Andrea and Melissa are playing squash Melissas mother had al

Andrea and Melissa are playing squash. Melissa’s mother had always told her to wear her safety goggles when playing squash because she might lose an eye! Andrea did not wear safety goggles because she did not believe a little squash ball could do such damage. The two decided to create their own “self-led mini experiment” to see who was correct. Melissa took a few steps back and then served the ball at Andrea’s face. Andrea, who by this time realized that maybe Melissa’s mom was on to something, quickly raised her racquet in front of her face in an attempt to bring the squash ball to a stop. The squash ball has a mass of .2 kg and is moving with a pre impact velocity of 50 m/s. Andrea’s racquet has a mass of 1.2 kg and is moving with a pre impact velocity of -4 m/s. Assume that the impact between the ball and racquet lasted for 1.3 s, the coefficient of restitution was .7 and that the force of impact maintained a constant value throughout impact. The following questions apply to Andrea’s racquet and the squash ball.

a. What was the velocity of the squash ball after impact? (1)

b. What was the velocity of the squash racquet after impact? (1)

c. What was the total momentum of the system before impact? (1)

d. What was the total momentum of the system after impact? (1)

e. What impulse was exerted on the ball by the racquet? (2)

f. How much work was done on the ball by the racquet? (2)

Solution

Initial velocitu of squash ball, u = 50m/s
mass = 0.3
Initial velocity of raquet = -4m/s
m=1.2
final velocity =f ball = v1, raquet = v2
Force = 1.2(4-v2)/Dt = 1.2 * a [ a = acc. of squash ball for 3 seconds]

a = 1.2(4 - V2)/1.3*0.2
V1 = -50 + 6(4 - V2)
and V1 - V2 = 0.7*54
or V2 = 9.57m/s (in the direction of original velocity of the squash ball)
V1 = 41.42m/s (in the direction opposite to the original direction of the aquash ball)
a =62.63m/s^2

1. 41.42m/s
2. -9.57 m/s
3. P = .2*50 - 4*1.2 = 5.2 kg m/s
4. P = 0.2*(-41.42) + 1.2*9.57 = 3.2 kg m/s
5. Impulse = 1.2(4+9.57) = 16.284 Kg m/s
6. Work done on the ball by the racquet = W
W = F*s
F = 16.284/1.3 = 12.526 N
s = -50*1.3 + 0.5*62.63*1.3^2 = -12.077m
W = 151.284 J