The puck in Figure P8.51 has a mass of 0.200 kg. Its original distance from the center of rotation is 40.0 cm,

Question

The puck in Figure P8.51 has a mass of 0.200 kg. Its original distance from the center of rotation is 40.0 cm, and it moves with a speed of 90.0 cm/s. The string is pulled downward 15.0 cm through the hole in the frictionless table. Determine the work done on the puck. (Hint: Consider the change of kinetic energy of the puck.)

Answer 1

From conservation of angular momentum, Iω remains constant, I being moment of inertia and ω being angular rate.
I = mr^2 and ω = v/r, so Iω = mvr = constant. Thus v remains inversely proportional to r. When r decreases from 0.4 to 0.25 m, v increases from 0.9 m/s to 1.44 m/s.
KE1 = mv1^2/2 = 0.081 J
KE2 = mv2^2/2 = 0.20736 J
The difference, 0.12636 J, is the work done on the puck.