Question

A cable stretches by an amount d when it supports a crate of mass M. The cable is then cut into three equal pieces. If the same crate is supported by any one of these pieces, by how much will the cable stretch?

Answer 1

Hooke's law is:

$$\epsilon=Y\sigma$$

Axial strain is:

$$\epsilon=\frac{\Delta l}{l}$$

Axial stress:

$$\sigma=\frac{F}{A}$$

So, if the area of the cable and mass of the crate (i.e. the force) remain the same, then the stress in the cable is constant. If the new length is one third the original length, then the deflection must be one third that of the original.

Answer:

$$\Delta l=\frac{d}{3}$$