# 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 ?

Apr 21, 2016

$529.2 N m$

#### Explanation:

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

$W = m g = 9 k g \cdot 9.8 \frac{m}{s} ^ 2 = 88.2 N$.

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

${F}_{\text{down plane}} = 88.2 \sin \left(\frac{\pi}{6}\right) = 88.2 N \cdot \frac{1}{2} = 44.1 N$.

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

${F}_{\text{up plane}} = 44.1 N$.

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

$\text{Work} = F d$,

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

$\text{Work} = 44.1 N \cdot 12 m = 529.2 N m$