# How much work would it take to push a  1 kg  weight up a  3m  plane that is at an incline of  pi / 4 ?

Jan 30, 2018

This requires 20.8 J of work done.

#### Explanation:

The definition of work is

$W = F \cdot \Delta d \cos \theta$

but care must be taken in using the formula as the angle $\theta$ must be the angle between the displacement $\left(\Delta d\right)$ and the force against which your are doing work.

Here, the force we work against is the force of gravity, so the angle in the above formula is the one between the incline and the vertical.

This means it is not $\frac{\pi}{4}$, as this is measured relative to the horizontal, but the compliment of $\frac{\pi}{4}$ which in this case also happens to be $\frac{\pi}{4}$! But keep this in mind for next time, when the given angle is something else!

So, if the mass of the object is $m$, the force of gravity on it is $m g$, which equals 9.8 N in this case.

$W = F \cdot \Delta d \cos \theta = 9.8 \times 3 \times \cos \left(\frac{\pi}{4}\right) = 20.8 J$

since $\cos \left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}}$