Answer to Question #289531 in Physics for Mom

Question

When you load a heavy box into a big moving truck, it is often easier to push it up a sloped frictionless ramp to the back of the truck than to lift it directly up into the truck. Yet, the change in the gravitational potential energy of the box is the same no matter how you get it from the ground into the moving truck.

Compare the amount of work you must do to lift the box directly into the truck with the amount of work you need to push the box up the frictionless ramp.

Answer 1

The amount of work is the same:

$$W_\text{directly}=mgh.\\\space\\ W_\text{incline}=mg\sin\theta·\dfrac h{\sin\theta}=mgh.$$