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 0.298 m . An object of mass 4.10 kg 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 2.65 m in 1.93 s , what is the mass of the wheel?

Express your answer with the appropriate units.

Explanation / Answer

here,

radius of wheel , r = 0.298 m

mass of object , mo = 4.1 kg

let the mass of the wheel be M

accelration of the system be a

x = 2.65 m , t = 1.93 s

using seccond equation of motion

x = 0 + 0.5 * a*t^2

2.65 = 0.5 * a*1.93^2

a = 1.42 m/s^2

and

a = m0*g /( I /r^2 + mo)

1.42 = 4.1 * 9.8 /( 0.5 * M + 4.1)

M = 48.39 kg

mass of the wheel is 48.39 kg

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