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 0.260m . An object of mass 4.30kg is suspended from the free end of the wire. The system is released from rest and the suspended object descends with constant acceleration.(Figure 1)

Part A

If the suspended object moves downward a distance of 3.40m in 1.86s , 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:
3.4 = 0 + 0 + 1/2a(1.86)^2
a = 1.96

v = v0 + at solve for v:
v = 0 + (1.96)(1.86)
v = 3.6559 m/s

mgh = 1/2mv^2 + 1/4MR^2(v/R)^2
where m = mass of object
M = mass of wheel
R = radius

(4.30)(9.8)(3.4) = 1/2(4.30)(3.6559)^2 + 1/4M(.26)^2(3.6559/.26)^2

solve for M:
M=34.27 kg

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