The original force – extension graph is a straight line and so the stress – strain graph will be as well. Since the stress is zero at zero strain then we only need to calculate one point on the graph. The simplest point to calculate corresponds to the maximum force, since we have all the data to hand.
Using the maximum stress and strain we can draw the stress – strain graph.
What is the meaning of the area under the curve now?
The shaded area under the graph is given by:
This means that the area under the curve is equal to the work done per unit volume.
How much force would be needed to achieve the same strain on a cable, 200 m long and 2 cm in diameter, made from the same steel?
How much energy would be needed to achieve this strain?
There are two ways of calculating the answer:
The second method is slightly quicker, requires fewer calculations but more importantly, in engineering figures are normally given as stresses and strains rather than forces and extensions. As a result the numbers can be dropped into a single equation.
Either way, it is not a good idea to stand too close to this cable, since if it were break there would be sufficient energy to accelerate the cable as a whole to well over 300 m s-1, and the end would be moving much faster. You might have experienced this on a small scale if you play a steel stringed guitar. Think how your finger feels when a string breaks when you are tuning, now multiply that up to the size of a trawlers steel hawsers. If these cables break they are quite capable of killing any sailor that gets in the way.