# How much work would it take to push a  8 kg  weight up a  1 m  plane that is at an incline of  pi / 4 ?

May 13, 2016

I found $54.8 J$

#### Explanation:

You can either use Newton's second law to find the force needed to push your weight up the ramp or you can use an "energetic" approach by considering that your work, $W$, will transfer energy into potential energy of your system, i.e., $W = U = m g h$.

The only problem is $h$: this is the final height that we can evaluate using trigonometry:

$h = \mathrm{ds} \in \left(\theta\right) = 1 \sin \left(\frac{\pi}{4}\right) = 0.707 \approx 0.7 m$

So that: $W = m g h = 8 \cdot 9.8 \cdot 0.7 = 54.8 J$