• Support PF! Buy your school textbooks, materials and every day products Here!

Hooke's law sanity check

  • Thread starter bmxicle
  • Start date
  • #1
55
0

Homework Statement


4 springs with a mass on each end are connected in series as below:

|
|
|
|
m1
|
|
|
|
m2
|
|
|
|
m3
|
|
|
|
m4

All the masses are mass m, the length of each spring is 1, and the spring constant is k, find the extension of each spring.


Homework Equations



f = ky

The Attempt at a Solution



So basically if i label each spring extension as [tex]y_1, \ y_2, \ y_3, \ y_4[/tex] then the only forces are the spring pulling from above, the spring pulling from below and the force of gravity on each mass. So for example for the second mass m2 from the top the equilibrium equation would be:

[tex] 0 = ky_2 - ky_3 -mg[/tex]

If this is right I can solve the rest of the problem easily, but I'm just getting thrown off by my use of newton's second law here.
 

Answers and Replies

  • #2
294
0
0=ky2−ky3−mg

This seems to be an accurate statement.

Now how can you rewrite the ky2 and ky3s into the variables you do know, which are m, k and g?
 
  • #3
Redbelly98
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
12,098
129
... the only forces are the spring pulling from above, the spring pulling from below and the force of gravity on each mass. So for example for the second mass m2 from the top the equilibrium equation would be:

[tex] 0 = ky_2 - ky_3 -mg[/tex]
Yes, you are on the right track.
 
  • #4
55
0
Thanks, I can solve the rest of it pretty easily now. I think I was just over thinking which springs were pulling where.
 

Related Threads for: Hooke's law sanity check

  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
5
Views
2K
Replies
1
Views
4K
Replies
3
Views
1K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
4
Views
2K
Top