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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 4: Linear MomentumConservation of Linear Momentum

Conservation of Linear Momentum (College Board AP® Physics 1: Algebra-Based): Exam Questions

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1
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Which of the following correctly describes a system in which conservation of momentum cannot be applied?

  • When no external forces act on the system.

  • When kinetic energy is lost or gained by the system.

  • When forces act within the system.

  • When an impulse is exerted on the system.

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2
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Two blocks, labeled X and Y, connected by a spring and placed on a frictionless horizontal surface. X is larger than Y to indicate its greater mass.

Two blocks, X and Y, are attached by a stretched spring and held at rest on a frictionless surface, as shown in the figure. Block X has twice the mass of block Y. When the blocks are released, the spring pulls them toward each other.

Which of the following quantities is the same for both blocks as they move toward each other?

  • Speed

  • Kinetic energy

  • Magnitude of momentum

  • Magnitude of acceleration

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3
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Two hockey pucks on a horizontal ice surface with the 0.2 kg puck moving at 4 m/s towards the stationary 0.3 kg puck.

Two ice hockey pucks of mass 0.2 kg and 0.3 kg respectively, collide on a frictionless ice surface, as shown in the figure. The 0.2 kg puck initially moves at 4 m/s and the 0.3 kg puck is initially at rest. After the collision, the 0.2 kg puck moves in the opposite direction at 1 m/s.

Which of the following is most nearly the final velocity of the 0.3 kg puck?

  • 1 space straight m divided by straight s

  • 2 space straight m divided by straight s

  • 3 space straight m divided by straight s

  • 4 space straight m divided by straight s

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4
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An object of mass 2 M is moving at speed v when it collides with a second object of mass M which is at rest. After the collision, the two objects move off together as a single object.

Which of the following correctly describes the type of interaction that occurred?

  • Inelastic

  • Perfectly inelastic

  • Elastic

  • Explosion

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5
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A cannon of mass 200 kg containing a cannonball of mass 10 kg is initially at rest. When the cannonball is fired, it leaves the cannon with a horizontal velocity of 100 m/s, and the cannon recoils.

Which of the following is most nearly the recoil speed of the cannon immediately after the cannonball is fired?

  • 5 space straight m divided by straight s

  • 10 space straight m divided by straight s

  • 20 space straight m divided by straight s

  • 50 space straight m divided by straight s

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1
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Diagram showing a bag being placed on a rectangular cart with wheels, with arrows indicating downward motion onto the cart and rightward movement of the cart.

A cart moves along a horizontal frictionless surface. A sandbag is then carefully dropped from a short height above the cart, as shown in the figure. The cart and sandbag continue to move horizontally together.

Which of the following correctly describes the change in speed of the cart immediately after the sandbag is dropped into it?

  • The speed of the cart increases because of the conservation of mechanical energy.

  • The speed of the cart decreases because of the conservation of momentum.

  • The speed of the cart decreases because of the conservation of mechanical energy.

  • The speed of the cart remains the same because the initial velocity of the sandbag is perpendicular to the direction of the cart's motion.

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2
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Diagram showing two carts on a track. The left cart, labeled "m," is moving right with velocity "v." The right cart, labeled "2m," is stationary.

A cart of mass m moving with a speed v along a track collides with a stationary cart of mass 2 m. After the collision, the carts are free to move along the track.

Which of the following describes the maximum kinetic energy that can be lost in the collision?

  • 0

  • 1 over 6 m v squared

  • 1 third m v squared

  • 1 half m v squared

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3
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A body of mass 3 M at rest explodes into two fragments of mass 2 M and M.

The fragment of mass M moves away with kinetic energy K subscript M and momentumspace p subscript M.

Which of the following expressions correctly represents the kinetic energy and momentum of the 2 M fragment?

Kinetic Energy of the 2M Fragment

Momentum of the 2M Fragment

A

1 half K subscript M

negative p subscript M

B

K subscript M

negative p subscript M

C

1 fourth K subscript M

negative 2 p subscript M

D

2 K subscript M

2 p subscript M

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    4
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    Two blocks labelled A and B on an inclined plane, with a compressed spring connecting them.

    Two blocks, A and B, are connected by a spring and placed on a frictionless slope, as shown in the figure. Block A is initially held at rest and the spring is slightly compressed. When block A is released, the blocks move down the slope and apart from each other as the spring stretches.

    How do the total momentum and the velocity of the center of mass of the two-block-spring system change after block A is released?

    Total Momentum

    Velocity of the Center of Mass

    A

    Increases

    Increases

    B

    Decreases

    Decreases

    C

    Remains Constant

    Increases

    D

    Remains Constant

    Remains Constant

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      5
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      A sequence of three diagrams: 1. At time t1, the 60 kg person jumps into the boat in which the 75 kg person is sitting. 2. The two people move towards and past each other in order to swap places. 3. At time t4, the two people have switched places.

      A person of mass 75 kg leaves the dock in their boat at a constant steady speed. The surface of the water is frictionless. At time t subscript 1, a person of mass 60 kg jumps horizontally into the boat, as shown in the figure. At a later time, the two people decide to swap places by walking past each other in opposite directions simultaneously. By time t subscript 4, they are seated in their new positions in the boat.

      Taking the right as the positive direction, which of the following graphs could represent the velocity of the center of mass of the two-person-boat system?

      • Graph showing velocity of center of mass (vCM) in m/s on the y-axis and time (t) in seconds on the x-axis. Graph shows constant positive velocity.
      • Graph showing velocity of center of mass (vCM) in m/s on the y-axis and time (t) in seconds on the x-axis. Graph shows constant positive velocity until midway between t1 and t2 where it falls instantaneously to zero, then gradually increases back to the original value at t4.
      • Graph showing velocity of center of mass (vCM) in m/s on the y-axis and time (t) in seconds on the x-axis. Graph shows constant positive velocity until midway between t1 and t2 where it falls instantaneously to zero, then gradually decreases to a negative value, and then instantaneously back to zero at t4.
      • Graph showing velocity of center of mass (vCM) in m/s on the y-axis and time (t) in seconds on the x-axis. Graph shows constant positive velocity until midway between t1 and t2 where it falls instantaneously to zero and stays at zero until t4.

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      1
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      Two circles labeled 'M' and '4M' are shown. The circle labeled '4M' has an arrow above it pointing left, indicating velocity 'v'.

      A small ball of mass M, initially at rest, collides elastically with a large ball of mass 4 M and velocity v. Throughout the interaction, the relative velocity of the balls remains constant.

      Which of the following expressions correctly represents the magnitude of the velocity of the small ball after the collision?

      • 3 over 5 v

      • 8 over 5 v

      • 2 v

      • 4 v

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      2
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      A diagram of a wheeled cart with a dotted line covering and an arrow indicating movement to the right on a flat surface.

      A cart filled with water moves along a horizontal frictionless surface at a constant speed. The cart develops a leak and continues to roll along the surface while water flows out at a constant rate, as shown in the figure.

      Which of the following correctly describes the change in speed of the cart after developing the leak?

      • The speed of the cart decreases because of the conservation of mechanical energy.

      • The speed of the cart increases because of the conservation of momentum.

      • The speed of the cart increases because of the conservation of mechanical energy.

      • The speed of the cart remains the same because of the conservation of momentum.

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      3
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      Diagram showing a ball of clay with mass 2m moving right at initial velocity v0, heading towards a block of mass m, which is attached to a spring with constant k.

      A clay ball of mass 2 m is moving horizontally with speed v subscript 0 just before colliding with a block of mass m, as shown in the figure. The block is attached to a massless spring with spring constant k which is initially at its equilibrium position. The clay sticks to the block, and the block compresses the spring.

      Which of the following expressions correctly represents the maximum compression of the spring?

      • v subscript 0 square root of fraction numerator 2 m over denominator k end fraction end root

      • v subscript 0 square root of fraction numerator 3 m over denominator k end fraction end root

      • 3 v subscript 0 square root of fraction numerator m over denominator 2 k end fraction end root

      • 2 v subscript 0 square root of fraction numerator m over denominator 3 k end fraction end root

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      4
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      Diagram showing a ballistic pendulum where a pellet hits a block suspended by a string, swinging to a final position at a height h above the initial position where the string makes a 35-degree angle.

      A 2.0 kg block initially hangs at rest at the end of a 1.0 m string of negligible mass, as shown in the figure. A pellet with a mass of 5.0 g is fired horizontally at the block and becomes embedded in it. After the collision, the block and the pellet rise together to a final height h and the string makes at an angle of 35° with the vertical.

      Which of the following expressions correctly relates the initial kinetic energy K subscript 0 of the bullet to the kinetic energy K of the block and bullet immediately after the collision?

      • K subscript 0 space equals space K

      • K subscript 0 space equals space 20 K

      • K subscript 0 space equals space 400 K

      • K subscript 0 space equals space 160 space 000 K

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      5
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      A collision between balls X and Y: before the collision, X moves at 10 m/s towards stationary Y. After the collision, X moves at 6 m/s at a 55° angle upward.

      Two identical balls, X and Y, are placed on a frictionless horizontal surface. Ball X initially moves at 10 m/s towards stationary ball Y, as shown in the figure. After the collision, ball X moves at 6 m/s along a path at 55° to its original direction.

      Which of the following diagrams could represent the motion of ball Y after the collision?

      • After the collision, Y moves directly to the right at 8 m/s.
      • After the collision, Y moves at 8 m/s at a 55° angle downward.
      • After the collision, Y moves at 8 m/s at a 35° angle downward.
      • After the collision, Y moves at 4 m/s at a 35° angle downward.

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