What is the total work done against the spring force?

[Lyphta]

Homework Statement

When a 75 gram mass is suspended from a vertical spring, the spring is stretched from a length of 4.0 cm to a length of 7.0 cm. If the mass is then pulled downward an additional 10.0 cm, what is the total work done against the spring force?

Homework Equations

U=mgh (Don't need the work equation because work = energy)
U= 1/2 k x^2 (equation for the elastic spring with potential energy.)

The Attempt at a Solution

mass = .075 kg
height = .21 m (.04+.07+.1 = .21m)
gravity = 9.81m/s^2

U=mgh
U= (.075)(9.81)(.21)
U= .15 J

I know the answer is wrong because the book says the answer is .21 J

 

[rl.bhat]

When there is no mass the length of the spring is 4 cm. When a 75 gram mass is suspended from a vertical spring, the spring is stretched from a length of 4.0 cm to a length of 7.0 cm. From this calculate the force constant k, and then calculate the work done. mgh is the work done when the body is falling freely.