Question

What is the mechanical advantage of a ramp that is 9 m long and 3 m high?

Answer 1

`9/3=3`

Explanation:

You have two choices to lift an object in this case. You either lift it straight up for 3m without the ramp; or you push it on the ramp and make it travel 9m long before it reaches 3 m high. Obviously the later case costs less effort but it takes longer time. Hence the term mechanical advantage `9/3 =3`. Basically you use 3 times less force to push the object on the ramp than lifting it straight up.

Or you can consider the forces used in this two cases.

The sine of the ramp is:

`sintheta = "opposite side"/"hypotenuse"= 3/9 =1/3`

The minimal force needed to push an object on the ramp is
`F_"inclined"= mgsintheta= 1/3mg`

The force needed to lift the object without the ramp is mg.

`"Mechanical Advantage" ="Force used without the ramp"/"Force used with the ramp"= (cancel(mg))/(1/3cancel(mg)) =3`