How Much Work Is Needed to Stretch a Spring from 12 cm to 16 cm?

[magma_saber]

Homework Statement

A spring has a relaxed length of 7 cm and a stiffness of 50 N/m. How much work must you do to change its length from 12 cm to 16 cm?

Homework Equations

1/2*k_ss²

The Attempt at a Solution

1/2*50*(.16-.12)² = 0.04

It shows the solution to be 0.14. It says the change in the energy of the spring is its change in potential energy, so the change in (1/2)k_ss². Be sure to use the stretch s, not the length, and use meters, not centimeters.

 

[Delphi51]

Looks like an algebra error and a misunderstanding of stretch.
Length 12 is a stretch of 12 - 7 = 5. Length 16 is a stretch of 16 - 7 = 9.
.5k(.09)^2 - .5k(.05)^2 is not equal to .5k(.09-.05)^2.