Question

An object with a mass of `4 kg` is hanging from an axle with a radius of `6 cm`. If the wheel attached to the axle has a radius of `12 cm`, how much work would it take to turn the wheel `8 cm`?

Answer 1

1.568J

Explanation:

The mass of the object lifted = `(m)=4kg`

The radius of the axle `(r)=6cm=0.06m`

The Circumference of the axle `(C_a)=2pir=2pixx0.06m`

The radius of the Wheel attached with the axle `(R)=12cm=0.12m`

The Circumference of the Wheel `(C_w)=2piR=2pixx0.12m`

When wheel turns `2pixx0.12m` the axle turns `2pixx0.06m`

So When wheel turns `8cmor0.08m` the axle turns

`(2pixx0.06m)/( 2pixx0.12m)xx0.08=0.04m`

So the work done to turn the wheel by 8cm is to work done to lift

the weight against gravity by `h=0.04m`

So work done `w =mgh=4xx9.8xx0.04=1.568J`