How much work would it take to push a # 6 kg # weight up a # 4 m # plane that is at an incline of # pi / 4 #?
It is always good to start a mathematical model with certain assumptions. Here, we are ignoring air resistance, friction, and assuming that gravity is a constant
The force straight down with gravity is given by
But since the plane gets in the way and the mass cannot move straight down, it would have to move down the
In order to move up the plane, you need to exert a force equal to or greater than the force down the plane, which means
Now, to find the work you use the equation