A golf club has a lightweight flexible shaft with a heavy block of wood or metal

Question

A golf club has a lightweight flexible shaft with a heavy block of wood or metal (called the head of the club) at the end. A golfer making a long shot off the tee uses a driver, a club whose 300g head is much more massive than the 46g ball it will hit. The golfer swings the driver so that the club head is moving at 37g just before it collides with the ball. The collision is so rapid that it can be treated as the collision of a moving 300g mass (the club head) with a stationary 46g mass (the ball); the shaft of the club and the golfer can be ignored. The collision takes 7.6 ms, and the ball leaves the tee with a speed of 64 m/s.

A) What is the change in momentum of the ball during the collision?

B) What is the speed of the club head immediately after the collision?

C) Is this a perfectly elastic collision?

D) If we define the kinetic energy of the club head before the collision as "what you paid" and the kinetic energy of the ball immediately after as "what you get," what is the efficiency of this energy transfer??

Explanation / Answer

let's say its velocity is -7.2m/s (I used a negative number to indicate downward motion). So it's momentum is 0.30kg * (-2.6m/s) = -2.16 kg m/s (using a negative number to indicate downward momentum). After the bounce, the ball's momentum is 0.30kg * 71 m/s = 21.3 kg m/s (now using positive numbers to indicate upward velocity/momentum) A) Change in ball's momentum is final momentum minus initial momentum: 21.3 - (-2.16) = 23.46 kg m/s B) Change in magnitude of the ball's momentum is: |21.3| - |-2.16| = 21.3 - 0.2.16 = 19.14 kg m/s C) The number in A makes more sense. When the ball bounced, first its downward momentum was reduced from 2.16 to zero, and then its upward momentum increased from zero to 21.3. Therefore, the total change was 23.46.

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