A uniform elastic plank moves overa smooth horizontal plane due to constantforce F_(0)distributeduniformly over the end face. The surfacearea of the end faceis equalto A and Young.s modulusof the material is Y. Find the compressive strain of the plank in the direction of acting force.

A uniform elastic plank moves overa smooth horizontal plane due to con

1.	A uniform elastic plank moves overa smooth horizontal plane due to constantforce F_(0)distributeduniformly over the end face. The surfacearea of the end faceis equalto A and Young.s modulusof the material is Y. Find the compressive strain of the plank in the direction of acting force.
Answer» Solution :The forceat any SECTIONIS due to inertiabehind the section . The stress therefore INCREASES from zero to MAXIMUM at the endwhere force is APPLIED. Consider a small ELEMENT of lengthdx at a distance x from the free end. The force `F_(x)=ma` `=((M)/(L)x)xx (F_(0))/(M)=(F_(0)x)/(L)` Elongation of the element`dl=(F_(x) (dx))/(AY) =(((F_(0)x))/(L)dx)/(AY)` Total dlongation `Deltal=int_(0)^(L) (F_(0))/(ALY)x dx=(F_(0))/(2ALY)L^(2)(or) Delta l=(F_(0)L)/(2AY)`