Question

A baseball has a mass of 0.145 kg. In batting practice, a batter hits a ball sitting at rest on top of a

post. The ball leaves the post with a horizontal speed of 30 m s−1.
(a) If there is a net nonzero force on a moving object, can the total work done on the object be zero?
Explain, using an example. (1)
(b) How much work did the force applied by the bat do on the ball? (2)
(c) During a game, the same batter swings at a ball thrown by the bowler and hits it so that the
ball moves away from him horizontally. Just before the ball is hit, it is traveling at a speed of
20 m s−1, and just after it is hit, it travels in the opposite direction at a speed of 30 m s−1. Find
the impulse applied to the ball. (3)
(d) What is the total work done on the baseball by the force exerted by the bat? How does this
result compare to the one from (b)? Find the average force the ball was hit with if the bat only
was in contact for 2 ms

Answer 1

Part (a):

If there is a net nonzero force on a moving object, the total work done on the object cannot be zero. This is because work is the product of force and displacement, and if there is a nonzero force acting on an object over a nonzero distance, work will be done on the object.

For example, if you push a box across the floor, a force is applied, and the box moves a certain distance due to that force. Work is done in this case, as the force causes a displacement.

Part (b):

To calculate the work done by the force applied by the bat on the ball, we can use the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy:

Work = Change in Kinetic Energy

The change in kinetic energy is given by:

Change in Kinetic Energy = 0.5 × Mass × (Final Velocity^2 - Initial Velocity^2)

Substitute the given values:

Change in Kinetic Energy = 0.5 × 0.145 kg × (30 m/s)^2

Calculate the value of the change in kinetic energy.

Part (c):

To calculate the impulse applied to the ball, we can use the impulse-momentum principle, which states that the impulse applied to an object is equal to its change in momentum:

Impulse = Change in Momentum

Change in Momentum = Mass × Final Velocity - Mass × Initial Velocity

Substitute the given values:

Change in Momentum = 0.145 kg × 30 m/s - 0.145 kg × 0 m/s

Calculate the value of the change in momentum.

Part (d):

We are asked to find the total work done on the baseball by the force exerted by the bat and also the average force the ball was hit with during the 2 ms of contact.

First, calculate the total work done using the formula from Part (b):

Total Work = Change in Kinetic Energy

Then, calculate the average force using the formula:

Average Force = Impulse / Time

Given the time of contact (2 ms), convert it to seconds (0.002 seconds), and then substitute the values:

Average Force = Change in Momentum / Time

Calculate the value of the average force.

Step-by-step explanation: