Help Solve 2012 F=ma Problem 21

[ksrivatsan]

Hi,

I'm just training for the 2013 F=ma exam, and I took some old exams. I tried to do the 2012 exam, and could not figure out problem 21. Can anyone help me, please?

Homework Statement

A spring system is set up as follows: a platform with weight 10 N is on top of two springs, each with a spring constant of 75 N/m. On top of the platform is a third spring with spring constant 75N/m. If a ball with weight of 5.0 N is fastened to the top of the third spring and then slowly lowered, by how much does the height of the spring system change?

(A) 0.033 m
(B) 0.067 m
(C) 0.100 m (correct answer)
(D) 0.133 m
(E) 0.600 m

Homework Equations

F=kx

The Attempt at a Solution

The bottom springs act as one spring with K=150 N/m, thus will contract 0.033 m under the weight
The top spring will compress 0.067 m under the weight
so is it just addition...?

 

[Doc Al]

The bottom springs act as one spring with K=150 N/m, thus will contract 0.033 m under the weight
The top spring will compress 0.067 m under the weight
so is it just addition...?

Yes, that's all there is to it. You are just combining the two compressions to get the total compression.

 

[ksrivatsan]

Thanks Doc Al!