A baseball $(m = 145 \textrm{ g})$ traveling 32 m/s moves a fielder’s glove backward 25 cm when the ball is caught. What was the average force exerted by the ball on the glove?

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Since we know a whole bunch of data about the ball, we are gonna figure out the net work done on the ball and figure out the force on the ball due to the glove. And then since the force on the ball due to the glove is a Newton's third-law counterpart to the force on the glove due to the ball, they will have equal size forces but just in opposite directions. So the change in kinetic energy of the ball is the net force on it times its displacement. But there's only one force on the ball that we care about; there's also gravity down, I suppose, but that doesn't matter here because we are just considering the horizontal direction and it's moving straight horizontal, we assume. So, the force on the ball due to the glove, is the net force and that's what we say right here. Now, the change in kinetic energy is one-half m v f squared but it comes to a rest so, the final kinetic energy is 0, and so we have the net force times the displacement of the ball equals the negative one-half mass times initial velocity squared. So, the force on the ball due to the glove then is negative m v i squared over 2d, because you can divide both sides by d here and that gives us negative 0.145 times 32 meters per second squared and divide by 2, divide by 0.25 meters— displacement of the ball and glove as it comes to a stop— and that is negative 3.0 times 10 to the 2 joules. So since the force on the glove due to the ball is the negative of the force on the ball due to the glove, we have the answer to our question, the force on the glove is 3.0 times 10 to the 2 newtons, positive, because the glove is going to the left and the force on the glove is also to the left and so they are in the same direction. So the work done by that force is positive.