A spring initially unstretched is first stretched by x, then stretched a further x (from x to 2x). If the work in the first stage is W₁ and in the second stage is W₂, find W₂/W₁.
Physics · Work , Power and Energy · kinetic enegy and work engery theorem
JEE Advanced

Question

A spring initially unstretched is first stretched by x, then stretched a further x (from x to 2x). If the work in the first stage is W₁ and in the second stage is W₂, find W₂/W₁.

G1 Physics · Accepted Answer

First-stage work W₁=½kx². Second-stage work from x to 2x is W₂=½k[(2x)²-x²]=3/2 kx². Therefore W₂/W₁=3.