Question

A nail is partially inserted into a block of wood, with a length of 0.0300 m protruding above the top of the block. To hammer the nail in the rest of the way, you drop a 20.0 kg metal cylinder onto it. The cylinder rides on vertical tracks that exert an upward friction force of 16.0 N on the cylinder as it falls. You release the cylinder from rest at a height of 1.50 m above the top of the nail. The cylinder comes to rest on top of the block of wood, with the nail fully inside the block. Use the work-energy theorem to find the speed of the cylinder just as it hits the nail.

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the metal cylinder = m = 20 kg

Height from which the cylinder is released = H₁ = 1.5 m

Height of the nail above the top of the block = H₂ = 0.03 m

Height through which the cylinder falls = H

H = H₁ - H₂

H = 1.5 - 0.03

H = 1.47 m

Friction force on the cylinder = f = -16 N (Negative as it opposes motion)

Speed of the cylinder just as it hits the nail = V

The initial potential energy of the cylinder plus the work done by friction is equal to the kinetic energy of the cylinder.

mgH + fH = mV²/2

(20)(9.81)(1.47) + (-16)(1.47) = (20)V²/2

V = 5.15 m/s

Speed of the cylinder just as it hits the nail = 5.15 m/s