Question

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`?

Answer 1

`W=PE = mgh= 1 kg xx 9.81 m/s^2xx8.69 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.

`5pi/12 =5xxcancel(180)/cancel(12) = 75`
The gives you an idea of the incline steepness
graph{1.5x [-10, 10, -1, 5]}

The hypotenuse = 9m thus
`sin75 = (opp)/(hyp) = (opp)/9`
`opp = 9 sin75 =m 8.69`
The work done is equivalent to potential energy gained
Thus`W=PE = mgh= 1 kg xx 9.81 m/s^2xx8.69 m = 85.3 J`