# In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball?

## The catcher does negative work, however, what I don't understand is I thought work could only be done by a force as long as it results in a displacement? The catcher does not cause a displacement?

Apr 7, 2018

The catcher must exert an amount of energy that is equal to or greater than the kinetic energy of the ball while it is in motion.

#### Explanation:

The catcher must exert an amount of energy on the ball equal to or greater than the kinetic energy of the ball while it is in motion. The kinetic energy, $K E$, of the ball while it is in motion is

$K E = \frac{m {v}^{2}}{2}$

where

$m =$ the mass of the ball, and

$v =$ the velocity of the ball, here 90 miles/hour $\approx 40.23 \frac{m}{s}$

If the ball had a mass of 0.2kg, the catcher would need to supply at least approximately

$\frac{\left(0.2\right) {\left(40.23\right)}^{2}}{2} = 161.8$ Joules

to stop it.

BUT in reality, because the process of stopping the ball is irreversible, the catcher probably exerts a little more energy than this. For instance, there is friction when the ball lands in the glove and this will raise the temperature of some of the elements in the system. This thermal energy must also come from the catcher.