AP Physics 1 : Linear Motion and Momentum

Study concepts, example questions & explanations for AP Physics 1

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Example Questions

Example Question #56 : Impulse And Momentum

A spaceship of mass  is motionless in space. The rocket is turned on and provides a constant force of . Assume the loss of mass due to spent fuel is negligible.

Determine the acceleration of the ship.

Possible Answers:

None of these

Correct answer:

Explanation:

Plugging in values

Example Question #57 : Impulse And Momentum

A spaceship of mass  is motionless in space. The rocket is turned on and provides a constant force of . Assume the loss of mass due to spent fuel is negligible.

Determine the momentum of the ship after .

Possible Answers:

None of these

Correct answer:

Explanation:

Plugging in values

Using

Using

Example Question #58 : Impulse And Momentum

Tom drops a ball of mass  from rest from a height . The ball bounces back to a height of . Find the magnitude of the impulse the ground imparted on the ball.

Possible Answers:

Correct answer:

Explanation:

Impulse is just the change in momentum. To find the velocity when the ball hits the ground, we need to use kinematics. We know the height the ball is dropped, the acceleration, and the initial velocity, so we can use the equation . The initial velocity is , and , so the equation becomes 

When the ball bounces back up it reaches a height of . In order to find the velocity immediately after it hits the ground, we can use the same equation with . This will lead it a velocity of 

Assuming up is positive, the magnitude of the impulse is just 

Example Question #52 : Impulse And Momentum

Two identical rockets are placed on the back of cars. Car  has a mass twice that of car . The rockets are identically fired for , then shut off.

How will the momentum of each car compare?

Possible Answers:

Impossible to determine

None of these

The heavier car has more momentum

They are the same

The lighter car has more momentum

Correct answer:

They are the same

Explanation:

Using 

Where  represents the impulse, which is the change in momentum.

It can be seen that since both cars have the same force applied for equal amount of time, they have identical final momentums.

Example Question #60 : Impulse And Momentum

An object's momentum as a function of time is the following:

, where  is some constant.  

What is the force of the object (as a function of time) that causes the motion?

Possible Answers:

Correct answer:

Explanation:

Therefore, we simply need to differentiate our momentum equation with respect to time to determine the force.  

Example Question #61 : Impulse And Momentum

An object travels for  with a force of . For the next , the object travels with a constant force of . What is the change in the momentum for the object in the first ?

Possible Answers:

Correct answer:

Explanation:

Therefore, to find the change in the momentum, we need to sum the force in the various time intervals. Remember, we are only interested in the first , not the entire time stated in the problem.

Example Question #62 : Impulse And Momentum

 truck is driving at  relative to the ground. A  rocket is launched from the roof backwards at  relative to the ground. Determine the final velocity of the truck. 

Possible Answers:

None of these

Correct answer:

Explanation:

Using conservation of momentum.

The initial momentum is the combined mass of the truck and the rocket moving together

The final momentum is made up of the momentum of the truck and the rocket, which are now moving in opposite directions

Combining equations

Plugging in values:

Solving for 

 

Example Question #63 : Impulse And Momentum

 man is running at . From that run, he jumps on a skateboard of mass of . Assuming no energy lost to friction, determine the final velocity of the man on the board.

Possible Answers:

None of these

Correct answer:

Explanation:

Using conservation of momentum:

The man and the skateboard are stuck together, and thus become one mass:

Plugging in values:

Solving for 

 

Example Question #64 : Impulse And Momentum

Two wagons are held together with a rope. Lodged between them, is a very powerful spring. The rope is suddenly cut, allowing the spring to launch the wagons. If the first wagon has a mass of , and obtains a maximum velocity of , determine the momentum of the second cart. The second cart has a mass of .

Possible Answers:

 in the opposite direction of the first cart

 in the same direction of the first cart

 in the same direction of the first cart

None of these

 in the opposite direction of the first cart

Correct answer:

 in the opposite direction of the first cart

Explanation:

Using conservation of momentum.

Since nothing is moving, the initial momentum is zero

The final momentum is made up of the momentum of the two carts

Combining equations

Plugging in values:

Solving for 

The negative sign symbolizes that it will move in the opposite direction of the first cart.

 

Example Question #65 : Impulse And Momentum

Two wagons are held together with a rope. Lodged between them, is a very powerful spring. The rope is suddenly cut, allowing the spring to launch the wagons. If the first wagon has a mass of , and obtains a maximum velocity of , determine the momentum of the second cart. The second cart has a mass of .

Possible Answers:

 in the same direction

 in the same direction

 in the opposite direction

 in the opposite direction

 in the opposite direction

Correct answer:

 in the opposite direction

Explanation:

Using conservation of momentum.

Since nothing is moving, the initial momentum is zero

The final momentum is made up of the momentum of the two carts

Combining equations

Plugging in values:

Solving for 

The negative sign symbolizes that it will move in the opposite direction of the first cart.

 

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