Question

How much work would it take to push a `9 kg` weight up a `12 m` plane that is at an incline of `pi / 6`?

Answer 1

`529.2Nm`

Explanation:

There is a vertical down force, called weight, which is given by

`W=mg=9kg*9.8m/s^2=88.2N`.

However, you can't actually move vertically down, because the plane gets in the way, so gravity instead acts as close as it can to straight down - it acts down the plane.

Using trigonometry, you can find the angle down the plane is

`F_("down plane")=88.2sin(pi/6)=88.2N*1/2=44.1N`.

If this is the force down the plane, the force up the plane in order to move it must be the same, so

`F_("up plane")=44.1N`.

The question is actually asking for work, which is given by

`"Work"=Fd`,

where `d` is distance, given as `12m` in the question, so

`"Work"=44.1N*12m=529.2Nm`