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

このデッキのカード

1. カード 1

   質問

   What separates a vector quantity from a scalar quantity?

   回答

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

2. カード 2

   質問

   When is the point-object model useful in kinematics?

   回答

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

3. カード 3

   質問

   When may the constant-acceleration kinematic equations be used?

   回答

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

4. カード 4

   質問

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

   回答

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

5. カード 5

   質問

   Why can horizontal and vertical projectile motion be analyzed separately?

   回答

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

6. カード 6

   質問

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

   回答

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

7. カード 7

   質問

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

   回答

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

8. カード 8

   質問

   What makes a reference frame convenient for a motion problem?

   回答

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

9. カード 9

   質問

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

   回答

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

10. カード 10

    質問

    What does average velocity measure?

    回答

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

11. カード 11

    質問

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

    回答

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

12. カード 12

    質問

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

    回答

    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.

13. カード 13

    質問

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

    回答

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

14. カード 14

    質問

    What does average acceleration measure?

    回答

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

15. カード 15

    質問

    What does a negative one-dimensional vector component mean?

    回答

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

16. カード 16

    質問

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

    回答

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

17. カード 17

    質問

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

    回答

    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.

18. カード 18

    質問

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

    回答

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

19. カード 19

    質問

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

    回答

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

20. カード 20

    質問

    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?

    回答

    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.

21. カード 21

    質問

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

    回答

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

22. カード 22

    質問

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

    回答

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

23. カード 23

    質問

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

    回答

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

24. カード 24

    質問

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

    回答

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

25. カード 25

    質問

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

    回答

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

26. カード 26

    質問

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

    回答

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

27. カード 27

    質問

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

    回答

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

28. カード 28

    質問

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

    回答

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

29. カード 29

    質問

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

    回答

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

30. カード 30

    質問

    Can an object have nonzero velocity and zero acceleration?

    回答

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

31. カード 31

    質問

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

    回答

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

32. カード 32

    質問

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

    回答

    Displacement. Area below the time axis contributes negative displacement.

33. カード 33

    質問

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

    回答

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

34. カード 34

    質問

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

    回答

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

35. カード 35

    質問

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

    回答

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

36. カード 36

    質問

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

    回答

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

37. カード 37

    質問

    How could video data test the independence of projectile components?

    回答

    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.

38. カード 38

    質問

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

    回答

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

39. カード 39

    質問

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

    回答

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

40. カード 40

    質問

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

    回答

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

41. カード 41

    質問

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

    回答

    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.

42. カード 42

    質問

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

    回答

    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.

43. カード 43

    質問

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

    回答

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

44. カード 44

    質問

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

    回答

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

45. カード 45

    質問

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

    回答

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

46. カード 46

    質問

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

    回答

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

47. カード 47

    質問

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

    回答

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

48. カード 48

    質問

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

    回答

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

49. カード 49

    質問

    What does translational equilibrium require?

    回答

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

50. カード 50

    質問

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

    回答

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

51. カード 51

    質問

    How do mass and weight differ?

    回答

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

52. カード 52

    質問

    How does static friction choose its magnitude before slipping begins?

    回答

    It matches the needed tangential contact force up to a maximum. In general, f_s ≤ μ_sN.

53. カード 53

    質問

    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?

    回答

    F_s = -kx. The sign shows that the spring force opposes the signed extension or compression and points toward the relaxed or natural length.

54. カード 54

    質問

    What direction does centripetal acceleration point in circular motion?

    回答

    Toward the circle's center. It changes the velocity's direction even when speed is constant.

55. カード 55

    質問

    What is the gravitational force magnitude between two point masses?

    回答

    F_g = Gm₁m₂/r². Here r is the center-to-center separation.

56. カード 56

    質問

    Why isn't the normal force always equal to an object's weight?

    回答

    It adjusts to the contact and acceleration conditions. Other vertical forces or vertical acceleration can change its magnitude.

57. カード 57

    質問

    What determines a friction coefficient in the simple model?

    回答

    The pair of contacting materials and their surface condition. It isn't a universal property of either material alone.

58. カード 58

    質問

    What is the centripetal-acceleration magnitude for speed v and radius r?

    回答

    a_c = v²/r. It is a kinematic requirement, not a separate force.

59. カード 59

    質問

    An elevator accelerates upward. How does the scale reading compare with a rider's weight?

    回答

    It is greater than the weight. Upward net force requires N - mg > 0.

60. カード 60

    質問

    What does a spring constant k measure, and what is its SI unit?

    回答

    It measures stiffness in N/m. A larger k means more force is needed for the same displacement in the linear range.

61. カード 61

    質問

    Three equal point masses are at (0,0), (3 m,0), and (0,3 m). Where is their center of mass?

    回答

    At (1 m,1 m). Average the x-coordinates and y-coordinates separately for equal masses.

62. カード 62

    質問

    What provides centripetal force?

    回答

    The inward component of real forces such as tension, gravity, friction, or a normal force. 'Centripetal force' names their net inward result.

63. カード 63

    質問

    How is near-surface gravitational field strength related to weight?

    回答

    F_g = mg. The local field strength g has units N/kg, equivalent to m/s².

64. カード 64

    質問

    How is weight resolved on an incline of angle θ measured from horizontal?

    回答

    mg sin θ points down the slope and mg cos θ points into the slope. These are components of one gravitational force.

65. カード 65

    質問

    What does Newton's third law say about an interaction between objects A and B?

    回答

    The force of A on B and the force of B on A have equal magnitude and opposite direction. They act on different objects.

66. カード 66

    質問

    What does signed tangential acceleration describe during circular motion?

    回答

    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.

67. カード 67

    質問

    What happens to gravitational force if the separation between two point masses doubles?

    回答

    It becomes one-fourth as large. The force follows an inverse-square dependence on distance.

68. カード 68

    質問

    How can an adjustable incline estimate a block's coefficient of static friction when no other applied force acts?

    回答

    Raise the incline slowly until the block just begins to slide. At that threshold, the simple block model gives μ_s = tan θ.

69. カード 69

    質問

    In an inertial frame, what determines the acceleration of a fixed-mass system's center of mass?

    回答

    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.

70. カード 70

    質問

    Which tension components act for a conical pendulum?

    回答

    The vertical component balances weight, and the horizontal component supplies centripetal force. The bob moves in a horizontal circle.

71. カード 71

    質問

    What does apparent weight measure for an object supported by one surface?

    回答

    The normal-force magnitude exerted by that support. It can differ from gravitational force when the object accelerates.

72. カード 72

    質問

    How are several forces combined to find net force?

    回答

    Add them as vectors, component by component. Opposing components subtract according to the chosen signs.

73. カード 73

    質問

    Why is tension uniform along one continuous ideal string?

    回答

    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.

74. カード 74

    質問

    A 0.5 kg object moves at 4 m/s in a circle of radius 2 m. What inward net force is required?

    回答

    4 N. F_in = mv²/r = 0.5 × 16 / 2.

75. カード 75

    質問

    What local equivalence links a uniform gravitational field with a uniformly accelerating reference frame?

    回答

    A uniform gravitational field and a uniformly accelerating reference frame can produce the same local mechanical effects. Local observations alone may not distinguish them.

76. カード 76

    質問

    For the same net force, what happens to acceleration if mass doubles?

    回答

    Acceleration is halved. From a = ΣF/m, acceleration is inversely proportional to mass.

77. カード 77

    質問

    How do static and kinetic friction coefficients usually compare for the same pair of surfaces?

    回答

    Typically μ_s > μ_k. Starting sliding usually requires a larger friction threshold than maintaining it.

78. カード 78

    質問

    How are radial and tangential acceleration combined when circular speed changes?

    回答

    Add the perpendicular components as vectors. The total magnitude is √(a_c² + a_t²).

79. カード 79

    質問

    A spherically symmetric planet has twice Earth's mass and the same radius. How does its surface g compare with Earth's?

    回答

    It is twice as large. Surface field strength follows g = GM/R².

80. カード 80

    質問

    Does a force have to point in the direction of motion?

    回答

    No. A force points in the direction of the interaction; it may speed up, slow down, or turn the object.

81. カード 81

    質問

    Where is the center of mass of a uniform object with a symmetric mass distribution?

    回答

    At its geometric center of symmetry. Symmetry lets opposite mass elements balance without a detailed sum.

82. カード 82

    質問

    How are speed, period, and frequency related in uniform circular motion?

    回答

    v = 2πr/T = 2πrf, with T = 1/f. One cycle covers one circumference.

83. カード 83

    質問

    Why is an object apparently weightless in free fall?

    回答

    Its support force is zero while it and its surroundings accelerate together under gravity. Gravity still acts.

84. カード 84

    質問

    Can forces balance along one axis while an object accelerates along another?

    回答

    Yes. Zero net force in one component gives zero acceleration only in that direction; another component can remain unbalanced.

85. カード 85

    質問

    Why don't Newton's third-law forces cancel on one object's free-body diagram?

    回答

    Only one force in the pair acts on that object. The partner force belongs on the other object's diagram.

86. カード 86

    質問

    On a frictionless banked curve, which force components create vertical balance and inward acceleration?

    回答

    The normal force's vertical component balances weight, while its horizontal component supplies the inward net force.

87. カード 87

    質問

    What motion results when the net force on an object is zero in an inertial frame?

    回答

    Constant velocity. Rest is the special case with constant velocity equal to zero.

88. カード 88

    質問

    A 3 kg cart has a net horizontal force of 12 N. What is its acceleration?

    回答

    4 m/s². Use a = ΣF/m = 12/3.

89. カード 89

    質問

    What does the observed equivalence of inertial and gravitational mass imply for free fall?

    回答

    Free-fall acceleration is independent of the falling object's mass. Inertial and gravitational mass are proportional and conventionally assigned equal numerical values.

90. カード 90

    質問

    Does friction in the simple dry-friction model depend on apparent contact area?

    回答

    No. For a fixed normal force and the same contacting materials, the model treats friction magnitude as independent of apparent contact area.

91. カード 91

    質問

    When should Hooke's-law predictions be treated cautiously?

    回答

    When deformation leaves the spring's linear elastic range. Force may no longer be proportional to displacement.

92. カード 92

    質問

    What bank angle θ supports speed v on an ideal frictionless curve of radius r?

    回答

    tan θ = v²/(rg). The result assumes no vertical acceleration and no friction.

93. カード 93

    質問

    Why do internal forces cancel when finding the net force on a complete system?

    回答

    They occur in equal-and-opposite pairs between system parts. Each pair sums to zero in the system's force total.

94. カード 94

    質問

    An elevator moves downward at constant speed. How does the scale reading compare with weight?

    回答

    It equals the weight. Constant velocity means zero acceleration and N - mg = 0.

95. カード 95

    質問

    What assumptions let an ideal pulley redirect a string without changing its tension magnitude?

    回答

    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.

96. カード 96

    質問

    What does inertia describe?

    回答

    An object's resistance to changes in velocity. Mass measures translational inertia.

97. カード 97

    質問

    For the same fixed-mass object or system across all measurements, what does the slope of a net-force-versus-acceleration graph represent?

    回答

    Its mass. Written as ΣF = ma, the graph has slope m when the object or system and its mass stay fixed.

98. カード 98

    質問

    Does zero net force mean no forces act?

    回答

    No. Several forces can act and cancel vectorially.

99. カード 99

    質問

    What is the common model for kinetic-friction magnitude?

    回答

    f_k = μ_kN. It applies while the surfaces slide under the model's assumptions.

100. カード 100

     質問

     How could hanging masses measure the spring constant of one ideal spring?

     回答

     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.

101. カード 101

     質問

     For the same object at the same circular radius, how does required inward net force change if speed doubles?

     回答

     It becomes four times as large. F_in = mv²/r depends on speed squared.

102. カード 102

     質問

     Where is the center of mass of two point masses on an x-axis?

     回答

     At x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂). It lies closer to the larger mass.

103. カード 103

     質問

     Why must net force, rather than one selected force, be used in ΣF = ma?

     回答

     All external forces contribute to acceleration. Ignoring a force changes the vector sum and the prediction.

104. カード 104

     質問

     Why can tension vary along a hanging chain with nonnegligible mass?

     回答

     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.

105. カード 105

     質問

     What makes a reference frame inertial?

     回答

     An object with zero net force has constant velocity in that frame. A frame accelerating relative to an inertial frame is noninertial.

106. カード 106

     質問

     How could carts test the proportionality between acceleration and net force?

     回答

     Keep total mass constant, vary the applied net force, and graph acceleration versus force. A line through the origin supports a ∝ ΣF.

107. カード 107

     質問

     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?

     回答

     T² ∝ r³. The circular orbit with the larger center-to-center radius has the longer period.

108. カード 108

     質問

     Which direction does kinetic friction act?

     回答

     Opposite the relative sliding of the contacting surfaces. It is not automatically opposite the object's velocity in every frame.

109. カード 109

     質問

     What does the slope of a spring-force-versus-displacement graph give?

     回答

     -k when signed force is graphed against signed displacement. The slope magnitude is the spring constant.

110. カード 110

     質問

     What is the minimum speed at the top of an ideal vertical loop of radius r when gravity alone supplies the inward force?

     回答

     v_min = √(gr). At the threshold, the support force or tension is zero.

111. カード 111

     質問

     What is translational kinetic energy?

     回答

     Energy associated with an object's translational motion. For a point-like object, K = ½mv².

112. カード 112

     質問

     How is work by a constant force calculated when its point of application undergoes a straight displacement?

     回答

     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.

113. カード 113

     質問

     What does power measure?

     回答

     The rate of energy transfer or conversion. P_avg = ΔE_transferred/Δt; when work is the relevant transfer, P_avg = W/Δt.

114. カード 114

     質問

     What does conservation of energy say for an isolated system?

     回答

     The system's total energy stays constant. Energy may change form or move among system parts, but it is not created or destroyed.

115. カード 115

     質問

     Can translational kinetic energy be negative?

     回答

     No. Mass is positive and speed is squared, so translational kinetic energy is zero or positive.

116. カード 116

     質問

     What does negative work by a force mean?

     回答

     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.

117. カード 117

     質問

     What is the near-surface change in gravitational potential energy?

     回答

     ΔU_g = mgΔy. It applies when g can be treated as constant.

118. カード 118

     質問

     When is a chosen system's mechanical energy K + U conserved?

     回答

     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.

119. カード 119

     質問

     What is the SI unit of power?

     回答

     The watt, W. One watt equals one joule per second.

120. カード 120

     質問

     For an object modeled as a particle, what connects net work by all forces to its change in translational kinetic energy?

     回答

     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.

121. カード 121

     質問

     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?

     回答

     v = √(2gh). The system's mgh decrease in gravitational potential energy becomes ½mv².

122. カード 122

     質問

     Does choosing a different zero level for potential energy change physical predictions?

     回答

     No. Only potential-energy differences enter measurable energy changes.

123. カード 123

     質問

     Can an engine do the same work with different average power?

     回答

     Yes. Doing the same work in less time requires greater average power.

124. カード 124

     質問

     When does a constant nonzero force do zero work over an interval?

     回答

     When its point of application has zero displacement or its displacement is perpendicular to the force. Then W = Fd cos θ is zero.

125. カード 125

     質問

     A particle-modeled block slides down a fixed frictionless track. Does the path shape affect its final speed at a given lower height?

     回答

     No. With only gravity doing work, the potential-energy change depends on height, not path.

126. カード 126

     質問

     How does translational kinetic energy change if speed doubles at constant mass?

     回答

     It becomes four times as large. Kinetic energy depends on v².

127. カード 127

     質問

     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?

     回答

     U_s = ½kx². Choosing zero energy at the relaxed length gives the same stored energy for equal-magnitude extension or compression.

128. カード 128

     質問

     What does signed area under a force-component-versus-position graph represent when position tracks that force's point of application?

     回答

     Work done by that force along the measured coordinate. Area below the position axis counts as negative work under the graph's sign convention.

129. カード 129

     質問

     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?

     回答

     14 J. The 6 J thermal-energy increase matches the mechanical-energy decrease.

130. カード 130

     質問

     What shape does a translational-kinetic-energy-versus-speed graph have for fixed mass?

     回答

     The right-hand half of an upward-opening parabola through the origin. Speed is nonnegative, and K is proportional to v², not v.

131. カード 131

     質問

     A machine transfers 600 J in 3 s. What is its average power?

     回答

     200 W. Divide energy transferred by elapsed time.

132. カード 132

     質問

     Why does the normal force do no work on a nonrotating block sliding across a fixed horizontal floor?

     回答

     The force is perpendicular to the horizontal displacement of its points of application. Their dot product is zero in this pure-translation model.

133. カード 133

     質問

     A coaster modeled as a particle moves on a fixed frictionless track. Where is its speed greatest?

     回答

     At the lowest accessible position. Gravitational potential energy is smallest there, so kinetic energy is largest.

134. カード 134

     質問

     Two objects have equal mass and velocities of equal magnitude but opposite direction. How do their translational kinetic energies compare?

     回答

     They are equal. Kinetic energy uses speed and has no direction.

135. カード 135

     質問

     What makes work by a conservative force path independent?

     回答

     It depends only on the initial and final configurations. Any two paths between the same endpoints give the same conservative-force work.

136. カード 136

     質問

     A 10 N force acts while its point of application moves 3 m in the force direction. How much work does the force do?

     回答

     30 J. Here θ = 0, so W = Fd = 10×3.

137. カード 137

     質問

     How is total potential energy built for a system with several interacting pairs?

     回答

     Add the potential energy assigned to each relevant pair. Count each interaction pair once and use one consistent reference choice.

138. カード 138

     質問

     How should external work appear in an energy equation?

     回答

     As energy transferred across the system boundary. A useful form is ΔE_system = W_external + other transfers.

139. カード 139

     質問

     How does a spring launch problem combine energy forms?

     回答

     Initial elastic energy becomes kinetic energy and possibly gravitational or thermal energy. Write only the forms present in the chosen initial and final states.

140. カード 140

     質問

     For a constant force parallel to the velocity of its point of application, how is instantaneous mechanical power calculated?

     回答

     P = Fv. More generally, P = F·v_point, so only the force component along that point's velocity contributes.

141. カード 141

     質問

     How does translational kinetic energy change if mass triples at constant speed?

     回答

     It triples. Kinetic energy is directly proportional to mass.

142. カード 142

     質問

     How much net work does a conservative force do around a path that returns to the initial configuration?

     回答

     Zero. The initial and final potential energies are the same.

143. カード 143

     質問

     Where is stable equilibrium on a potential-energy-versus-position graph?

     回答

     At a local minimum. Small displacements produce forces that point back toward the minimum.

144. カード 144

     質問

     Which displacement belongs in the work done by a force on a rigid object?

     回答

     The displacement of that force's point of application. Using the center-of-mass displacement can be wrong when the object also rotates.

145. カード 145

     質問

     What happens to mechanical energy when kinetic friction acts inside the chosen system?

     回答

     Some mechanical energy becomes thermal energy. The broader system's total energy still balances.

146. カード 146

     質問

     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?

     回答

     Graph v² versus drop height h. Under those conditions, v² = 2gh, so the slope should be 2g.

147. カード 147

     質問

     If two students start and finish a stair climb at the same speeds, how could data compare their average mechanical output power against gravity?

     回答

     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.

148. カード 148

     質問

     How can force-sensor data measure work when force changes as its point of application moves?

     回答

     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.

149. カード 149

     質問

     Why is potential energy assigned to a system rather than one isolated object?

     回答

     It belongs to an interaction between system parts. Gravitational potential energy, for example, belongs to the object–Earth system.

150. カード 150

     質問

     How can work by a nonconservative force depend on path?

     回答

     Different routes can have different force histories or path lengths. Kinetic-friction work, for example, can change with distance traveled.

151. カード 151

     質問

     A 2 kg cart moves at 3 m/s. What is its translational kinetic energy?

     回答

     9 J. K = ½(2)(3²) = 9 J.

152. カード 152

     質問

     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?

     回答

     W_f = -f_k d. The negative sign follows from friction pointing opposite the block's displacement in this stated setup.

153. カード 153

     質問

     A 2 kg object rises 5 m where g = 10 m/s². What is ΔU_g?

     回答

     +100 J. ΔU_g = mgΔy = 2 × 10 × 5.

154. カード 154

     質問

     Why are energy bar charts useful?

     回答

     They make initial energy, final energy, and transfers explicit. A correct chart respects the chosen system and reference levels.

155. カード 155

     質問

     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?

     回答

     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.

156. カード 156

     質問

     A nonrotating 1 kg block starts from rest and receives 18 J of net work. What speed does it reach?

     回答

     6 m/s. For this pure-translation model, ΔK = 18 J = ½(1)v².

157. カード 157

     質問

     Why is gravitational potential energy lower when two attracting point masses—or nonoverlapping spherical bodies—are closer in the inverse-square model?

     回答

     Energy must be supplied to separate them. With zero chosen at infinite center-to-center separation, U_g = -GMm/r.

158. カード 158

     質問

     What does a steep potential-energy graph imply about force magnitude in one dimension?

     回答

     A large force magnitude. Force points toward decreasing potential energy and corresponds to the negative slope of U(x).

159. カード 159

     質問

     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?

     回答

     10 J. U_s = ½(80)(0.50²).

160. カード 160

     質問

     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?

     回答

     200 W. P = Fv_point = 50 × 4.

161. カード 161

     質問

     If potential energy decreases by 30 J and no energy crosses the system boundary, what happens to the other energy forms?

     回答

     They increase by a total of 30 J. Often kinetic energy rises, but thermal or other forms may share the increase.

162. カード 162

     質問

     Does an object's translational kinetic energy depend on the reference frame?

     回答

     Yes. Different inertial observers can measure different speeds and therefore different K = ½mv² for the same object.

163. カード 163

     質問

     Why can work depend on the system boundary?

     回答

     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.

164. カード 164

     質問

     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?

     回答

     12 J. The signed area is ½×4×6.

165. カード 165

     質問

     A motor transfers 50 J into a chosen system while another device transfers 12 J out. What is the net system-energy change?

     回答

     +38 J. Add the signed transfers across the boundary: 50 J - 12 J.

166. カード 166

     質問

     What is the clearest first step in an energy-conservation problem?

     回答

     Choose the system and the initial and final states. That choice determines which energies and transfers belong in the equation.

167. カード 167

     質問

     Why can energy methods solve some problems without finding time?

     回答

     Energy connects states through position, speed, and transfers. Time is absent unless power or a time-dependent process matters.

168. カード 168

     質問

     Why can a force's instantaneous mechanical power be zero while the force is nonzero?

     回答

     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.

169. カード 169

     質問

     What is the SI unit of kinetic energy?

     回答

     The joule, J. One joule equals 1 kg·m²/s².

170. カード 170

     質問

     How is work by a conservative force related to potential-energy change?

     回答

     W_conservative = -ΔU. When the conservative force does positive work, potential energy falls.

171. カード 171

     質問

     Where is unstable equilibrium on a potential-energy-versus-position graph?

     回答

     At a local maximum. A small displacement produces a force that pushes the system farther away.

172. カード 172

     質問

     For a particle moving in a circle at constant speed, does the inward net force change its translational kinetic energy?

     回答

     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.

173. カード 173

     質問

     Why should thermal energy not be written as a force?

     回答

     Thermal energy is an energy store, not an interaction force. Friction is the interaction that converts or transfers energy.

174. カード 174

     質問

     How could a ramp experiment test mechanical-energy conservation for a cart–Earth system when the cart is modeled as a particle?

     回答

     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.

175. カード 175

     質問

     According to the plotted power's definition and sign convention, what does signed area under a power-versus-time graph represent?

     回答

     Energy transferred or converted over the interval. Interpret positive and negative areas using the graph's stated sign convention and what its power represents.

176. カード 176

     質問

     What is linear momentum?

     回答

     p = mv. Momentum is a vector in the direction of velocity and uses SI units kg·m/s.

177. カード 177

     質問

     How is a multi-object system's total momentum found?

     回答

     Add every object's momentum as a vector. In one dimension, add signed values.

178. カード 178

     質問

     For a chosen object or system, what is external impulse?

     回答

     The change in its momentum: J_external = Δp. For constant net external force, J_external = F_net,external Δt.

179. カード 179

     質問

     What experimental uncertainty matters strongly when comparing collision kinetic energies?

     回答

     Velocity uncertainty. Because K depends on v², small speed errors can produce larger relative energy errors.

180. カード 180

     質問

     Why can two objects bounce apart yet still collide inelastically?

     回答

     Bouncing does not guarantee kinetic-energy conservation. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.

181. カード 181

     質問

     A 3 kg cart moves right at 4 m/s. What is its momentum if right is positive?

     回答

     +12 kg·m/s. p = mv = 3 × 4.

182. カード 182

     質問

     Why can momentum be negative while kinetic energy cannot?

     回答

     Momentum carries direction through velocity's sign. Kinetic energy depends on speed squared.

183. カード 183

     質問

     When is a system's total linear momentum conserved?

     回答

     When the net external impulse is zero or negligible during the interval. Internal impulses cancel in the system total.

184. カード 184

     質問

     Two equal masses collide elastically in one dimension; one is initially at rest. What commonly happens?

     回答

     They exchange velocities. The incoming mass stops and the other leaves with its speed under the ideal conditions.

185. カード 185

     質問

     Can total kinetic energy increase in an explosion?

     回答

     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.

186. カード 186

     質問

     How is total momentum related to center-of-mass velocity?

     回答

     p_total = Mv_cm. M is the system's total mass.

187. カード 187

     質問

     How does a nonzero external impulse affect system momentum?

     回答

     It changes total momentum by that impulse. J_external = Δp_system.

188. カード 188

     質問

     Two carts start at rest and push apart with negligible external horizontal impulse. How do their final momenta compare?

     回答

     They are equal in magnitude and opposite in direction. The system began with zero total momentum.

189. カード 189

     質問

     What are equivalent SI units for impulse?

     回答

     N·s and kg·m/s. Both represent a change in momentum.

190. カード 190

     質問

     What defines an elastic collision?

     回答

     Both total momentum and total kinetic energy are conserved for the chosen isolated system. Individual objects may exchange both quantities.

191. カード 191

     質問

     How can a force sensor and motion detector test the impulse–momentum theorem for one cart?

     回答

     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.

192. カード 192

     質問

     A person jumps right from a stationary boat. Neglecting external horizontal impulse, which way does the boat move?

     回答

     Left. The person and boat acquire opposite momenta so total momentum remains zero.

193. カード 193

     質問

     Why must momentum signs be kept through an impulse calculation?

     回答

     Impulse changes a vector quantity. Reversal can make Δp larger than either momentum magnitude alone.

194. カード 194

     質問

     What defines a perfectly inelastic collision?

     回答

     The objects stick together after impact. Momentum is conserved in an isolated system, but kinetic energy decreases as much as the constraints allow.

195. カード 195

     質問

     Why can momentum be conserved during a collision even when large forces act?

     回答

     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.

196. カード 196

     質問

     Two objects have equal speed. Which has the larger momentum magnitude?

     回答

     The object with larger mass. At equal speed, momentum is proportional to mass.

197. カード 197

     質問

     How is momentum conservation written for a two-dimensional isolated interaction?

     回答

     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.

198. カード 198

     質問

     For a chosen object or system, how is average net external force related to impulse?

     回答

     F_avg,external = Δp/Δt. For the same momentum change, a longer interaction time gives a smaller average force.

199. カード 199

     質問

     Which conservation law alone can determine the shared final velocity of a sticking collision?

     回答

     Linear momentum conservation, if external impulse is negligible. Kinetic energy is not conserved in the sticking process.

200. カード 200

     質問

     Two equal momentum vectors point along +x and +y. What direction does their total momentum point?

     回答

     At 45° between the positive axes. Equal perpendicular components produce that resultant direction.

     

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201. カード 201

     質問

     If external impulse during a collision is small but not zero, what should experimental data show?

     回答

     Final total momentum should be close to, but not exactly equal to, initial total momentum. The difference estimates external impulse.

202. カード 202

     質問

     A force–time pulse has the same area but twice the peak force and half the duration. How does its impulse change?

     回答

     It does not change. Impulse depends on total signed area, not peak force alone.

203. カード 203

     質問

     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?

     回答

     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.

204. カード 204

     質問

     How can a nearly frictionless cart track improve a momentum-conservation test?

     回答

     It reduces external horizontal impulse during the collision. That makes the two-cart system closer to isolated.

205. カード 205

     質問

     How does an object's momentum change if its speed doubles at constant mass?

     回答

     Its momentum magnitude doubles. Momentum depends linearly on speed.

206. カード 206

     質問

     For a chosen object or system, what does signed area under its net-external-force-versus-time graph represent?

     回答

     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.

207. カード 207

     質問

     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?

     回答

     The heavier piece moves at half the speed of the lighter piece. Their momentum magnitudes must match.

208. カード 208

     質問

     Why is sticking evidence of an inelastic collision?

     回答

     The objects share one final velocity, while some translational kinetic energy becomes internal or thermal energy through deformation. Translational kinetic energy is not conserved.

209. カード 209

     質問

     Can a moving two-object system have zero total momentum?

     回答

     Yes. Equal and opposite momenta cancel even though each object is moving.

210. カード 210

     質問

     A constant 6 N net external force acts on a chosen object for 0.5 s. What impulse does it deliver?

     回答

     3 N·s in the force direction. Multiply the net external force by the interaction time.

211. カード 211

     質問

     What does a momentum-versus-velocity graph's slope represent for one object?

     回答

     Its mass. The relationship p = mv is linear through the origin.

212. カード 212

     質問

     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?

     回答

     +2 m/s. Momentum conservation gives (2×3 + 1×0)/(2+1).

213. カード 213

     質問

     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?

     回答

     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.

214. カード 214

     質問

     A 2 kg ball changes velocity from +3 m/s to -1 m/s. What impulse acts on it?

     回答

     -8 N·s. Δp = m(v_f - v_i) = 2(-1 - 3).

215. カード 215

     質問

     What remains conserved in an isolated inelastic collision?

     回答

     Total momentum. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.

216. カード 216

     質問

     Why does choosing both colliding objects as the system simplify momentum analysis?

     回答

     Their contact forces become internal. Only external impulse can change the system total.

217. カード 217

     質問

     For a chosen object or system, what does the slope of its momentum-versus-time graph represent?

     回答

     Net external force. A steeper slope means a larger force in the slope's signed direction.

218. カード 218

     質問

     Why do airbags reduce injury force during a stop?

     回答

     They increase the stopping time for roughly the same momentum change. That lowers the average force.

219. カード 219

     質問

     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?

     回答

     2 m/s. Momentum 4 kg·m/s is shared by 2 kg.

220. カード 220

     質問

     For a defined collision system with zero or negligible net external impulse, how can before-and-after velocity measurements classify the collision?

     回答

     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.

221. カード 221

     質問

     What is angular displacement?

     回答

     The signed angle through which a rigid body rotates. In calculations, radians make the linear–angular relationships direct.

222. カード 222

     質問

     For a rigid body rotating about a chosen fixed axis, what does angular velocity measure?

     回答

     Signed angular displacement per time about that axis. Average angular velocity is ω_avg = Δθ/Δt under one sign convention.

223. カード 223

     質問

     For a rigid body rotating about a chosen fixed axis, what does angular acceleration measure?

     回答

     Change in signed angular velocity per time about that axis. Average angular acceleration is α_avg = Δω/Δt.

224. カード 224

     質問

     What does rotational inertia measure?

     回答

     Resistance to angular acceleration about a specified axis. It depends on mass and how that mass is distributed relative to the axis.

225. カード 225

     質問

     What is the lever arm in a torque calculation?

     回答

     The perpendicular distance from the axis to the force's line of action. It is not always the full distance to the contact point.

226. カード 226

     質問

     For a planar rigid object in an inertial frame, what two conditions give simultaneous translational and rotational equilibrium?

     回答

     ΣF_external = 0 and Στ_external = 0 about a fixed axis. Static equilibrium also requires the object to be at rest.

227. カード 227

     質問

     Two points lie on the same rotating rigid disk. Which rotational quantities are the same?

     回答

     They share angular displacement, angular velocity, and angular acceleration. Their linear speeds and accelerations can differ with radius.

228. カード 228

     質問

     How is rotational inertia found for a collection of point masses?

     回答

     I_total = Σmᵢrᵢ². Each rᵢ is that mass's perpendicular distance from the chosen axis.

229. カード 229

     質問

     What determines the magnitude of torque from one force about a chosen axis?

     回答

     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.

230. カード 230

     質問

     What is Newton's second law for a rigid system rotating about an axis fixed in an inertial frame?

     回答

     Στ_external = Iα when rotational inertia I about that axis is constant. Net external torque and angular acceleration use the same signed-axis convention.

231. カード 231

     質問

     For a point on a rigid body rotating about a fixed axis, how is signed arc displacement related to signed angular displacement in radians?

     回答

     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.

232. カード 232

     質問

     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?

     回答

     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.

233. カード 233

     質問

     At an instant when ω ≠ 0, what do the signs of angular velocity and angular acceleration show about rotational speed?

     回答

     Matching signs mean the rotation speeds up; opposite signs mean it slows down. The sign convention chooses which rotation direction is positive.

234. カード 234

     質問

     How are clockwise and counterclockwise torques combined?

     回答

     Choose one direction as positive and add signed torques. Net torque is the algebraic sum about the same axis.

235. カード 235

     質問

     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?

     回答

     Angular-acceleration magnitude doubles. Under those conditions, |α| is directly proportional to |Στ_external|.

236. カード 236

     質問

     Why must an axis be named when stating rotational inertia?

     回答

     The same object has different rotational inertia about different axes. Mass distribution relative to the chosen axis changes.

237. カード 237

     質問

     For one rigid body rotating about a fixed axis, what does the slope of its angular-position-versus-time graph represent?

     回答

     Signed angular velocity about that axis. A constant slope means constant angular velocity under the graph's sign convention.

238. カード 238

     質問

     Why is torque's unit N·m not called a joule?

     回答

     Torque and energy are different physical quantities despite matching unit dimensions. Torque describes rotational effectiveness of a force.

239. カード 239

     質問

     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?

     回答

     4 rad/s². |α| = |Στ_external|/I = 8/2.

240. カード 240

     質問

     Where can the weight of a rigid object be treated as acting in a uniform gravitational field?

     回答

     At the object's center of mass. That single force gives the same net gravitational force and torque.

241. カード 241

     質問

     For a point on a rigid body rotating about a fixed axis, how is tangential-speed magnitude related to angular velocity?

     回答

     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.

242. カード 242

     質問

     For constant angular acceleration about one fixed axis, what does ω = ω₀ + αt retrieve?

     回答

     Angular velocity after elapsed time t. Use signed angular quantities about that axis over an interval with constant α.

243. カード 243

     質問

     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?

     回答

     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.

244. カード 244

     質問

     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?

     回答

     Its constant rotational inertia I about that axis. The graph follows Στ_external = Iα.

245. カード 245

     質問

     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?

     回答

     The hoop. More of its mass lies far from the axis.

246. カード 246

     質問

     Why can a rigid object have zero net external force but nonzero net external torque?

     回答

     External forces can cancel as vectors while acting along different lines. The resulting couple can still change the object's rotation.

247. カード 247

     質問

     Which constant-angular-acceleration equation connects angular velocity and angular displacement about one fixed axis without time?

     回答

     ω² = ω₀² + 2αΔθ. Use signed quantities about that axis over an interval with constant α.

248. カード 248

     質問

     A 10 N perpendicular force acts 0.40 m from a pivot. What torque magnitude does it produce?

     回答

     4 N·m. τ = rF for a perpendicular force.

249. カード 249

     質問

     For a rigid body rotating about a fixed axis, how is the signed tangential-acceleration component related to angular acceleration?

     回答

     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.

250. カード 250

     質問

     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?

     回答

     Their rotational inertias about those axes can differ because their mass distributions differ. Mass alone doesn't set rotational response.

251. カード 251

     質問

     For one rigid body rotating about a fixed axis, what does signed area under its angular-velocity-versus-time graph represent?

     回答

     Signed angular displacement about that axis. Area below the time axis contributes negative angular displacement under the graph's sign convention.

252. カード 252

     質問

     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?

     回答

     The object's center-of-mass vertical line reaches the edge of its support region. Beyond that point, gravity produces an unbalanced tipping torque.

253. カード 253

     質問

     A point is twice as far from a rigid wheel's fixed axis as another point. How do their tangential speeds compare?

     回答

     The farther point moves twice as fast. v_t is proportional to radius for their common angular-speed magnitude |ω|.

254. カード 254

     質問

     Does moving the chosen pivot change an individual force's torque?

     回答

     Yes. Torque depends on the axis, though a correctly solved physical prediction stays consistent.

255. カード 255

     質問

     How does the parallel-axis theorem relate rotational inertia to a parallel axis a distance d from the center of mass?

     回答

     I = I_cm + Md². Shifting the axis away from the center of mass increases rotational inertia.

256. カード 256

     質問

     How could an experiment determine a rigid wheel's constant rotational inertia about an axis fixed in an inertial frame?

     回答

     Apply several known signed net external torques about that axis, measure signed angular acceleration, and graph torque versus α. The slope is I.

257. カード 257

     質問

     For a point at perpendicular distance r > 0 from a rigid body's fixed rotation axis, what is the radial-acceleration magnitude?

     回答

     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.

258. カード 258

     質問

     How could a meterstick experiment test torque balance?

     回答

     Hang known forces at measured lever arms and compare signed r_perp F values at equilibrium. Repeat with different pivot choices.

259. カード 259

     質問

     For uniform rotation at frequency f, what is the angular-speed magnitude?

     回答

     |ω| = 2πf. One revolution is 2π rad, and uniform rotation has the same angular-speed magnitude throughout the cycle.

260. カード 260

     質問

     Why is choosing the pivot at an unknown support force often useful?

     回答

     That force then has zero lever arm and drops out of the torque equation. The physical equilibrium does not depend on the calculation shortcut.

261. カード 261

     質問

     Among parallel axes through or near a rigid object, which gives the minimum rotational inertia?

     回答

     The parallel axis through the center of mass. Any offset adds the positive term Md².

262. カード 262

     質問

     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?

     回答

     It becomes one-third as large. For each stated system, α = Στ_external/I.

263. カード 263

     質問

     A rigid wheel of radius 0.50 m has angular-speed magnitude 6 rad/s about its fixed axis. What is the rim speed?

     回答

     3 m/s. v_t = r|ω| = 0.50 × 6.

264. カード 264

     質問

     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?

     回答

     3 m from the pivot. Balance torque magnitudes: 30×2 = 20×r.

265. カード 265

     質問

     For constant angular acceleration about one fixed axis, what does Δθ = ω₀t + ½αt² retrieve?

     回答

     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.

266. カード 266

     質問

     A 20 N force acts at 30° to a radius vector of magnitude 0.60 m from a chosen axis. What torque magnitude results?

     回答

     6 N·m. |τ| = rF sin θ = 0.60 × 20 × sin 30°.

267. カード 267

     質問

     How does moving mass farther from a rotation axis affect rotational inertia?

     回答

     It increases rotational inertia strongly. For a point mass, I = mr².

268. カード 268

     質問

     How can angular-acceleration data compare two rigid objects' constant rotational inertias about comparable axes fixed in an inertial frame?

     回答

     Apply the same measured net-external-torque magnitude about each axis and compare |α|. The object with smaller angular-acceleration magnitude has larger I.

269. カード 269

     質問

     Why must angular displacement be in radians for Δs = rΔθ?

     回答

     Radians define angle as arc length divided by radius. Degree measure would require a conversion factor.

270. カード 270

     質問

     When does a nonzero force produce zero torque about an axis?

     回答

     When its line of action passes through the axis. The lever arm is then zero.

271. カード 271

     質問

     What is angular momentum for a rigid object rotating about an axis fixed in an inertial frame?

     回答

     L = Iω about that axis. Use one signed-axis convention consistently for L and ω.

272. カード 272

     質問

     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?

     回答

     v_cm = R|ω|. Here R is the constant rolling radius; the contact point is instantaneously at rest relative to the surface.

273. カード 273

     質問

     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?

     回答

     W = τΔθ when torque and angular displacement use the same signed axis. The angle must be in radians.

274. カード 274

     質問

     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?

     回答

     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.

275. カード 275

     質問

     When is a chosen system's angular momentum about an axis fixed in an inertial frame conserved?

     回答

     When net external torque on the system about that axis is zero or negligible over the interval. Internal torques cannot change the system total.

276. カード 276

     質問

     What does kinetic friction do to mechanical energy while a wheel slips on a stationary surface?

     回答

     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.

277. カード 277

     質問

     What is the angular-momentum magnitude of a translating point object about a chosen fixed point in an inertial frame?

     回答

     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.

278. カード 278

     質問

     For a satellite of negligible mass relative to a fixed central body, how do speed and energy change along one gravity-only elliptical orbit?

     回答

     Speed and kinetic energy are greatest near the central body, while gravitational potential energy is greatest farther away. Total mechanical energy stays constant.

279. カード 279

     質問

     What is a rigid body's rotational kinetic energy about a fixed axis?

     回答

     K_rot = ½Iω². It depends on rotational inertia about that axis and angular speed.

280. カード 280

     質問

     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)?

     回答

     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)).

281. カード 281

     質問

     How could a rotating-platform experiment test angular-momentum conservation about the platform's axis, treated as fixed in the lab's inertial frame?

     回答

     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.

282. カード 282

     質問

     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?

     回答

     K = -U_g/2 and E = U_g/2 = -K. Since U_g = -GMm/r, this gives K = GMm/(2r) and E = -GMm/(2r).

283. カード 283

     質問

     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?

     回答

     P = τω for signed torque and angular velocity about the same axis. It is the rotational counterpart of P = F·v_point.

284. カード 284

     質問

     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?

     回答

     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.

285. カード 285

     質問

     Does angular-momentum conservation require rotational kinetic-energy conservation?

     回答

     No. Internal work can change rotational kinetic energy while angular momentum stays constant.

286. カード 286

     質問

     Why do astronauts feel weightless in orbit even though gravity acts on them?

     回答

     They and their spacecraft are in continuous free fall together. Apparent weight is small because support forces are small.

287. カード 287

     質問

     Two wheels spin at the same angular speed. Which has more rotational kinetic energy?

     回答

     The wheel with larger rotational inertia. At common ω, K_rot is proportional to I.

288. カード 288

     質問

     For a chosen system, what does the slope of its angular-momentum-versus-time graph about an axis fixed in an inertial frame represent?

     回答

     Net external torque on the system about that axis. A constant slope means constant signed net external torque there.

289. カード 289

     質問

     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?

     回答

     120 W. Using signed quantities about the shaft axis, P = τω = 12×10.

290. カード 290

     質問

     While a rigid wheel is slipping on a stationary surface, how are the magnitudes v_cm and R|ω| related?

     回答

     No no-slip equality applies. Their values evolve separately until friction may bring the contact point to rest relative to the surface.

291. カード 291

     質問

     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?

     回答

     v_escape = √(2GM/r). At that threshold, total mechanical energy is zero with the object reaching infinity at zero speed.

292. カード 292

     質問

     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?

     回答

     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.

293. カード 293

     質問

     For a chosen object or system, what is angular impulse about an axis fixed in an inertial frame?

     回答

     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.

294. カード 294

     質問

     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?

     回答

     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.

295. カード 295

     質問

     For a satellite of negligible mass relative to a fixed central body, how does angular momentum behave along one gravity-only elliptical orbit?

     回答

     It stays constant because gravity exerts zero torque about the central body. The satellite moves faster when closer and slower when farther away.

296. カード 296

     質問

     How does rotational kinetic energy change if angular speed doubles at fixed I?

     回答

     It becomes four times as large. Rotational kinetic energy depends on ω².

297. カード 297

     質問

     Why should external torque be evaluated about the same axis used for angular momentum?

     回答

     Both quantities depend on the chosen axis. Mixing axes breaks the conservation statement.

298. カード 298

     質問

     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?

     回答

     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.

299. カード 299

     質問

     Why can static friction act on a rigid object rolling without slipping on a stationary rigid surface without necessarily dissipating mechanical energy?

     回答

     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.

300. カード 300

     質問

     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?

     回答

     v = √(GM/r). Gravity supplies the inward net force.

301. カード 301

     質問

     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?

     回答

     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.

302. カード 302

     質問

     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?

     回答

     Net rotational work, equal to the system's change in rotational kinetic energy. Torque and angular position must use the same signed axis.

303. カード 303

     質問

     Why can't the rolling condition alone prove that friction points uphill or downhill?

     回答

     Friction direction depends on the tendency to slip and the applied forces or torques. Solve the dynamics instead of guessing from motion.

304. カード 304

     質問

     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?

     回答

     E = -GMm/(2r). A larger circular orbit has greater, less-negative energy even though its speed is lower.

305. カード 305

     質問

     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?

     回答

     Rotational inertia decreases while angular momentum stays constant. Therefore Iω remains constant by increasing ω.

306. カード 306

     質問

     What makes simple harmonic motion a special kind of periodic motion?

     回答

     Its restoring force or torque is proportional to displacement and points toward equilibrium. Periodic motion alone does not guarantee this relationship.

307. カード 307

     質問

     What does the amplitude of an SHM displacement graph represent?

     回答

     The maximum distance from equilibrium. It is nonnegative even though displacement alternates sign.

308. カード 308

     質問

     How are period and frequency related?

     回答

     T = 1/f. Period is seconds per cycle; frequency is cycles per second, measured in hertz.

309. カード 309

     質問

     What is the period of a mass m on an ideal spring of constant k when spring mass and damping are negligible?

     回答

     T = 2π√(m/k). The motion must stay in the spring's linear SHM range.

310. カード 310

     質問

     For one-dimensional SHM, what is the equilibrium position?

     回答

     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.

311. カード 311

     質問

     How far apart in phase are displacement and velocity in SHM?

     回答

     One-quarter cycle. Velocity reaches an extremum when displacement crosses zero.

312. カード 312

     質問

     When can a simple pendulum be modeled as SHM?

     回答

     For small angular displacements. Then the restoring torque is approximately proportional to angular displacement.

313. カード 313

     質問

     An oscillator completes 12 cycles in 6 s. What are its frequency and period?

     回答

     f = 2 Hz and T = 0.5 s. Frequency is cycles per time, and period is its reciprocal.

314. カード 314

     質問

     For a horizontal ideal spring oscillator, what is potential energy at displacement x from its relaxed equilibrium length when U_s = 0 there?

     回答

     U_s = ½kx². It has the same value at +x and -x.

315. カード 315

     質問

     At the equilibrium position of SHM, is the oscillator necessarily at rest?

     回答

     No. The restoring force or torque and acceleration along the SHM coordinate are zero there, but speed is usually greatest.

316. カード 316

     質問

     How does a spring oscillator's period change if k becomes four times as large?

     回答

     The period is halved. T is proportional to 1/√k.

317. カード 317

     質問

     How are acceleration and displacement related along the SHM coordinate?

     回答

     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.

318. カード 318

     質問

     For a horizontal ideal spring oscillator with amplitude A, what is total mechanical energy when U_s = 0 at the relaxed equilibrium length?

     回答

     E = ½kA². It stays constant when dissipative effects are negligible.

319. カード 319

     質問

     In a small-angle pendulum, where are speed and gravitational potential energy greatest?

     回答

     Speed is greatest at the bottom; gravitational potential energy is greatest at the turning points. Energy trades between those forms.

320. カード 320

     質問

     How can frequency be read from an oscillation-versus-time graph?

     回答

     Measure the time between repeating equivalent points to find T, then use f = 1/T. Adjacent peaks are one period apart.

321. カード 321

     質問

     Why does an ideal mass–spring oscillator exhibit SHM?

     回答

     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.

322. カード 322

     質問

     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?

     回答

     1 J. E = ½(50)(0.20²).

323. カード 323

     質問

     At maximum positive displacement in SHM, what are velocity and acceleration?

     回答

     Velocity is zero; acceleration has maximum magnitude toward equilibrium. With positive displacement, acceleration is negative.

324. カード 324

     質問

     How does a spring oscillator's period change if its mass becomes four times as large?

     回答

     The period doubles. T is proportional to √m.

325. カード 325

     質問

     Why isn't uniform circular motion itself one-dimensional SHM?

     回答

     The object travels around a circle, not back and forth along one line. Its projection onto a diameter does follow SHM.

326. カード 326

     質問

     For the same ideal oscillator, how does total SHM energy change if amplitude doubles while k or mω² stays fixed?

     回答

     It becomes four times as large. Under those fixed system parameters, total energy is proportional to A².

327. カード 327

     質問

     In one-dimensional SHM, what are speed and acceleration along the SHM coordinate at equilibrium?

     回答

     Speed is maximum, while acceleration along the SHM coordinate is zero. The restoring force or torque vanishes there.

328. カード 328

     質問

     Does changing amplitude change the period of an ideal spring oscillator or small-angle pendulum?

     回答

     No within the ideal SHM model. The period depends on system parameters, not amplitude.

329. カード 329

     質問

     How is maximum speed related to amplitude and angular frequency in SHM?

     回答

     v_max = ωA. Maximum speed occurs at equilibrium.

330. カード 330

     質問

     For a horizontal ideal spring oscillator, how can kinetic energy at displacement x from equilibrium be found for amplitude A?

     回答

     K = ½k(A² - x²). Subtract spring potential energy from the constant total.

331. カード 331

     質問

     How far apart in phase are displacement and acceleration in SHM?

     回答

     Half a cycle, or 180°. When displacement is nonzero, acceleration has the opposite sign; at equilibrium, both are zero.

332. カード 332

     質問

     What is the period of a small-angle simple pendulum of length L when damping is negligible?

     回答

     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.

333. カード 333

     質問

     If x(t) is at a positive maximum at t = 0, what qualitative pattern follows over one cycle?

     回答

     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.

334. カード 334

     質問

     At equilibrium, how are a horizontal ideal spring oscillator's energies divided?

     回答

     Kinetic energy is maximum and spring potential energy is minimum. With x measured from equilibrium, U_s = 0 at x = 0.

335. カード 335

     質問

     An SHM object is at negative displacement and moving toward equilibrium. What signs do velocity and acceleration have if positive is right?

     回答

     Both are positive. Motion and restoring acceleration point right toward equilibrium.

336. カード 336

     質問

     How does a pendulum's period change if its length becomes nine times as large?

     回答

     The period triples. T is proportional to √L.

337. カード 337

     質問

     If SHM starts at maximum positive displacement, what equation gives its position?

     回答

     x(t) = A cos(2πft). A is amplitude, f is frequency, and t is elapsed time.

338. カード 338

     質問

     What feature would rule out ideal SHM in a force-versus-displacement-from-equilibrium graph?

     回答

     A restoring-force relationship that is not a straight line through the origin over the motion's range. Ideal SHM needs F ∝ -x.

339. カード 339

     質問

     At a horizontal ideal spring oscillator's turning points, how are kinetic and spring potential energy divided?

     回答

     Kinetic energy is zero and spring potential energy is maximum. The object momentarily stops at |x| = A.

340. カード 340

     質問

     For the same ideal spring with negligible damping and spring mass, which graph can determine k from measured periods and attached masses?

     回答

     Graph T² versus m. For T = 2π√(m/k), the slope is 4π²/k.

341. カード 341

     質問

     What makes a substance a fluid?

     回答

     It deforms continuously under a shear force and takes the shape of its container. Liquids and gases are fluids.

342. カード 342

     質問

     What is mass density?

     回答

     Mass per volume: ρ = m/V. Its SI unit is kg/m³.

343. カード 343

     質問

     For pressure that is uniform over a surface patch, how is it related to normal force and area?

     回答

     P = F_perpendicular/A. Pressure is a scalar field even though the contact force has direction.

344. カード 344

     質問

     What is volume flow rate?

     回答

     Volume passing a cross-section per time: Q = ΔV/Δt. Its SI unit is m³/s.

345. カード 345

     質問

     What is the buoyant-force magnitude on an object immersed in a static fluid whose density is uniform over the displaced volume?

     回答

     The weight of the displaced fluid: F_B = ρ_fluid gV_displaced. Here ρ_fluid is the uniform density over that volume.

346. カード 346

     質問

     What conditions support the basic Bernoulli model used here?

     回答

     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.

347. カード 347

     質問

     Under the ideal model, how does average density predict whether a free object floats or sinks?

     回答

     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.

348. カード 348

     質問

     How are volume flow rate, cross-sectional area, and average fluid speed normal to that area related?

     回答

     Q = Av. This gives the volume crossing a completely filled pipe section per time.

349. カード 349

     質問

     How does a static fluid exert force on a surface?

     回答

     Many particle–surface interactions produce a net force perpendicular to the surface. A static fluid does not exert a tangential shear force.

350. カード 350

     質問

     How does pressure change with depth in a static uniform fluid?

     回答

     It increases by ΔP = ρgΔh. Greater depth means more fluid weight above each unit area.

351. カード 351

     質問

     What force balance holds for an object floating at rest when buoyancy and weight are its only vertical forces?

     回答

     F_B = mg. The object's weight equals the weight of the fluid it displaces.

352. カード 352

     質問

     What is the continuity equation for steady incompressible flow in one filled pipe?

     回答

     A₁v₁ = A₂v₂. The same volume flow rate passes each cross-section.

353. カード 353

     質問

     Why does a static fluid produce an upward buoyant force?

     回答

     Pressure is greater on the object's lower surfaces than on its upper surfaces. The vertical pressure forces do not cancel.

354. カード 354

     質問

     What is the absolute pressure at depth h below the open surface of a static, uniform liquid?

     回答

     P_abs = P_atm + ρgh. ρgh is the gauge pressure from the liquid column.

355. カード 355

     質問

     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?

     回答

     Downward. Weight exceeds buoyant force, so the initial net force and acceleration point downward.

356. カード 356

     質問

     Water's average speed normal to a 0.020 m² pipe cross-section is 3 m/s. What is the volume flow rate?

     回答

     0.060 m³/s. Q = Av = 0.020×3.

357. カード 357

     質問

     What does the slope of a mass-versus-volume graph represent for one uniform material?

     回答

     Density. Since m = ρV, the line's slope is ρ.

358. カード 358

     質問

     How do gauge pressure and absolute pressure differ?

     回答

     Gauge pressure is measured relative to atmospheric pressure; absolute pressure is measured relative to vacuum. P_abs = P_atm + P_gauge.

359. カード 359

     質問

     For a fully submerged rigid object in a static, incompressible, uniform fluid, does buoyant force increase with depth?

     回答

     No. Displaced volume, fluid density, and g stay constant, so F_B stays constant despite higher absolute pressure.

360. カード 360

     質問

     For steady incompressible flow in a filled pipe, what happens to speed if cross-sectional area halves?

     回答

     It doubles. Continuity keeps Av constant.

361. カード 361

     質問

     When does a fluid element's velocity change?

     回答

     Its velocity changes when a nonzero net force acts on it. Pressure forces and gravity can contribute to that net force.

362. カード 362

     質問

     For steady, incompressible, nonviscous flow along the same flow path, what does Bernoulli's equation express?

     回答

     Conservation of mechanical energy per unit volume. Along that flow path, P + ½ρv² + ρgy stays constant under the stated conditions.

363. カード 363

     質問

     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?

     回答

     V_sub/V_object = ρ_object/ρ_fluid. A less-dense object floats with a smaller fraction submerged.

364. カード 364

     質問

     For steady incompressible flow in a filled pipe, what happens to speed if pipe radius halves?

     回答

     It becomes four times as large. Area is proportional to radius squared.

365. カード 365

     質問

     What does Pascal's principle say for a confined incompressible fluid at rest?

     回答

     An applied pressure change is transmitted throughout the fluid. The same pressure change acts at every connected point.

366. カード 366

     質問

     In a uniform static fluid, what does the slope of gauge pressure versus depth represent?

     回答

     ρg. For known g, the slope can determine fluid density.

367. カード 367

     質問

     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?

     回答

     Upward. Buoyant force exceeds weight, so the initial net force and acceleration point upward.

368. カード 368

     質問

     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?

     回答

     8 m/s. Continuity gives v₂ = A₁v₁/A₂.

369. カード 369

     質問

     What physical quantity does each term in P + ½ρv² + ρgy share?

     回答

     Energy per unit volume, equivalent to pressure. Every term uses units of pascals.

370. カード 370

     質問

     In one static fluid of uniform density, what experimental graph could test F_B = ρ_fluid gV_displaced?

     回答

     Graph measured buoyant force versus displaced volume. A line with slope near ρ_fluid g supports the model.

371. カード 371

     質問

     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?

     回答

     0.75, or 75%. Use the density ratio for floating equilibrium.

372. カード 372

     質問

     A main pipe splits into two outlets during steady incompressible flow. What flow-rate relation holds?

     回答

     Incoming flow rate equals the sum of outgoing flow rates. Q_in = Q_out,1 + Q_out,2.

373. カード 373

     質問

     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?

     回答

     v = √(2gh). Both locations are open to atmospheric pressure, and the large surface makes the upper-fluid speed negligible.

374. カード 374

     質問

     Why does the same force create more pressure on a smaller area?

     回答

     Pressure is inversely proportional to area for fixed perpendicular force. Concentrating the force raises F/A.

375. カード 375

     質問

     A sample has mass 0.60 kg and volume 2.0×10⁻⁴ m³. What is its density?

     回答

     3.0×10³ kg/m³. Divide mass by volume.

376. カード 376

     質問

     What conservation law underlies the continuity equation for incompressible flow?

     回答

     Conservation of mass. Constant density turns equal mass flow into equal volume flow.

377. カード 377

     質問

     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?

     回答

     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.

378. カード 378

     質問

     What is the SI unit of pressure?

     回答

     The pascal, Pa. One pascal equals 1 N/m².

379. カード 379

     質問

     How do pressures compare at the same horizontal level in one connected static fluid?

     回答

     They are equal. Container shape does not change pressure at a fixed elevation.

380. カード 380

     質問

     What does specific gravity compare?

     回答

     A substance's density with water's density. It is a dimensionless ratio, commonly ρ_substance/ρ_water.

381. カード 381

     質問

     How could collecting outflow test a volume flow rate predicted from area and average normal speed?

     回答

     Measure collected volume over a timed interval and compare ΔV/Δt with Av. Repeat trials and include volume and timing uncertainty.

382. カード 382

     質問

     How does the particle model distinguish a fluid from a rigid solid?

     回答

     Fluid particles can rearrange and flow past one another. A rigid solid resists sustained shape change.

383. カード 383

     質問

     At equal height along the same flow path in steady, incompressible, nonviscous flow, how are pressure and speed related?

     回答

     The faster region has lower static pressure. Along that flow path at equal height, P + ½ρv² remains constant.

384. カード 384

     質問

     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?

     回答

     200 N. F_B = ρgV = 1000×10×0.020.

385. カード 385

     質問

     Why can a steel ship float even though steel is denser than water?

     回答

     Its hollow shape makes the ship's overall average density less than water. It displaces enough water for buoyant force to balance weight.

386. カード 386

     質問

     How does an ideal hydraulic lift with a confined incompressible fluid at rest multiply force?

     回答

     Equal pressure change gives F₁/A₁ = F₂/A₂. The larger-area piston produces the larger force.

387. カード 387

     質問

     For steady, incompressible, nonviscous efflux with negligible losses, what graph can test Torricelli's relation while fluid head h varies?

     回答

     Graph v² versus h. With both locations open to atmospheric pressure and upper-surface speed negligible, the model predicts slope 2g.

388. カード 388

     質問

     What does incompressible mean in the introductory ideal-fluid model?

     回答

     A fluid element's density stays effectively constant as it moves. Its volume does not appreciably shrink under pressure changes.

389. カード 389

     質問

     At two points along the same flow path in steady, incompressible, nonviscous flow, how are pressure and height related when speed is equal?

     回答

     Pressure is lower at the higher point. P + ρgy remains constant.

390. カード 390

     質問

     How can water displacement measure an irregular solid's volume?

     回答

     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.

391. カード 391

     質問

     Two equal-volume samples have densities ρ and 3ρ. How do their masses compare?

     回答

     The denser sample has three times the mass. From m = ρV, mass scales with density at fixed volume.

392. カード 392

     質問

     How can scale readings in air and water determine buoyant force?

     回答

     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.

393. カード 393

     質問

     Static water has ρ = 1000 kg/m³. Using g = 10 m/s², what gauge pressure is 3 m below its open surface?

     回答

     30,000 Pa. P_gauge = ρgh = 1000×10×3.

394. カード 394

     質問

     During steady incompressible outflow, why can a large tank's top-surface speed be neglected compared with outlet speed?

     回答

     The tank's surface area is much larger than the outlet area. Continuity then makes the top-surface speed much smaller.

395. カード 395

     質問

     For a chosen fluid element in a horizontal region, what can a pressure difference do?

     回答

     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.

396. カード 396

     質問

     How can buoyancy measurements in a static fluid of known uniform density determine an irregular object's volume?

     回答

     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.

397. カード 397

     質問

     A 200 N perpendicular force acts on area 0.040 m². What pressure does it create?

     回答

     5,000 Pa. P = F/A = 200/0.040.

398. カード 398

     質問

     Why doesn't a hydraulic lift multiply energy?

     回答

     The large-force piston moves a shorter distance. Ideally, input work equals output work.

399. カード 399

     質問

     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?

     回答

     10 m/s. Both locations are at atmospheric pressure, so v = √(2gh) = √100.

400. カード 400

     質問

     An object floats first in water and then in a denser liquid. How does its submerged fraction change?

     回答

     It decreases in the denser liquid. Less displaced volume is needed to provide the same buoyant force.

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

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