Question

How much work would it take to push a `6 kg` weight up a `4 m` plane that is at an incline of `pi / 4`?

Answer 1

`166.31Nm`

Explanation:

It is always good to start a mathematical model with certain assumptions. Here, we are ignoring air resistance, friction, and assuming that gravity is a constant `9.8m/s^2` downwards.

The force straight down with gravity is given by

`F=ma`

where `m` is the mass of `6kg` and `a` is acceleration of gravity, `9.8m/s^2`, so

`F_("vertical down")=6kg*9.8m/s^2=58.8N`.

But since the plane gets in the way and the mass cannot move straight down, it would have to move down the `pi/4` plane. Using trigonometry, this gives a force down the plane of

`F_("down plane")=58.8N*cos(pi/4)`
`=58.8cos45=41.578N`

In order to move up the plane, you need to exert a force equal to or greater than the force down the plane, which means

`F_("up plane")=41.578N`

Now, to find the work you use the equation

`W=Fd`,

where `F` is the force we have already found and `d` is the distance of `4m` up the plane, so

`W=41.578N*4m=166.31Nm`