(a) Distinguish between stress and strain as used in elasticity. (b) When a force of 40 N is applied to the free end of an elastic cord, an extension of 5cm...
Question 1 Report
(a) Distinguish between stress and strain as used in elasticity.
(b) When a force of 40 N is applied to the free end of an elastic cord, an extension of 5cm is produced in the cord. Calculate the work done on the cord.
Answer Details
(a) Stress and strain
Stress is the force acting per unit cross-sectional area of the material:
\[ \text{stress} = \frac{\text{force}}{\text{area}} \quad (\text{unit: N m}^{-2}\ \text{or Pa}) \]Strain is the extension produced per unit original length of the material:
\[ \text{strain} = \frac{\text{extension}}{\text{original length}} \quad (\text{no unit, it is a ratio}) \]Thus stress measures the intensity of the applied load while strain measures the relative deformation it produces.
(b) Work done on the cord
For an elastic cord obeying Hooke's law, the work done equals the elastic potential energy stored, given by the area under the force-extension graph:
\[ W = \tfrac{1}{2}Fe \]With \(F = 40\,\text{N}\) and \(e = 5\,\text{cm} = 0.05\,\text{m}\):
\[ W = \tfrac{1}{2}(40)(0.05) = 1.0\,\text{J} \]Download The App On Google Playstore
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