The radius of a wheel is 0.550 m. A rope is wound around the outer rim of the wh

Question

The radius of a wheel is 0.550 m. A rope is wound around the outer rim of the wheel. The rope is pulled with a force of magnitude 4.59 N, u? Winding the rope and making the wheel spin CCW about its central axis. Ignore the mass of the rope. How much rope u? Winds while the wheel makes 1.00 revolution? How much work is done by the rope on the wheel during this time? What is the torque on the wheel due to the rope? What is the angular displacement Delta theta, in radians, of the wheel during 1.00 revolution? How much Show that the numerical value of the work done is equal to the product tau Delta theta.

Explanation / Answer

Here ,

radius of wheel , r = 0.550 m

force , F = 4.59 N

a)

for 1 revolutions

rope unwinds = 2 *pi *r

rope unwinds = 2 * pi * 0.55

rope unwinds = 3.46 m

b)

work done by the rope = distance * tension

work done by the rope = 3.46 * 4.59 J

work done by the rope = 15.9 J

c)

Torque = Force * radius

Torque = 4.59 * 0.550 N.m

Torque = 2.525 N.m

d)

durinig one revolution

angle , theta = 2 pi rad

theta = 6.282 rad

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