Answer:
The modulus of resilience is [tex]3.028\times 10^{6}[/tex] joules per cubic meter.
Explanation:
At first we assume that allow behaves elastically, then the formula for the modulus of resilience ([tex]U_{r}[/tex]), measured in joules per cubic meter, is:
[tex]U_{r} = \frac{\sigma_{y}^{2}}{2\cdot E}[/tex] (Eq. 1)
Where:
[tex]\sigma_{y}[/tex] - Yield strength, measured in pascals.
[tex]E[/tex] - Modulus of elasticity, measured in pascals.
If we know that [tex]\sigma_{y} = 805\times 10^{6}\,Pa[/tex] and [tex]E = 107\times 10^{9}\,Pa[/tex], then the modulus of resilience is:
[tex]U_{r} = \frac{(805\times 10^{6}\,Pa)^{2}}{2\cdot (107\times 10^{9}\,Pa)}[/tex]
[tex]U_{r} = 3.028\times 10^{6}\,\frac{J}{m^{3}}[/tex]
The modulus of resilience is [tex]3.028\times 10^{6}[/tex] joules per cubic meter.
