Question

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

Answer 1

`W=6.48gpicolor(white)(x)"N"`

Explanation:

Here's the picture as I see it:

The circumference of the axle is given by:

`c_1=2pixx0.27=0.54pi"m"`

The circumference of the wheel is given by:

`c_2=2pixx0.18=0.36pi"m"`

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

How many turns `n` 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"`