Question

A force of 30 newtons is applied to a machin e through a distance of 10 meters. The machine is designed to lift an objec t to a height of 2 meters. If the total work output for the machine is 18 newton-meters (N-m), what is the techanical advantage of the machine?

Answer 1

The machine's mechanical advantage is equal to `0.3`.

Explanation:

The term mechanical advantage simply tells you how good a machine is at multiplying the force put into it.

More specifically, it tells you what the ratio between the force you get out and the force you put in will be.

`"M.A." = F_"out"/F_"in"`

In your case, you know that you put in a force of `"30 N"`.

Moreover, you know that the work output for the machine is `"18 N m"`.

Work is defined as

`W = F * d * cosalpha" "`, where

`F` - force;
`d` - the distance for which the force acts;
`alpha` - the angle between the direction of movement and the force.

In your case, the force is applied to lift an object at a height of `"2 m"`. Since no mention of an angle was made, you know that this force, which will be the machine's output force, will be equal to

`F_"out" = W/(d * cosalpha) = W/(d * 1) = W/d`

`F_"out" = ("18 N"color(red)(cancel(color(black)("m"))))/(2color(red)(cancel(color(black)("m")))) = "9 N"`

The mechanical advantage of the machine will thus be

`"M.A." = F_"out"/F_"in" = (9color(red)(cancel(color(black)("N"))))/(30color(red)(cancel(color(black)("N")))) = color(green)("0.3")`