physics conceptual help?

Question

An elevator of mass m rises a vertical distance h with upward acceleration equal to one-tenth g. how much work does the elevator cable do on the elevator

I know the answer is 1.1 mgh but i dont know how to get this . when i do it i get .1mgh so i dont know where the extra 1 comes in

Answer 1

Work energy WE = FS; where F is a motivating force acting in the direction of and over the distance of S.\

For the elevator, F = W + f; where W = mg the weight of the elevator and f = ma the reactive force as it accelerates upward. Therefore WE = (W + f)h = m(g + a)h. As a = .1 g, we have WE = m(1.1 g)h = 1.1 mgh...and there you have it.

The physics is this...as the elevator rises, it has to work against its rest weight (W = mg) and the reactive force (f = ma) as it accelerates upward. Both W and f are carried the distance h, which is why WE = (W + f)h is the work.