WORK DETERMINED UTILIZING FORCE (INTEGRAL APPLICATION)

Question

A chain 71 meters long whose mass is 26 kilograms is hanging over the edge of a tall building and does not touch the ground. How much work is required to lift the top 14 meters of the chain to the top of the building? Use that the acceleration due to gravity is 9.8 meters per second squared. 

Answer 1

Say we have already lifted a length x of a length L chain. The gravitational force on the remaining length of L-x is F(x) = mg(L-x)/L. To calculate the amount of work required to lift a length y of this chain we integrate ∫F(x)dx from 0 to y ⇒ mg/L (Ly - y²/2) = mgy(2L-y)/(2L).