Question

A golf club hits a stationary ball with a force of 45.8N. The impact lasts for 5ms and the ball ends up with final velocity of 45.8 m/s. What is the mass of the golf ball? What is the kinetic energy of the ball and the power required to accelerate it?

Answer 1

We know that:

Impulse = Change in momentum = F_avg*dt

F_avg = dP/dt = m*dV/dt

F_avg = m*(Vf - Vi)/dt

m = mass of golf ball = ?

Vi = Initial speed of ball = 0 m/s

Vf = final speed of ball = 45.8 m/s

dt = impact time = 5 ms = 5*10^-3 sec

F_avg = Average force applied = 45.8 N

So,

m = F_avg*dt/(Vf - Vi)

m = 45.8*5*10^-3/(45.8 - 0)

m = mass of ball = 5*10^-3 kg = 5.0 gm

KE = kinetic energy of ball = (1/2)*m*V^2

KE = (1/2)*5.0*10^-3*45.8^2

KE = 5.24 J

Power required to accelerate the ball will be:

Power = Work-done/time interval = W/dt

P = dKE/dt = (KEf - KEi)/dt

P = (0.5*5.0*10^-3*45.8^2 - 0)/(5.0*10^-3)

P = 1048.82 W

Let me know if you've any query.