# Hooke's law sanity check

• bmxicle
In summary, four springs with a mass on each end are connected in series with all masses being equal to m, spring length of 1, and spring constant k. The problem is to find the extension of each spring. By labeling each spring extension as y_1, y_2, y_3, and y_4, and using the equilibrium equation of 0 = ky_2 - ky_3 - mg, the problem can be easily solved by rewriting the variables in terms of m, k, and g.

## Homework Statement

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

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m1
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m2
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m3
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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.

f = ky

## The Attempt at a Solution

So basically if i label each spring extension as $$y_1, \ y_2, \ y_3, \ y_4$$ 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:

$$0 = ky_2 - ky_3 -mg$$

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.

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?

bmxicle said:
... 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:

$$0 = ky_2 - ky_3 -mg$$
Yes, you are on the right track.

Thanks, I can solve the rest of it pretty easily now. I think I was just over thinking which springs were pulling where.