Remember, once again, the formula for calculating work: W = force(F) x distance(D). The whole point of a machine is to decrease the amount of force needed to do a certain amount of work. So if we want the same amount of work, but we decrease the force, from the equation we see that we need to increase the distance over which the force is acting. The mechanical advantage is basically a measure of how much we are able to decrease the input force and get the same amount of work.
Let’s look at an example. If you want to lift that 50 lb box of books up to the platform which is 5 feet high, you have to change the potential energy of the box. (You are raising it up to a higher level, increasing its potential gravitational energy.) This change in energy is equal to the work done on the box. Let’s say you have two ways available to get the box up onto the platform. You could lift it up directly above yourself, which is a shorter distance, but requiring more force, or use a ramp, which is a longer distance, but requires less force. Either way you do it, the work is the same (ignoring the forces of friction), because you are only changing the ratio between force and distance. The longer the ramp (the less steep), the smaller the required force. If you double the length of the ramp, you will halve the required force. Dividing the length of a ramp (which is the maximum distance) by the height (which is the minimum distance) is the ramp’s mechanical advantage.
Mechanical Advantage of a Ramp
MA of Ramp = Length ÷ Height
Let’s say you found a very smooth board to help you move that 50 lb box. The board is 10 feet long. You lay one end up on the platform, and slide the box right up the ramp with ease. Your MA would be 10 feet/5 feet = 2. If the board you found was 20 feet long, your MA would be 20 ft/5 ft = 4. You’ve doubled the distance and the mechanical advantage, so you’ve halved the force needed to do the work.
Try one
Now you need to move a 100 lb box up 5 feet. What would your MA be if the board was 25 feet long?
