Question

At a major league baseball game, a pitcher delivers a 45 m/s (100.7 mph) fastball to the first player at bat, who bunts (meets the pitch with a loosely held stationary bat) so that the ball leaves the bat at only 5 m/s (11.2 mph) directly back towards the pitcher. The second player at bat also receives a 45 m/s fastball from the pitcher, but he swings his bat hard and sends the ball in a fast line drive directly back towards the pitcher at 50 m/s (111.8 mph). The mass of a standard baseball is 0.145 kg.

Calculate the impulse delivered to the baseball by the baseball bat for the first player (who bunts the ball). Assume the initial pitch is in the positive x-direction, and the ball moves in the negative x-direction after it strikes the bat.
Calculate the impulse delivered to the baseball by the baseball bat for the second player (who hits the fast line drive). Assume the initial pitch is in the positive x-direction, and the ball moves in the negative x-direction after it strikes the bat.
Calculate the magnitude of the work done by the baseball bat on the baseball for the first player (who bunts the ball). Report your answer as a positive number for positive work done on the ball or a negative number for negative work done on the ball.
Calculate the work done by the baseball bat on the baseball for the second player (who hits the fast line drive). Report your answer as a positive number for positive work done on the ball or a negative number for negative work done on the ball.

Answer 1

The impulse delivered to the baseball by the baseball bat for the first player who bunts the ball is -0.725 kg m/s. The impulse delivered to the baseball by the baseball bat for the second player who hits a line drive is 7.25 kg m/s. The magnitude of the work done by the baseball bat on the baseball for the first player who bunts the ball is 32.625 J. The work done by the baseball bat on the baseball for the second player who hits a line drive is -326.25 J.

Step-by-step explanation:

Impulse is the change in momentum of an object, and it is equal to the force applied to the object multiplied by the time over which the force is applied. For the first player who bunts, the initial momentum of the ball is 0, since it is stationary, and the final momentum is mass times final velocity, which is (0.145 kg)(-5 m/s). Therefore, the change in momentum is (0.145 kg)(-5 m/s) - 0 = -0.725 kg m/s. Since impulse is equal to change in momentum, the impulse delivered to the ball is also -0.725 kg m/s.

For the second player who hits a line drive, the initial momentum is still 0, and the final momentum is (0.145 kg)(50 m/s). So the change in momentum is (0.145 kg)(50 m/s) - 0 = 7.25 kg m/s. Therefore, the impulse delivered to the ball by the bat is 7.25 kg m/s.

The work done by a force on an object is equal to the force multiplied by the displacement of the object in the direction of the force. Since the first player bunts the ball back in the opposite direction, the displacement is negative 45 m. So the work done by the bat on the ball is (-45 m)(-0.725 kg) = 32.625 J.

Similarly, for the second player who hits a line drive, the displacement is still negative 45 m, so the work done by the bat on the ball is (-45 m)(7.25 kg) = -326.25 J.