Homework Help: 3 identical springs hanging from ceiling

1. May 6, 2006

FlipStyle1308

I got the following problem wrong, and don't know why, so hopefully somebody would be able to help me out!

Three identical (massless) springs are hung from the ceiling.
Spring 1: Nothing hung from spring. The spring's bottom is 0.2 m below the ceiling.
Spring 2: A 7 N object is hung from the spring. The spring's bottom is 0.5 m below the ceiling.
Spring 3: An object of unknown weight is hung from the spring. The spring's bottom is 1 m below the ceiling.

a. Find the spring constant that each spring has.
b. Find the weight of the unknown object.

For A, I used k = 4pi^2(0.7143)/1. I got 0.7143 as my mass by using F=ma, and I used 1 for T, since no time or frequency was given for either of the 3 springs. I guess since part A was wrong, that answer led to my answer for part B to be wrong also.

2. May 6, 2006

nrqed

You are using the wrong equation. That equation can only be used when the mass is oscillating!!!!

And I have no idea how you got your mass!

No, use that at equilibrium, k x = mg. You then find the spring constant from spring 2. Since they are identical, they all have the same k.
Now use that equation again to find the mass for spring 3 (the answer will be obvious)

3. May 6, 2006

FlipStyle1308

I got the same answer I had before. 14? Or should it be -14?

4. May 6, 2006

nrqed

14 N/m is the correct answer (k is never negative). Are you saying this is the wrong answer?

EDIT: Wait, I had not noticed the 0.2 meter of spring 1. So you must use a distance of 0.3 m, not 0.5m in the equation!

5. May 6, 2006

FlipStyle1308

Oh, so it's the distance below the original location of the spring without a mass?

6. May 6, 2006

nrqed

Yes. In the equation kx = mg, the x represents the *extra stretch* of the spring when the mass is attached as compared to when there was no mass at all.

7. May 6, 2006

FlipStyle1308

So 23.3 = k, and the weight of the unknown object is 18.64?

8. May 6, 2006

FlipStyle1308

Never mind, it's correct, thanks!