# How much work would it take to push a  1 kg  weight up a  5 m  plane that is at an incline of  pi / 3 ?

Dec 27, 2016

The work done is found by

$W = m g \times \Delta d \cos \left(\frac{\pi}{6}\right) = 42.4 J$

#### Explanation:

In any situation where a force acts and an object moves, the work done by or against that force is given by

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

where $\theta$ is the angle between the directions of $\vec{F}$ and $\vec{\Delta} d$

Since the force we work against here is the force of gravity and the displacement is upward at an angle of $\frac{\pi}{3}$ relative to the horizontal , the angle between ${F}_{g}$ and $\Delta d$ is $\frac{\pi}{6}$

Therefore, the work done is

$W = m g \times \Delta d \cos \left(\frac{\pi}{6}\right) = \left(1\right) \left(9.8\right) \left(5\right) \left(\frac{\sqrt{3}}{2}\right) = 42.4 J$