A 2500 N force stretches a wire by 1 mm. A second wire of the same material is twice as long and has twice the diameter. How much force is needed to stretch the second wire by 1 mm?

Question

A 2500 N force stretches a wire by 1 mm.  A second wire of the same material is twice as long and has twice the diameter.  How much force is needed to stretch the second wire by 1 mm?

anonymous · Answer

Since the wire is twice as long, the force will be half of the original, but since the area of the section of the wire was increased: A=pi(2r)^2=4pi r^2=4A0 the force then is increased by a factor of 4.
Finally: F=4F0/2=2F0, in your case F=5000N