Explain what is meant by the ultimate tensile strength of a material.
A heavy oceanographic sensor package is suspended from a research vessel by high-strength alloy cables of the same length. Each cable has a uniform cross-section and a diameter of 4.00 mm4.00\text{ mm}4.00 mm.
A team of marine engineers investigate how the extension xxx varies with the applied force FFF for one of these cables. The results of their investigation are shown in the force-extension graph below.
Describe how a suitable measuring device may have been used by the engineers to demonstrate that the cable had a uniform cross-section along its length.
Use the graph to determine the force constant kkk in N m−1\text{N m}^{-1}N m−1 of the cable.
Determine the breaking stress σ\sigmaσ of the cable. Assume that the cross-sectional area of the cable remains constant during the test.
Explain why the work done on the cable when its extension changes from 3.0 mm3.0\text{ mm}3.0 mm to 4.0 mm4.0\text{ mm}4.0 mm is greater than when its extension changes from 1.0 mm1.0\text{ mm}1.0 mm to 2.0 mm2.0\text{ mm}2.0 mm.
