A uniform rod of length L and mass Mis
pulled horizontally on a smooth surface with a
force F elongation of the rod of a material of
young's modulus Y is
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PHYSICS
A uniform rod of length L and mass M is pulled horizontally on a smooth surface with a force F. Determine the elongation of rod if Young's modulus of the material is Y.
December 27, 2019avatar
Ashu Utge
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ANSWER
Under the action of the external force, the rod accelerates with a = F/m. The magnitude of stress decreases as one moves away from the point of application of the force.
Therefore, the strain also decreases as one moves towards the free end.
To determine the total elongation of the rod, let us consider a small element of length dx at a distance x from the free end of the rod. The magnitude of force at this section is F' = Fx/L. Therefore, the stress at this Section is
and elongation dδ produced in this differential element is
Thus, total elongation is
answer now you can calculate maintally