Hooke's law states that it takes a force equal to kΔx is required to stretch a sorting a distance Δx beyond its rest length.

Question

A) determine a formula in terms of k & Δx that represents the amount of work required to stretch a spring to a distance Δx. Hint: since the force is constant, you must use the formula Work=average force x distance

B) calculate how much energy is stored within a spring that has a spring constant of 80.0N/m and is stretched to a length of 0.35m

Answer 1

A)
W=∫F•dx=-∫kx•dx (limits ↓0↑x) =kx²/2
or
ΔW=F•Δx =-kx •Δx,
W=ΣΔW= Σ(-kx•Δx)=
=- kx Σ{(0-x)/2}= kx²/2
B)
W= kx²/2=80•0.35/2 =14 J