A cable applies a vertical force to a crate with a mass of 70.0 kg. It first lifts the crate to a height of 12.0 m above the floor, and then lowers it back to the floor. What is the total work done by the force?

The total work done is zero.

Explanation:

Given;

mass of the crate, m = 70.0 kg

height above ground through which the crate is lifted, h = 12.0 m

The only work associated in lifting and lowering this crate is gravitational potential energy.

Potential Energy during lifting = - mgh

= - 70 x 9.8 x 12

= - 8232 J

Potential Energy during lowering = mgh

= 70 x 9.8 x 12

= 8232 J

Total total work done by the force = - 8232 J + 8232 J = 0

Therefore, the total work done is zero.