# How much work would it take to push a  1 kg  weight up a  9 m  plane that is at an incline of  (5pi) / 12 ?

Jan 20, 2016

#### Answer:

$W = P E = m g h = 1 k g \times 9.81 \frac{m}{s} ^ 2 \times 8.69 m = 85.3 J$

#### Explanation:

The work done will be equivalent to potential energy gained as the object climbs incline of 9 m. So we need to calculate the side opposite the 75 degree angle. 75 degrees is steep angle indeed.

$5 \frac{\pi}{12} = 5 \times \frac{\cancel{180}}{\cancel{12}} = 75$
The gives you an idea of the incline steepness
graph{1.5x [-10, 10, -1, 5]}

The hypotenuse = 9m thus
$\sin 75 = \frac{o p p}{h y p} = \frac{o p p}{9}$
$o p p = 9 \sin 75 = m 8.69$
The work done is equivalent to potential energy gained
Thus$W = P E = m g h = 1 k g \times 9.81 \frac{m}{s} ^ 2 \times 8.69 m = 85.3 J$