Answer:
Mechanical advantage: 4. Speed is multiplied
Explanation:
The mechanical advantage of gear combination is
[tex]MA = \frac{N_i}{N_o}[/tex]
where
[tex]N_i[/tex] is the number of teeth in the input gear
[tex]N_o[/tex] is the number of teeth in the output gear
Here we have
[tex]N_i = 40\\N_o = 10[/tex]
So we find
[tex]MA = \frac{40}{10}=4[/tex]
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
[tex]MA= \frac{\omega_o}{\omega_i}[/tex]
where
[tex]\omega_i[/tex] is the angular speed of the input gear
[tex]\omega_o[/tex] is angular speed of the output gear
So re-arranging the equation, we find
[tex]\omega_o = MA \cdot \omega_i = 4 \omega_i[/tex]
so, the speed of the output gear is 4 times larger than the speed of the input gear.
