Explain what is meant by the ultimate tensile strength of a material.
An acrobatic platform is suspended by steel wires of the same length. Each wire has a uniform cross-section and a diameter of 3.00 mm.
A group of engineers investigate how the extension x x\,x varies with applied force F F\,F for one of the wires. The results of the investigation are shown in the force-extension graph below.
The wire breaks when the force is 2.1 kN2.1\text{ kN}2.1 kN.
Describe how a suitable measuring device may have been used by the engineers to demonstrate that the wire had a uniform cross-section.
Use the graph to determine the force constant k k\,k in N m−1\text{N m}^{-1}N m−1 of the wire.
Determine the breaking stress σ \sigma\,σ of the wire. Assume that the cross-sectional area of the wire remains constant during the test.
Explain why the work done on the wire when its extension changes from 3.0 mm to 4.0 mm is greater than when its extension changes from 1.0 mm to 2.0 mm.
