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?

1 Answer
May 14, 2016

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