AP Physics 1 Exam Question: Impulse and Momentum

A 0.2 kg ball is initially at rest on a smooth horizontal surface. A force of 10 N is applied to the ball for 2 seconds. Determine the resulting change in momentum of the ball. Provide your answer in kg·m/s.

Answer:

To determine the change in momentum of the ball, we first need to calculate the impulse applied to it. Impulse is defined as the product of force and time:

Impulse = Force * Time

Given that the force applied to the ball is 10 N and the time for which the force is applied is 2 seconds, we can substitute these values into the equation:

Impulse = 10 N * 2 s

Impulse = 20 N·s

Now, according to the impulse-momentum principle, impulse is equal to the change in momentum:

Impulse = Change in Momentum

So, the change in momentum of the ball is equal to 20 N·s. Since momentum is defined as the product of mass and velocity, we can express this change in momentum in terms of both mass and velocity.

Change in Momentum = Mass * Change in Velocity

Since the ball is initially at rest, its initial velocity is zero. Therefore, the change in velocity is equal to the final velocity.

Change in Momentum = Mass * Final Velocity

Now, we need to determine the final velocity of the ball. We can use the relationship between force, impulse, and mass to calculate the final velocity. Force is defined as the rate of change of momentum:

Force = Change in Momentum / Time

Rearranging the equation, we get:

Change in Momentum = Force * Time

Now, we can substitute the given values into this equation:

20 N·s = (0.2 kg) * Final Velocity

Dividing both sides of the equation by 0.2 kg, we obtain:

Final Velocity = 20 N·s / 0.2 kg

Final Velocity = 100 m/s

Therefore, the final velocity of the ball is equal to 100 m/s. Finally, we can substitute this value back into the equation for change in momentum to obtain the result:

Change in Momentum = (0.2 kg) * (100 m/s)

Change in Momentum = 20 kg·m/s

Hence, the resulting change in momentum of the ball is 20 kg·m/s.