Work done by motor against gravity

[k_squared]

Homework Statement

Homework Equations

Conservation of Energy: ∑T₁+∑U_1-2=T∑₂

The Attempt at a Solution

∫[/B](600+2s²)ds - 100*9.8*15 = (1/2)mv².

However, the term of work done by the force is less than the term of work done by gravity! The book has a solution, which is exactly this except the term of work done by the motor is multiplied by 2. Could it have something to do with the pulley? Otherwise, I don't get it.

Thanks.

 

[SteamKing]

Well, the motor is shown connected to the weight by means of the pulley, so you can't assume that the pulley is not there.

You should draw a free body of the sheave and see how its presence affects the force provided by the motor and on the weight being lifted.