area. Continuity then makes the top-surface speed much smaller.
Tarjeta 395
Pregunta
For a chosen fluid element in a horizontal region, what can a pressure difference do?
Respuesta
It creates a net pressure force from higher pressure toward lower pressure and can accelerate the element by Newton's second law. Other forces must also be included when they matter.
Tarjeta 396
Pregunta
How can buoyancy measurements in a static fluid of known uniform density determine an irregular object's volume?
Respuesta
Measure buoyant force while the object is fully submerged, then use V = F_B/(ρ_fluid g). The fluid density must be uniform over the displaced volume.
Tarjeta 397
Pregunta
A 200 N perpendicular force acts on area 0.040 m². What pressure does it create?
Respuesta
5,000 Pa. P = F/A = 200/0.040.
Tarjeta 398
Pregunta
Why doesn't a hydraulic lift multiply energy?
Respuesta
The large-force piston moves a shorter distance. Ideally, input work equals output work.
Tarjeta 399
Pregunta
A large open tank has steady, incompressible, nonviscous efflux with negligible losses. Using g = 10 m/s², what speed leaves an opening 5 m below the surface when upper-surface speed is negligible?
Respuesta
10 m/s. Both locations are at atmospheric pressure, so v = √(2gh) = √100.
Tarjeta 400
Pregunta
An object floats first in water and then in a denser liquid. How does its submerged fraction change?
Respuesta
It decreases in the denser liquid. Less displaced volume is needed to provide the same buoyant force.

An orange sphere traces an orbital path between a wave, a rotating disc, and a fluid ripple on a dark grid.

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