Question

How much work would it take to push a `1 kg` weight up a `2 m` plane that is at an incline of `(5pi) / 12`?

Answer 1

Same Work as if there was no plane

Explanation:

Asuming there is no friction coefficient which i think is the case. And knowing that gravitational force is a conservative field ( the route the mass follows doesn't mind, the only important thing is the initial and final position)

As all the forces are conservative, you don't care about whether the work has been done in a plane or with a massless rope or Jesus brought it to Saturn and brought it back to the final position at the top of the plate.

So `W=mgh_2-mgh_1=mg\Delta h=1kg\cdot 9.81m/s^2 \cdot 2m\approx 20J`

PS: I've assumed that your plate is 2 meters high, if you meant that the hypotenusa of the plane is 2m, then `\Delta h=sin(5\pi/12)\cdot2 m\approx 1.93m` instead of `\Delta h=2`