Solving Physics Homework: Spring Length & Work Done

[gwhite00]

Homework Statement

A vertical spring is 10.0 cm long when supporting a 20.0 kg mass, and it is 12.0 cm long when supporting a 32.0 kg mass. Assume the stretch is linear with the load.

a) What is the length of the spring with zero load? (0.06666667)

b) How much work would be done in stretching the spring from 10.0 cm to 15.0 cm? (17.15)

Homework Equations

ΔU = -W = mgy_f - mgy_i

The Attempt at a Solution

a) After converting cm to m, I substituted in all the given information and found that they potential energy of the system was 18.032. But when I substituted that in with the unknown height, I got .16 m which can't be true. Especially when the given answer is 0.0666667.

I have no idea what I'm doing wrong.

b) I'm not even sure where to start.

 

[Doc Al]

a) After converting cm to m, I substituted in all the given information and found that they potential energy of the system was 18.032. But when I substituted that in with the unknown height, I got .16 m which can't be true. Especially when the given answer is 0.0666667.

You'll solve part a using force analysis and Hooke's law, not energy methods. (Aside from that, your energy equation neglects spring potential energy.)