A golf ball with mass 5.0 x 10^-2 kg is struck with a club. The force on the bal

Question

A golf ball with mass 5.0 x 10^-2 kg is struck with a club. The force on the ball varies from zero when contact is made up to some maximum value (when the ball is maximally deformed) and then back to zero when the ball leaves the club, as in a graph of force vs. time. Assume that the ball leaves the club face with a velocity of +44 m/s.

(a) Find the magnitude of the impulse due to the collision.

(b) Estimate the duration of the collision and the average force acting on the ball.Find the impulse delivered to the ball.

Answer (a)The problem is essentially one dimensional. Note that vi = 0, and calculate the change in momentum, which equals the impulse. I = p = pf pi = (5.0 102 kg)(44 m/s) 0 = +2.2 kg · m/s

Answern(B) Estimate the duration of the collision and the average force acting on the ball. Estimate the time interval of the collision, t, using the approximate displacement (radius of the ball) and its average speed (half the maximum speed). t = x vav = 2.0 102 m 22 m/s = 9.1 10-4 s

Estimate the average force. Fav = p t = 2.2 kg · m/s 9.1 104 s = +2.4 103 N

A good golfer achieves maximum momentum transfer by shifting weight from the back foot to the front foot, transmitting the body's momentum through the shaft and head of the club. This timing, involving a short movement of the hips, is more effective than a shot powered exclusively by the arms and shoulders. Following through with the swing ensures that the motion isn't slowed at the critical instant of impact.

MY QUESTION: What average club speed would double the average force? (Assume the final velocity is unchanged.) This last part is what I need help with. The part about "What average club speed would double the average force"

I ALSO need to know how the radius is calculated in part B? I was trying to follow the example and cannot figure out how the radius is calculated when the only information I have is the mass ??? Thank you! :)   I understand the calculations done....but the radius???

Explanation / Answer

avg speed here = 31.1 m/s

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