Question

An output gear has 10 teeth and an input gear has 40 teeth. What is the mechanical advantage of gear combination? Is force or speed multiplied in this example

Answer 1

Mechanical advantage: 4. Speed is multiplied

Step-by-step explanation:

The mechanical advantage of gear combination is

`MA = (N_i)/(N_o)`

where

`N_i` is the number of teeth in the input gear

`N_o` is the number of teeth in the output gear

Here we have

`N_i = 40\\N_o = 10`

So we find

`MA = (40)/(10)=4`

In this example, it is the speed to be multiplied: the speed of the output gear is 4 times larger than the speed of the input gear. In fact, the mechanical advantage can be rewritten as

`MA= (\omega_o)/(\omega_i)`

where

`\omega_i` is the angular speed of the input gear

`\omega_o` is angular speed of the output gear

So re-arranging the equation, we find

`\omega_o = MA \cdot \omega_i = 4 \omega_i`

so, the speed of the output gear is 4 times larger than the speed of the input gear.