Is a spring longer hanging or flat on a table?

[dav1d]

Homework Statement

Is a spring longer hanging or flat on a table?

Homework Equations

logic.

The Attempt at a Solution

I think the answer would be hanging because then the mass of the spring pulls it down a bit, thus stretching it more than when it is flat.

 

[256bits]

I would agree.
A good example of the type of spring we are talking about is a slinky toy.

 

[dav1d]

But how do I write it using math/formulas.

 

[springwave]

It would be difficult to do that, because the spring must be considered massive, and hence will have different tensions at different points.

But I guess you can prove it if you make an assumption that if any point in the spring has tension, then it is possible only if it is elongated.

Now just divide the spring into two parts, and draw the free body diagram of the bottom part. Now prove that a certain tension must exist at the join point, to keep the bottom part of the spring in equilibrium.

 

[rwisz]

However, this also depends on the tension of the spring and other factors. It would be best to conduct an experiment to accurately determine the length of the spring in both scenarios.