Momentum - AP Physics B

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Question

A baseball pitcher throws a baseball at horizontally in the positive direction to a batter, who hits the ball in the opposite direction at . What is the change in momentum of the baseball if the baseball has a mass of ?

Answer

In order to calculate the change in momentum, we must find the initial and final momentum of the baseball, and then find the difference.

Use the given velocities and mass to calculate the initial and final values.

The initial momentum is positive because the problem states that the ball was originally thrown in the positive direction. The final momentum is negative due to the change in direction.

Now we find the change in momentum:

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Question

A baseball pitcher throws a baseball at horizontally in the positive direction to a batter, who hits the ball in the opposite direction at . What is the change in momentum of the baseball if the baseball has a mass of ?

Answer

In order to calculate the change in momentum, we must find the initial and final momentum of the baseball, and then find the difference.

Use the given velocities and mass to calculate the initial and final values.

The initial momentum is positive because the problem states that the ball was originally thrown in the positive direction. The final momentum is negative due to the change in direction.

Now we find the change in momentum:

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Question

Ball A, traveling to the right, collides with ball B, traveling to the left. If ball A is 4kg and ball B is 6kg, what will be the final velocity and direction after a perfectly inelastic collision?

Answer

A perfectly inelastic collision is when the two bodies stick together at the end. At the beginning the two balls are traveling separately with individual momentum values. Using the momentum equation , we can see that ball A has a momentum of (4kg)(7m/s) to the right and ball B has a momentum of (6kg)(8m/s) to the left. The final momentum would be the mass of both balls times the final velocity, (4+6)(vf). We can solve for vf through conservation of momentum; the sum of the initial momentum values must equal the final momentum.

Note: ball B's velocity is negative because they are traveling in opposite directions.

The negative sign indicates the direction in which the two balls are traveling. Since the sign is negative and we indicated that traveling to the left is negative, the two balls must be traveling 2m/s to the left after the perfectly inelastic collision.

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Question

Ball A, traveling to the right, collides with ball B, traveling to the left. If ball A is 4kg and ball B is 6kg, what will be the final velocity and direction after a perfectly inelastic collision?

Answer

A perfectly inelastic collision is when the two bodies stick together at the end. At the beginning the two balls are traveling separately with individual momentum values. Using the momentum equation , we can see that ball A has a momentum of (4kg)(7m/s) to the right and ball B has a momentum of (6kg)(8m/s) to the left. The final momentum would be the mass of both balls times the final velocity, (4+6)(vf). We can solve for vf through conservation of momentum; the sum of the initial momentum values must equal the final momentum.

Note: ball B's velocity is negative because they are traveling in opposite directions.

The negative sign indicates the direction in which the two balls are traveling. Since the sign is negative and we indicated that traveling to the left is negative, the two balls must be traveling 2m/s to the left after the perfectly inelastic collision.

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Question

Two astronauts, Ann and Bob, conduct a collision experiment in a weightless, frictionless environment. Initially Ann moves to the right with a momentum of , and Bob is initially at rest. In the collision, the two astronauts push on each other so that Ann's final momentum is to the left. What is Bob's final momentum?

Answer

Apply conservation of momentum before and after the collision.

.

Taking left to be the negative direction, and noting that Bob's initial momentum is 0 since he is at rest, we can use the provided information to see that .

Solving for , we get . Since this answer is positive, Bob's momentum is in the positive direction (to the right).

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Question

Two astronauts, Ann and Bob, conduct a collision experiment in a weightless, frictionless environment. Initially Ann moves to the right with a momentum of , and Bob is initially at rest. In the collision, the two astronauts push on each other so that Ann's final momentum is to the left. What is Bob's final momentum?

Answer

Apply conservation of momentum before and after the collision.

.

Taking left to be the negative direction, and noting that Bob's initial momentum is 0 since he is at rest, we can use the provided information to see that .

Solving for , we get . Since this answer is positive, Bob's momentum is in the positive direction (to the right).

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