If the suspended object moves downward a distance of 2.70m in 2.12s , what is th

Question

If the suspended object moves downward a distance of 2.70m in 2.12s , what is the mass of the wheel?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 0.278m . An object of mass 4.40kg is suspended from the free end of the wire. The system is released from rest and the suspended object descends with constant acceleration

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 0.278m . An object of mass 4.40kg 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 2.70m in 2.12s , what is the mass of the wheel?

Explanation / Answer

x = x0 + v0 t + 1/2a t2

2.7 = 0 + 0 + 1/2 a * 2.122

a = 1.20

v = v0 + a t

v = 0 + (1.20)(2.12) = 2.54

m g h = 1/2 m v2 + 1/4 M R2 (v/R)2

(4.40 * 9.8 * 2.7) = 1/2 (4.40)(2.54)2 + 1/4 M (0.278)2 (2.54 / 0.278)2

116.424 = 14.19 + 1.61 M

M = 63.5 kg

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