# AP Physics 1 : Impulse and Momentum

## Example Questions

### Example Question #51 : Impulse And Momentum

An arrow of mass  is shot directly upward with an initial velocity of . What is the momentum of the arrow after  and in what direction? Neglect air resistance.

Explanation:

Since the arrow is shot directly upward, we can easily calculate the velocity of the arrow after 8 seconds:

Plugging in our values, we get:

Which is also:

Then using the expression for momentum, we get:

### Example Question #51 : Impulse And Momentum

Deep in space Object has mass and is initially traveling with velocity .  At , it collides with Object , which has mass and is initially motionless. The two objects stick together.

How should the final momentum relate to the initial momentum?

The final momentum will be greater because the objects stuck together

There is not enough information to determine the final momentum

They will be the same

The final momentum will be less because the objects stuck together

They will be the same

Explanation:

Momentum is always conserved in a closed system. Thus, since this system has no external forces acting on it (such as gravity, friction, electromagnetism, etc.) then momentum will be the same at the end as in the beginning.

### Example Question #233 : Linear Motion And Momentum

Deep in space, mass  is traveling at , it then collides with mass . After the collision, mass  is motionless. Mass  then collides with and sticks to mass . Determine the final velocity of the mass  mass  combination.

All three of the masses are identical.

None of these

Explanation:

The initial collision in completely elastic, all of the momentum and energy is transferred to the second mass.

The second collision is completely inelastic, all of the momentum is retained by the two objects that stick together.

Since all three of the masses are identical:

Combining equations

### Example Question #511 : Ap Physics 1

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

Determine the velocity of the ship after

Explanation:

Plugging in values

Using

### Example Question #52 : Impulse And Momentum

Two football players are pushing on each other during a play. The offensive player is pushing the defensive player backwards. What can be said about the forces in this situation?

None of these

The players are exerting unequal forces on each other, the offensive player is exerting more force on the defensive player.

The players are exerting unequal forces on each other because the offensive player is exerting more force on the ground that the defensive player.

The players are exerting equal forces on each other, however, the offensive player is exerting more force on the ground that the defensive player.

It is impossible to determine anything without knowing the mass of each player.

The players are exerting equal forces on each other, however, the offensive player is exerting more force on the ground that the defensive player.

Explanation:

Based on Newtons laws, the players are exerting equal forces on each other. The reason the offensive player is "winning" is that he is able to push harder against the ground than the defensive player.

### Example Question #51 : 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.

None of these

Explanation:

Plugging in values

### Example Question #51 : 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 .

None of these

Explanation:

Plugging in values

Using

Using

### Example Question #52 : 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.

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 #51 : 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?

None of these

Impossible to determine

The heavier car has more momentum

They are the same

The lighter car has more momentum

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 #52 : 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?