A thin, light wire is wrapped around the rim of a wheel, as shown in the followi

Question

A thin, light wire is wrapped around the rim of a wheel, as shown in the following figure. The wheel rotates without friction about a stationary horizontal axis that passes through the center of the wheel. The wheel is a uniform disk with radius 0.252 . An object of mass 4.05 is suspended from the free end of the wire. The system is released from rest and the suspended object descends with constant acceleration. Part A If the suspended object moves downward a distance of 2.95 in 2.06 , what is the mass of the wheel? Express your answer with the appropriate units.

Explanation / Answer

x = x0 + v0t + 1/2at^2 solve for a: 2.95 = 0 + 0 + 1/2a(2.06)^2 a = find it v = v0 + at solve for v: v = 0 + (a)(2.14) v = find this mgh = 1/2mv^2 + 1/4MR^2(v/R)^2 where m = mass of object M = mass of wheel R = radius (4.05)(9.8)(2.95) = 1/2(4.05)(v)^2 + 1/4M(.252)^2(v/.252)^2 solve for M: M = get answer kg

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