question_answer

A uniform plank of Young's modulus \[\Upsilon \] is moved over a smooth horizontal surface by a constant horizontal force F. The area of transverse section of the plank is A. Find the compressive strain on the plank in the direction of the force.

Answer:

                As the force at the other end of the plank is zero, so the average stretching force \[=\frac{F+0}{2}=\frac{F}{2}\]                 \[\therefore \]  \[\text{Stress = }\frac{\text{F}}{\text{2A}}\] \[\text{Strain = }\frac{Stress}{\Upsilon }=\frac{1}{2}\frac{F}{A\Upsilon }.\]