An object with a mass of 8 kg8kg is hanging from an axle with a radius of 27 cm27cm. If the wheel attached to the axle has a radius of 18 cm18cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?

1 Answer
Jan 28, 2016

W=6.48gpicolor(white)(x)"N"W=6.48gπxN

Explanation:

Here's the picture as I see it:

MFDocs

The circumference of the axle is given by:

c_1=2pixx0.27=0.54pi"m"c1=2π×0.27=0.54πm

The circumference of the wheel is given by:

c_2=2pixx0.18=0.36pi"m"c2=2π×0.18=0.36πm

If the wheel turns the circumference of the axle then it must turn through a distance of 0.54pi"m"0.54πm.

How many turns nn is this?

n=(0.54cancel(pi))/(0.36cancel(pi))=3/2

The no. of turns the axle completes must be the same so the total distance the axle rotates is:

3/2xx0.54pi"m"

=0.81pi"m"

The work done in lifting the 8kg mass is given by:

W=mgh

:.W=8gxx0.81pi

W=6.48gpicolor(white)(x)"J"