Question

An object with a mass of `5 kg` is hanging from an axle with a radius of `12 cm`. If the wheel attached to the axle has a radius of `38 cm`, how much work would it take to turn the wheel a length equal to the circumference of the axle?

Answer 1

As shown in the figure
The radius of the Wheel `R=38cm`
The radius of the Axle `r=12cm`
The mass of the object `m=5kg`
The Weightof the object `W=mg=5xx9.8N`
P is the applied force.
The Displacement of Applied force(P)=Circumference of the axle `=d=2xxpixx12cm=24pixx10^-2m`
The working principle of wheel -axle system may be compared with the working principle of First Kind of lever

So
`PxxR=Wxxr=>P=Wxxr/R=5xx9.8xx12/38N`

Hence the Work done `=Pxxd=5xx9.8xx12/38xx24pixx10^-2J=11.7J`