Answer:
Since stress is greater than ultimate strength, the wire will break.
Step-by-step explanation:
The titanium wire is experimenting an axial load. Ultimate strength equals [tex]2.20\times 10^{8}\,Pa[/tex]. The wire shall break if and only if stress is at least equal to ultimate strength. The equation for axial stress ([tex]\sigma[/tex]), measured in pascals, in the wire with circular cross-section is:
[tex]\sigma = \frac{4\cdot F}{\pi\cdot D^{2}}[/tex] (1)
Where:
[tex]F[/tex] - Axial force, measured in newtons.
[tex]D[/tex] - Cross-section diameter, measured in meters.
Please notice that axial force is the weight of the man hanging from wire.
If we know that [tex]F = 800\,N[/tex] and [tex]D = 0.002\,m[/tex], then the axial stress experimented by the titanium wire is:
[tex]\sigma = \frac{4\cdot (800\,N)}{\pi\cdot (0.002\,m)^{2}}[/tex]
[tex]\sigma \approx 2.546\times 10^{8}\,Pa[/tex]
Since stress is greater than ultimate strength, the wire will break.
