A wire is stretched by 8 mm when a load of 60 N is applied.
What will be the extension of a wire of the same material having four times the cross-sectional
area and twice the original length, when the same load is applied?

Question

A wire is stretched by 8 mm when a load of 60 N is applied.
What will be the extension of a wire of the same material having four times the cross-sectional
area and twice the original length, when the same load is applied?

mathmale · Answer

Overall, this is a problem involving Hooke's Law:  F=kx, where x is the distance a spring of spring constant k is stretched by a force F.  This type of problem usually starts out by providing F and x and expecting you to calculate k.

We can do that here for the original wire.  Find k.

Now the wire material stays the same, but the wire radius changes (by what factor and why?).  And the wire is now twice as long.  We need to figure out how this is going to affect the spring constant, k.

Anyone want to brainstorm on that?