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?
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 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 k2pi radians.
I hope this helps,