Rate of Change of Momentum (College Board AP® Physics 1: Algebra-Based)

A professional tennis player hits a tennis ball of mass 60 g which travels at 34 m/s just before it makes contact with the racket. The ball is in contact with the racket for 5 ms before recoiling in the opposite direction at 40 m/s.

What is the average force exerted by the racket on the ball? Take the ball's initial velocity to be the positive direction.

A      –888 N

B      –72 N

C      72 N

D      888 N

The correct answer is A

Answer:

Step 1: Analyze the scenario

• When the tennis ball comes into contact with the racket, the racket exerts a force on the ball over a time interval of 5 ms

• This force changes the ball's momentum by

  • decelerating it from 34 m/s to 0 m/s in the positive direction

  • accelerating it from 0 m/s to 40 m/s in the opposite (negative) direction

Step 2: List the known quantities

• Mass of the ball, = 60 g = 0.06 kg

• Time interval, = 5 ms = 0.005 s

• Initial velocity, = +34 m/s (positive direction)

• Final velocity, = –40 m/s (negative direction)

Step 3: Determine an expression for the average force

• Since force is equal to the rate of change of momentum:

Step 4: Calculate the average force

• The answer is therefore A

Be aware that multiple-choice options are designed to catch you out, so you need to be especially careful when vector quantities are involved! If an object changes direction, this must be reflected by the change in the sign of the velocity (and momentum).

Sometimes it can help to do a sense check, for example, in the worked example above, the ball's change in speed is (40 - 34) = 6 m/s, whereas the ball's change in velocity is (-40 - 34) = -74 m/s

• The large magnitude reflects the fact that the ball's speed reduced to zero in the positive direction before it increased in the negative direction

• The negative sign indicates the ball's final velocity is in the opposite direction to its initial velocity