Question

A man weighing 800 N is hanging from a 2 mm diameter titanium wire with a cross-section of 3 x 10^-6 m^2. Will the wire break?

Answer 1

Since stress is greater than ultimate strength, the wire will break.

Explanation:

The titanium wire is experimenting an axial load. Ultimate strength equals
`2.20* 10^(8)\,Pa`. The wire shall break if and only if stress is at least equal to ultimate strength. The equation for axial stress (
`\sigma`), measured in pascals, in the wire with circular cross-section is:

`\sigma = (4\cdot F)/(\pi\cdot D^(2))` (1)

Where:

`F` - Axial force, measured in newtons.

`D` - Cross-section diameter, measured in meters.

Please notice that axial force is the weight of the man hanging from wire.

If we know that
`F = 800\,N` and
`D = 0.002\,m`, then the axial stress experimented by the titanium wire is:

`\sigma = (4\cdot (800\,N))/(\pi\cdot (0.002\,m)^(2))`

`\sigma \approx 2.546* 10^(8)\,Pa`

Since stress is greater than ultimate strength, the wire will break.