Spring constant - cut spring in half

[reising1]

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If you cut a spring in half, the constant of each of the new springs is k*2, where k is the original constant of the full length spring.

Does it then follow that if you take 2 springs, both with constant k, and weld them together to make a new spring twice as long, then the constant of the new spring will be 0.5k?

 

[grburst]

If you cut a spring in half, the constant of each of the new springs is k*2, where k is the original constant of the full length spring.

Does it then follow that if you take 2 springs, both with constant k, and weld them together to make a new spring twice as long, then the constant of the new spring will be 0.5k?

Let's say I have two springs, and I already know that both have spring constant k. I weld them together at their edge. Now I have a longer new spring. I don't know what its spring constant is.

Then, I cut that new spring in half at exactly the point where I welded the old two springs together. I have my exact original two springs back with no modifications.

According to your first statement, the spring constant of each of the two springs is K*2, where K is the spring constant of the long spring I just cut. But I already know the spring constant of each of these springs: it's k. Therefore, K*2 = k and K = k/2.

So if your first statement is true, the second statement must be true as well.

 

[reising1]

Let's say I have two springs, and I already know that both have spring constant k. I weld them together at their edge. Now I have a longer new spring. I don't know what its spring constant is.

Then, I cut that new spring in half at exactly the point where I welded the old two springs together. I have my exact original two springs back with no modifications.

According to your first statement, the spring constant of each of the two springs is K*2, where K is the spring constant of the long spring I just cut. But I already know the spring constant of each of these springs: it's k. Therefore, K*2 = k and K = k/2.

So if your first statement is true, the second statement must be true as well.

Well said, thanks.