You need to push a 500 kg grand piano onto a stage that is 3 m above the ground. If you can only apply a maximum force of 1000 N, what is the minimum distance from the stage that you should begin building your ramp?
To solve this question, you need to understand the concept of mechanical advantage (MA). Mechanical advantage refers to a scenario where you put into a smaller force and get a greater force output. The compensation for that, however, is that you will need to exert the force for a longer distance.
MA = d_input / d_output = F_output / F_input
By rearranging the above we have: d_input = F_output / F_input * d_output = 500 * 10 / 1000 * 3 = 15 m. So we need to longest side of the ramp would 15 m. So the distance from the stage = sqrt(15^2 - 3^2) = 14.7 m (3 significant figures)