# How much work would it take to push a  3 kg  weight up a  13 m  plane that is at an incline of  (5pi) / 12 ?

Jan 23, 2017

The work done is $369$ joules, and is done to increase the potential energy of the mass as we lift it against gravity.

#### Explanation:

If we are not considering any frictional effect (the problem gives no information that would enable us to do so), then the only work done is in raising the mass against the force of gravity.

$\text{Work} = \Delta U = m g h$

where $h$ is the vertical height through which the mass moves, and is equal to $\mathrm{ds} \int h \eta$, where $d$ is the distance of travel along the incline.

Using the values in this problem

$\Delta U = \left(3\right) \left(9.8\right) 13 \sin \left(\frac{5 \pi}{12}\right) = 369 J$