Problem VI The \"sweet spot\" of a tennis racket is the spot where the player fe

Question

Problem VI The "sweet spot" of a tennis racket is the spot where the player feels the least vibra- tion through his wrist and forearm when he hits the In this problem you will ignore many factors but still make an ac- curate computation of the location of the sweet spot. Assume that there are no ex- ternal forces on the racket shown in the sketch. The sweet spot of the racket is in- dicated by a cross. When the ball hits theFBekwand stationary racket on the sweet spot, the velocity of the center of the grip right after the collision is zero (so that if a player were holding it, he wouldn't feel the grip jar forward or backward during the collision). The mass of the tennis racket is m 0.5 kg, and its moment of inertia about axis A through the center of mass is =(0.5 kg)(0.15 m)2 1 CM -0.20 m 1. If the ball hits the racket beneath the sweet spot, will the initial velocity of the grip be forward or backward? Use Helping Question 13 if you don't know. Key 17 2. If the ball hits the racket above the sweet spot, will the initial velocity of the grip be forward or backward? Key 1 3. What is the distance d between the center of mass and the sweet spot? Stuck? Use Helping Questions 14 and 15. Key 6

Explanation / Answer

Ans for Q3 : The distance between the sweet spot and the centre of mass(CM) is 0.05 m.

It may be found from the parallel axes theorem for moment of inertia.

Before answering Q1 and Q2,

The sweet spot is not the point from where the ball rebounds with maximum velocity. Actually the racket has three types of independent motion rotation, vibration and translation. force at hand is felt due to all these. the sweet spot is a vibrational node.

Ans for Q1 and Q2: If the ball hits the racket beneath or above the sweet spot, for both the cases the grip of the racket will move in forward direction for rotation of the racket.

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