# How much work would it take to push a  8 kg  weight up a  5 m  plane that is at an incline of  pi / 4 ?

Jan 13, 2017

The work done against the force of gravity is 277 joules.

#### Explanation:

The reason work must be done in this situation is that an applied force must act against gravity.

Work done on against (or by) a force is defined by

$W = F \Delta \mathrm{dc} o s \theta$

where $\theta$ is the angle between the direction of travel of the object and the direction of the force being applied.

You need to notice that in a problem such as this, the angle of the incline (and therefore of $\Delta d$) is stated with respect to the horizontal, but because gravity is a vertical force, the angle we use in the formula is not this angle, but rather, we use its compliment ($\frac{\pi}{2} - \theta$), because $\theta$ must be measured with respect to ${F}_{g}$.

That said, this time, both angles would be $\frac{\pi}{4}$, but in the future, if faced with this question, try to keep this in mind.

The work done is $W = F \left(\Delta d\right) \cos \left(\frac{\pi}{4}\right) = \left(8\right) \left(9.8\right) \left(5\right) \left(\frac{\sqrt{2}}{2}\right) = 277 J$