# How much work would it take to push a  2 kg  weight up a  2m  plane that is at an incline of  (5pi) / 12 ?

Jan 22, 2018

$37.9 J$

#### Explanation:

The formula for work is $W = F \mathrm{dc} o s \theta$. In this case the incline does not give us the required value for $\theta$. We need to use the complement of the incline.

$\theta = \text{completment of incline" = } \frac{\pi}{2} - \frac{5 \pi}{12} = \frac{6 \pi}{12} - \frac{5 \pi}{12} = \frac{\pi}{12}$

Here, $F = 2 \cdot 9.81 = 19.62 N , d = 2 m , \cos \theta = \cos \left(\frac{\pi}{12}\right) = 0.9659$

Now multiply: $19.62 \cdot 2 \cdot 0.9659$

$W \cong 37.9 J$