Hi can someone help me with this problem, I am particularly concerned whether th

Question

Hi can someone help me with this problem, I am particularly concerned whether the calculated force needs to be doubled in the end.

A tennis ball has a mass of 0.057kg. A prof. tennis player hits the ball hard enough to give it a speed of 50m/s. The ball hits a wall and bounces back with almost the same speed (50m/s). The ball is crushed by 2cm at the instant when its speed is momentarily zero (when it hits the wall) before rebounding.
Making the very rough estimate that the large force the wall exerts on the ball is approximately constant during contact, determine the approximate magnitude of the Force.Hint. Consider the time it takes for the ball to come to rest.


Thank you for the help!

Explanation / Answer

Mass of the ball m = 0.057 Kg Initial speed u = 50 m/s Final speed v = - 50 m/s Change in momentum = m(u - v) = 0.057(50 + 50) = 5.7 Kg m/s Time of contact t = Compression/average velocity                             = S/[(u+0)/2]                             = (2*0.02)/50                             = 0.0008 s   From Impulse formula                   Ft = Change in momentum        F * 0.0008 = 5.7                     F = 7125 N   

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