The radius of a wheel is 0.600 m. A rope is wound around the outer rim of the wh

Question

The radius of a wheel is 0.600 m. A rope is wound around the outer rim of the wheel. The rope is pulled with a force of magnitude 4.75 N, unwinding the rope and making the wheel spin CCW about its central axis. Ignore the mass of the rope.

(a) How much rope unwinds while the wheel makes 1.00 revolution?
m

(b) How much work is done by the rope on the wheel during this time?
J

(c) What is the torque on the wheel due to the rope?
N · m

(d) What is the angular displacement , in radians, of the wheel during 1.00 revolution?
rad

(e) Show that the numerical value of the work done is equal to the product .
=  J

Explanation / Answer

radius = r = 0.6 m

Force = F = 4.75 N

a) 1 revolution = 2 pi r = 2 * pi * 0.6 = 3.769 m

b) Work done = F x d = 4.75 * 3.769 = 17.9 J

c) Torque = F x r = 4.75 * 0.6 = 2.85 Nm

d) Angular displacement = 2 pi * 1 = 2 * pi * 1 = 6.28 rad

e) Work done = T * delta theta = 2.85 * 6.28 = 17.9 J

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