A baseball of mass 250g, pitched with a speed of 40m/s, is caught by a catcher, whose glove moves backward 0.25m while stopping the ball.

a)what is the kenetic energy of the ball?
b)how much work did the catcher's glove do on the ball?
c) what was the average stopping force on the ball?

KE=1/2 m v^2

work=change in KE
force*distance=work

To answer these questions, we need to apply the principles of kinetic energy, work, and average force. Let's go step by step:

a) To find the kinetic energy of the ball, we can use the formula:

Kinetic Energy = 1/2 * mass * velocity^2

Given that the mass of the baseball (m) is 250g (convert to kg by dividing by 1000: 0.25 kg) and the velocity (v) is 40 m/s, we can substitute these values into the formula:

Kinetic Energy = 1/2 * 0.25 kg * (40 m/s)^2
= 1/2 * 0.25 kg * 1600 m^2/s^2
= 200 J (joules)

Therefore, the kinetic energy of the ball is 200 joules.

b) To determine the work done on the ball by the catcher's glove, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy:

Work = Change in Kinetic Energy

Since the ball comes to a stop after being caught by the catcher's glove, its final kinetic energy is zero. Therefore, the work done can be calculated using the initial kinetic energy:

Work = Kinetic Energy(initial) - Kinetic Energy(final)
= 200 J - 0 J
= 200 J

Hence, the catcher's glove does 200 joules of work on the ball.

c) To find the average stopping force on the ball, we can use the work-energy theorem again. The work done is equal to the force applied multiplied by the distance over which the force is applied:

Work = Force * Distance

Rearranging the formula, we can solve for force:

Force = Work / Distance

Given that the work done is 200 J and the distance over which the glove moves is 0.25 m, we can substitute these values into the formula:

Force = 200 J / 0.25 m
= 800 N (newtons)

Therefore, the average stopping force on the ball is 800 newtons.