Lifting things with levers
Physics Narrative for 11-14
Conservation of energy: trading force for height
Here we show how the required relationship between force and length to pivot to achieve a much lower lifting force is the consequence of the conservation of energy.
In episode 02 of the SPT: Energy topic we referred to a fundamental rule expressed by some people as:
You can never get owt for nowt!. In physics this is expressed more formally as the principle of conservation of energy.
Let's think for a moment about a particular event which involves lifting something. To make this happen a minimum amount of energy must be shifted from the chemical store of your arm to the gravity store of the object in the Earth's field. This is connected to levers and doors – just follow the argument for the moment!
We can calculate the energy shifted here (see episode 04 of the SPT: Energy topic) using:energy shifted = force exerted × height
force exerted is the magnitude of the force needed to lift the object and height is the distance through which that force moves. You'll meet this relationship rather often, usually as: energy = force × distance
You can get the same job done in four stages, using one quarter of the force but compensating for this reduction by having to lift four times the height. This compensation leaves the energy shifted unchanged, but it does make the job easier since you need to exert a smaller force to lift each of the quarters.
Another way forward is to get this
quadruple-length-lift over with in one smooth action by using a lever.
Designing a lever for this task
But how can we set up this lever to lift the object by exerting just one quarter of the force? We know that the same quantity of energy must be shifted as with a direct lift (never getting anything for nothing). Then the design of the lever becomes very simple. To lift the object with a force which is one quarter of the force of gravity acting on the object, you need to use a lever where you push four times further from the pivot than the position of the object.