# How do gears provide a mechanical advantage?

1. Jan 2, 2013

### theBEAST

For example in this video at 5:00:

They show by turning the gear with little force allows for one to move a VERY HEAVY gate to operate the sea locks.

I don't understand how this is possible. Could anyone please explain the physics/theory behind this?

Thanks!

Last edited by a moderator: Sep 25, 2014
2. Jan 3, 2013

### Staff: Mentor

The short version is that the gears amplify the torque because they make each turn of the input gear equal a fraction of a turn on the output gear. So turning one gear 10 turns may only get you 1 turn on the other, which amplifies the torque.

The basic mechanism used for mechanical advantage is the Lever. From the linked article:

It boils down to the fact that when one end of the lever moves a shorter distance in the same time, the force must increase for the power to remain the same. Same with the gears.

3. Jan 3, 2013

### A.T.

As Drakkith said, gears are basically levers that can operate continuously. See:
http://en.wikipedia.org/wiki/Lever

They allow you to trade distance for force, or the other way around. For example this simple gear outputs less force, but more velocity than goes in:

Here the lever mechanism is indicated as a red line:

4. Jan 3, 2013

### HallsofIvy

Staff Emeritus
There is a law of "conservation of energy", not "conservation of force" and all "mechanical advantage" laws are based on that. If you have a cog of radius R m and turn it through on complete turn, $2\pi$ radians, by applying force F Newtons, then its surface has moved through a distance of $2\pi R$ m and so you have done $2\pi RF$ Joules work on it.

If a chain or other ratcheting mechanism causes another cog, of radius r, to turn through the same distance, by "conservation of energy" you have done $2\pi r f= 2\pi RF$ Joules of work on it also and so must have applied $f= (2\pi RF)/(2\pi r)= (R/r)F$ Newtons force. "R/r" is the "mechanical advantage".

5. Jan 4, 2013

### theBEAST

If the other cog, of radius r, turned through the same distance that the cog with radius R turned, then they must have the same work. Since work is F*d, then they both must have the same force? I am kind of confused by how you equated:

$2\pi r f= 2\pi RF$

$2\pi R f= 2\pi RF$

since they travel the same distance $2\pi R$