W_g = mgdcos(phi)
The Attempt at a Solution
So the angle between the force doing work (x component of F_g) and the displacement (down the hill) is 0 degrees. aka phi is 0 degrees. This is true for (a), (b) and (c).
so since cos(0) = 1, the work done by gravity is just mgd. d is greatest for (c), then (b) then (a), so W_g is greatest for (c) then (b) then (a)
However the answers say that work done by gravity is same in all cases.
The textbook says work is generally path dependent, however when only conservative forces (like gravity) are acting, work is not path dependent. So I have a flaw in my understanding somewhere.
potential gravitational energy = mgh, and height is the same in all cases. Can someone explain how this all works?