# Elongation due to tensile forces on a cylindrical object

I have been presented with the following problem. I think that I'm okay with calculating the stress and strain, but am unsure on how to tackle the elongation. I think we would need to assume that the tensile force is constant, but I'm not entirely sure of this. Would you be able to point me in the right direction?

Question 1 Consider a cylindrical copper rod with a diameter of 0.8 cm and length of 10.2 cm. A tensile force is applied to the rod of 50 N. Find: a) The stress in the rod b) The rod’s strain c) The elongation of the rod

• Yes, the tensile force is constant on both ends, as you hole a rod with two hands and stretch it. In order to maintain structural equilibrium, each hand will have to exert an equal amount of force.
– r13
Jul 31 at 2:18

The elongation is by definition

$$\delta= \frac{\sigma L}{E} = \frac{(T/A)L}{E}$$

• T is tension

• A area

• L length

Usually in problems like that you don't have enough information to assume anything else apart from uniformity throughout the cross section.

Additionally if you make the assumption that the force is distributed uniformly along the cross section then the shape of the cross section is irrelevant. Only the surface area of the cross section matters.

At that low stress, below the yield strength , there will be no elongation. Only elastic strain.

• Where there's strain, there's elongation. I think you're thinking about permanent, plastic elongation, but the deformation under elastic stresses can still be called "elongation," if only temporary.
– Wasabi
Aug 1 at 1:11
• It can be called elongation , but it is elastic strain. Aug 1 at 1:20