When a golf club strikes a golf ball, the club is in contact with the ball for about .0016 s. The 45-g ball acquires a speed of 71 m/s.
a) What is the magnitude of the impulse applied to the ball?
b) Estimate the magnitude of the average force exerted by the club on the ball in kilo-Newtons.
Force*time=change in momentum=mass*changeVelocity
To find the answers to these questions, we can use the concepts of impulse and average force.
a) The impulse applied to the ball can be calculated using the formula:
Impulse = Change in momentum = mass x change in velocity
Given:
Mass of the ball (m) = 45 g = 0.045 kg
Change in velocity (Δv) = final velocity - initial velocity = 71 m/s - 0 m/s = 71 m/s
Impulse = 0.045 kg × 71 m/s = 3.195 kg·m/s
Therefore, the magnitude of the impulse applied to the ball is 3.195 kg·m/s.
b) The average force exerted by the club on the ball can be calculated using the formula:
Average Force = Impulse / Time
Given:
Impulse = 3.195 kg·m/s
Time (Δt) = 0.0016 s
Average Force = 3.195 kg·m/s / 0.0016 s = 1996.88 N
To convert this to kilo-Newtons (kN), we divide by 1000:
Average Force = 1996.88 N / 1000 = 1.997 kN (rounded to three significant figures)
Therefore, the magnitude of the average force exerted by the club on the ball is approximately 1.997 kN.