# An object with a mass of #200 kg# is hanging from an axle with a radius of #6 cm#. If the wheel attached to the axle has a radius of #32 cm#, how much work would it take to turn the wheel a length equal to the circumference of the axle?

##### 2 Answers

The work is

#### Explanation:

The load is

The radius of the axle is

The radius of the wheel is

The effort is

Taking moments about the center of the axle

The force is

The distance is

The work is

The work done is 138.5 J.

#### Explanation:

The circumference of the axle is

Therefore the object is lifted a distance,

By the principle of conservation of energy, the work that was done is equal to the increase in the object's gravitational potential energy, GPE.

This could also be calculated by multiplying the torque by the angular translation. The torque would be equal and opposite the torque that the object's weight applies to the axle. The angular translation would be k*2*pi radians.

I hope this helps,

Steve