The mass of a regulation tennis ball is 60.0 g (although it can vary slightly),

Question

The mass of a regulation tennis ball is 60.0 g (although it can vary slightly), and tests have shown that the ball is in contact with the tennis racket for 35.0 ms . (This number can also vary, depending on the racket and swing.) We assume a 35.0 ms contact time in this problem. In the 2011 Davis Cup competition, Ivo Karlovic made one of the fastest recorded serves in history, which was clocked at 156 mi/h (70 m/s).

Part A

What impulse and what average force did Karlovic exert on the tennis ball in his record serve?

J= _ kg*m/s

Part B

What average force did Karlovic exert on the tennis ball in his record serve ?

F= _ N

Part C

If his opponent returned this serve with a speed of 55.0m/s, what impulse did his opponent exert on the ball, assuming purely horizontal motion?

J= _ kg*m/s

Part D

If his opponent returned this serve with a speed of 55.0m/s, what average force did his opponent exert on the ball, assuming purely horizontal motion?

F= _ N

Explanation / Answer

Solution:

A) mass of the tennis ball = m = 0.060 kg

Time of impact = t = 0.035 s

Velocity = 70 m/s

Impulse = Force * time = Change in momentum

Impulse = (0.060) (70) = 4.2 kg m/s (or Ns)

B ) Average Force = impulse / time = 4.2 / 0.035 = 120 N

C) If the player served at 70 m/s towards left, the ball's return velocity by the opponent = 55m/s in the opposite direction .

Impulse = m(vf-vi) = (0.06) ( 55 -(-70)) = 7.5 kg m/s

D) Average force exerted bythe opponent on the ball = F = 7.5/0.035 = 214 N

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