How much does each sample stretch by?
(Take g as 9.8 N kg-1 and the Young’s Moduli of steel and rubber as 210 GPa and 0.1 GPa respectively)
Rearranging we get:
For all three samples:
For the metal samples:
Applying the formula to the different materials:
Steel:
Tungsten:
Rubber:
Calculate the stress and the % strain in each sample.
Stress is given by the force divided by the cross sectional area.
In this question the force is the same for each sample but the cross sectional areas are different.
For the tungsten:
For the steel:
For the rubber:
Strain is given by the extension divided by the original length.
In this question the original length is the same for each sample but the extensions are different.
For the tungsten:
For the steel:
For the rubber:
Which material would you chose to suspend a 10 kg by in practice and why?
Initially the rubber seems an attractive choice, followed by tungsten with steel being the least attractive option. However an engineering solution needs a little more thought.
The two metal wires are very thin and so their weight is insignificant compared to the 10 kg mass that they support. However the rubber bar would have a mass of around 2.3 kg and so it would stretch even further, due to its own weight.
Tungsten is a very expensive metal compared to steel and so an engineer would reject tungsten on cost grounds (rubber would also be rejected on the same grounds).
Of the three materials steel would be by far the most attractive. The only exception would be if the 10 kg mass had to be suspended whilst in a very high temperature environment. Here, tungsten’s high melting point might make it more attractive.
