A professional golfer is examining a video of a practice swing. The high-speed f

Question

A professional golfer is examining a video of a practice swing. The high-speed footage shows that his club is in contact with the ball (which was initially at rest on the tee) for only 0.771 milliseconds, and the radar gun clocks the speed of the ball as 131 mph after it comes off the club. The golf ball has a mass of 45.9 grams. What is the magnitude of the impulse imparted to the ball by the club? What is the magnitude of the average force of contact between the club and the ball? Assume that the force acting between the club and the ball is in a constant direction, and that the force of gravity plays a negligible role in the brief collision. Impulse can be defined in two different ways. One definition relates the impulse to the average force, and the other definition relates impulse to momentum. You will need to use both relationships here. One mile is equal to approximately 1609.3 meters.

Explanation / Answer

Let's stat the problem.
Part a: What is the magnitude of the impulse imparted to the ball by the club?

Impulse = m (Vfinal - Vinitial)
m = mass of ball = 45.9 gram = 0.0459 Kg
Vinitial = 0 m/s (since it was at rest.)
Vfinal = 131 mile/hour = 58.562 m/s

Impulse = 0.0459 Kg (58.562 m/s - 0 m/s) = 2.687 KG-m/s

Part b:

Force(ave) = Impulse / (delta t)
delta t = 0.771 millisecond = 0.000771 second

Force(ave) = 2.687Kg-m/s / 0.000771 s =3485.08 Kg m/s^2 or Newton
the magnitude of the average force = 3485.08 Newton

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