 Dr. Christopher S. Baird # How do levers create energy if the conservation of energy does not allow energy to be created?

Category: Physics      Published: July 2, 2013 Levers maximize force by minimizing distance, but the energy inputted is the same. In this image, the length of the arrow represents the distance over which the force is applied and the width of the arrow represents the magnitude of the force. The energy inputted, which is force times distance, remains constant. Levers increase the force by decreasing the distance. Public domain image, source: Christopher S. Baird.

Levers do not create energy. Levers convert a small force applied over a long distance to a large force applied over a small distance. Work is the force times the distance, W = Fd, so the total work done is the same with or without the lever. Look closely at a lever as you use it. The end that lifts the fridge moves a very small distance d as the job is carried out, but the end of the lever that your hand is pushing on moves a large distance as the job is carried out. Because the total work done must be constant, and work is force times distance, the force must go up if the distance goes down. The lever converts the little force of your hand at one end to a large force at the other end; large enough to do a big job. But it does this at the cost of a larger distance. You must therefore push on the one end of the lever for a longer time than you would have to without the lever.

According to the work energy theorem, the amount of work you do on a system becomes the energy contained in the system. Because the work is constant with or without the lever, the energy is also constant. A lever therefore does not create energy. The energy inputted to do a certain job is exactly the same with or without the lever. The lever just maximizes efficiency. Human muscles are built for endurance, and not short-term, high-intensity performance. It is easier for humans to carry 10 pounds up 100 steps than to carry 100 pounds up 10 steps, even though the total mechanical energy required for both jobs is exactly the same. Even though the total mechanical energy required is the same, one job is easier because human muscles operate more efficiently at low intensities for a long time. If a person tries to carry 100 pounds up 10 steps, he would waste a lot of energy that would end up as heat because of the inefficiency of human muscle for such a task. The person in this case would have to expend more total energy to get the job done: the energy to lift the 100 pounds up the 10 steps + all the energy that gets wasted to heat because of the muscle's inefficiency in this performance mode.

All simple machines – levers, pulleys, ramps, screws, gears, etc – operate on this same principle. They increase efficiency by allowing a high-force/small-distance job to be accomplished by humans who operate best in low-force/large-distance mode. But the total work and total energy expended for a given job is always they same, no matter what machine you use.