Calculate the elastic potential energy added to a spring with k = 20 N/m when the spring is stretched

Question

Calculate the elastic potential energy added to a spring with k = 20 N/m when the spring is stretched

a) 0.30m

b) an additional 0.30 m

Explain.

Answer 1

This is a relatively easy problem once you know the formula for elastic potential energy and what the symbols [variables] in the formula mean. PE_s = 1/2 kx², where k represents the force constant [ how stiff the spring is] and has units of N/m and x is the physical distance the spring is being compressed or stretched in meters.

so PE_s = 1/2(20)(.3)² = 0.9 J , if you doubled x it would increase the PE_s by a factor of 4 as x is being squared in the formula, so 0.9 x 4 = 3.6 J would be the PE_s if spring stretch an additional 0.30 m.