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 0.274 m . An object of mass 4.15 kg is suspended from the free end of the wire. The system is released from rest and the suspended object descends with constant acceleration.

If the suspended object moves downward a distance of 2.60 m in 2.02 s , what is the mass of the wheel?

Explanation / Answer

let,

radius of the disk, r=0.274 m

mass of the disk is m1

mass of the object, m2=4.15kg

distance travelled, d=2.6m

time taken, t=2.02 sec

tension in wire is T

now,

d=1/2*a*t^2

2.6=1/2*a*2.02^2

=====> a=1.27 m/sec^2

acceleration, a=1.27 m/sec^2

and

force equation for the object,

m2*a=m2*g-T ----(1)

and

for the disk,

Torque=rXT

rXT=I*alpa

r*T=1/2*m1*r^2*(a/r)

T=1/2*m1*a ------(2)

from (1) and (2)

m2*a=m2*g-(1/2*m1*a)

m2*a=m2*g-(1/2*m1*a)

4.15*(1.27)=4.15*9.8-(1/2*m1*1.27)

=====> m1=55.75kg

mass of the wheel, m1=55.75 kg

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