how gears and gear ratios don’t break the laws of conservation of energy.

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In [this video](https://youtu.be/umN2iHsw3UY?t=479) a lego motor lifts ~54kg using gear ratios, how can this be possible when the motor only lifts ~3kg by itself? Isn’t that like putting 1 energy into something and getting 18 out of it?

In: Engineering
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Think of gears like levers: You trade a lot of distance at a little force for a short distance with a lot of force. You don’t end up with any more energy overall, it just applies over an adjusted distance.

Nope. The energy is constant. That’s how gears, levers and pulleys all function. Work is Force * distance and it’s measured in units of energy. For rotating components, it’s Torque * rotational rate = Power (power is the rate of change of energy).

Pulleys and levers work by decreasing required force, but increasing the distance travelled (ergo work is constant).

Gears work by trading off torque for rotational rate (power is constant)

When a machine reduces the force, it increases the distance. Energy is force multiplied by distance. You reduce the force by half, you have to cover the twice the distance to maintain the same energy.

Let’s say that if you were to do a straight deadlift of that 54 kg object, there is a one meter distance. However, if you apply 3 kg of force, and when you add up all the distance those gears travelled, it would 18 metres and not 1 m.

The overall energy doesn’t change, but you alter other properties…

In this case, by gearing down a motor you allow it to carry much more weight, but you also cause it work much more slowly.

So if you were to lift a weight with your small motor and geared winch, bif you were to run your motor for a minute overall, you are choosing between lifting a 10kg weight five times, or a 50kg weight once – over the course of a minute you have lifted the same 50kg worth of load (so you have used the same amount of energy), but accomplished it in two different ways.