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

Answer:

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#