The fastest server in women\'s tennis is Venus Williams, who recorded a serve of
ID: 1543582 • Letter: T
Question
The fastest server in women's tennis is Venus Williams, who recorded a serve of 209 km/h at the French open in 2007. Suppose that the mass of her racket was 330 g in the mass of the ball was 58 g. A) If her racket was moving at 200 km/h when it hit the ball, approximately what was the rackets velocity after hitting the ball? B) How much was the impulse on the ball and on the racket? C) If her racket pushed on the ball for a distance of 101 mm, what was the time for contact between the ball and the racket? How much was the force on the ball? On the racket? The fastest server in women's tennis is Venus Williams, who recorded a serve of 209 km/h at the French open in 2007. Suppose that the mass of her racket was 330 g in the mass of the ball was 58 g. A) If her racket was moving at 200 km/h when it hit the ball, approximately what was the rackets velocity after hitting the ball? B) How much was the impulse on the ball and on the racket? C) If her racket pushed on the ball for a distance of 101 mm, what was the time for contact between the ball and the racket? How much was the force on the ball? On the racket?Explanation / Answer
A)
Mass of racket = m1= 0.330kg
Mass of ball = m2 = 0.058kg
Initial velocity of racket = v1i=200km/h = (200000m/3600s) = 55.56m/s
Initial velocity of ball = v2i = 0m/s
Collision between the racket and the ball is inelastic.
Hence,
Final velocity of the racket = v1f = [(m1-m2)/(m1+m2)]v1i
v1f = [(0.330-0.058)/(0.330+0.058)]*55.56
v1f = 38.95m/s
Final velocity of the ball = v2f = [(2m1)/(m1+m2)]v1i
V2f = [(2*0.330)/(0.330+0.058)]*55.56
v2f = 94.5m/s
B)
Jracket = m1(v1f-v1i) = 0.330(38.95-55.56) = -5.5 kg*m/s
Jball = m1(v2f-v2i) = 0.058(94.5-0) = 5.5 kg*m/s
C)
By using kinematic equation on racket,
v1f^2 =v1i^2 +2*a*d
38.95^2 = 55.56^2 +2*a*0.101
Calculating acceleration of racket = a = -7771.3 m/s^2
Force on racket = F1 = m1*a = 0.330*-7771.3 = -2564.5 N
By Newton’s 3rd law
Force on the ball = - force on the racket
F2= -F1 = 2564.5 N
By Newton’s 2nd law,
t = Jracket /F1 = 5.5/2564.5 = 0.002s = 2ms
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