Momentum Exam Review | AP Physics 1

Two objects of the same mass travel in the same direction along a horizontal surface. Object X has a speed of 5 m/s and object Y has a speed of 2 m/s, as shown in the figure. After a period of time, object X collides with object Y. Consider the situation in which the objects collide but do not stick together. Which of the following predictions is true about the center of mass of the two-object system immediately after the collision?

• The center of mass does not move.

• The velocity of the center of mass does not change

• The velocity of the center of mass decreases in speed.

• The velocity of the center of mass increases in speed.

Answer explanation

The center of mass is moving prior to the collision. Since there are no external forces exerted on the system, the momentum of the system does not change. Since the total momentum of the system is the same as the momentum of the center of mass, the center of mass must continue moving in the same direction with the same velocity as it did prior to the collision.

Tags

NGSS.HS-PS2-2

Two objects of the same mass travel in the same direction along a horizontal surface. Object X has a speed of 5 m/s and object Y has a speed of 2 m/s, as shown in the figure. After a period of time, object X collides with object Y. Consider the situation in which object X has a speed of 2m/s and object Y has a speed of 5m/s after the collision takes place. After the collision, both objects travel in the same direction. Which of the following predictions must be true about how the momentum  p→ of the two-object system and the kinetic energy K of the two-object system change from before the collision to after the collision?

• p: Remains constant K: Remains constant

• p: Remains constant K: Decreases

• p: Decreases K: Remains constant

• p: Decreases K: Decreases

Answer explanation

To determine whether the momentum of the system is conserved, one must first determine the momentum of the two object system before the collision and after the collision. The momentum of the system before the collision is calculated as follows. Σp→0=pX0+pY0 Σp→0=MvX0+MvY0 Σp→0=5M+2MΣp→0=7M. The momentum of the system after the collision is calculated as follows. Σp→f=pXf+pYfΣp→f=MvXf+MvYfΣp→f=2M+5MΣp→f=7M. Therefore, the total momentum of the system is conserved. One must then determine how the kinetic energy of the two object system changes from before the collision to after the collision. The kinetic energy of the system before the collision is calculated as follows. ΣK0=KX0+KY0ΣK0=12MvX02+12MvY02ΣK0=12M(2)2+12M=(5)2ΣK0=2M+12.5M=14.5M. The kinetic energy of the system after the collision is calculated as follows. ΣKf=KXf+KYfΣKf=12MvXf2+12MvYf2ΣKf=12M(5)2+12M=M(2)2ΣKf=12.5M+2M=14.5M. Therefore, the total kinetic energy of the system is conserved.

Tags

NGSS.HS-PS2-2

NGSS.HS-PS3-1

A student performs an experiment in which a 4kg object travels across a horizontal surface with an initial speed velocity of 6m/s and a 2kg object travels across a horizontal surface with an initial speed velocity of −3m/s. The objects travel toward each other and collide. Data collected from the experiment were used to create the velocity versus time graph shown that contains information about both objects before and after the collision. The positive direction is considered to be to the right. Which of the following statements are true regarding the data from the experiment?

• Both objects always travel in the positive direction during the experiment.

• Kinetic energy is conserved during the experiment.

• The position of the center of mass of the system remains constant during the experiment

• The velocity of the center of mass of the two-object system remains constant during the experiment

Answer explanation

Correct. The total momentum of the system immediately before the collision is 18kg⋅m/s as shown by adding the momentum of the 2kg object to the momentum of the 4 kg object at all points before the collision. The total momentum of the system immediately after the collision is 18kg⋅m/s as shown by adding the momentum of the 2kg object to the momentum of the 4kg object at all points after the collision. The momentum of the system is also shown to remain constant during the collision. This means that the momentum of the system is conserved throughout the experiment. Therefore, if the mass of the two-object system remains constant, the velocity of the center of mass of the two-object system will also remain constant.

Tags

NGSS.HS-PS2-1

NGSS.HS-PS2-2

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• D

Answer explanation

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NGSS.HS-PS2-2

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Answer explanation

To find total impulse (increase of momentum), Take the area underneath the ENTIRE graph. Don't forget the portion at the bottom of the graph as well.

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NGSS.HS-PS2-1

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Answer explanation

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NGSS.HS-PS2-2

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Answer explanation

If the two cars "connect", they are involved in an inelastic collision. Both their speed and subsiquent kinetic energy collectively will be reduced.

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NGSS.HS-PS2-1

NGSS.HS-PS2-2

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Answer explanation

If the speed of the ball is the same both before and after the collision, its subsiquent height will be the same given the same gravitational acceleration before and after the collision.

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NGSS.HS-PS2-1

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Answer explanation

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NGSS.HS-PS2-2

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Answer explanation

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NGSS.HS-PS2-2