A $$5$$ kg rod of square cross section $$5cm$$ on a side and $$1m$$ long is pulled along a smooth horizontal surface by a force applied at one end. The rod has a constant acceleration $$of2m/s2$$ . Determine the elongation in the rod. (Young$$’s modulus of the material of the rod $$is5$$×$$109N/m2$$ $$)

Question

A  $$5$$ kg rod of square cross section $$5cm$$ on a side and $$1m$$ long is pulled along a  smooth horizontal surface by a force applied at one end. The rod has a  constant acceleration $$of2m/s2$$     . Determine the elongation in the rod. (Young$$’s  modulus of the material of the rod $$is5$$×$$109N/m2$$      $$)

Infinity Learn · Accepted Answer

Let the force applied be p: $$thenP=ma=5$$×$$2=10NFor$$ the element shown in the following $$figureT=ml(l$$−$$x)$$×$$a=51(1$$−$$x)$$×$$2=10(1$$−$$x)Elongation$$ in dx is Δ$$(dx)dx=T/AY$$Δ$$(dx)=10(1$$−$$x)(5$$×$$10$$−$$2)2$$×$$15$$×$$109dxTotal$$ elongationΔ$$l=$$∫$$0110(1$$−$$x)25$$×$$10$$−$$4$$×$$15$$×$$109dx=0.4$$×$$10$$−$$6m$$

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A 5 kg rod of square cross section 5cm on a side and 1m long is pulled along a smooth horizontal surface by a force applied at one end. The rod has a constant acceleration of2m/s2 . Determine the elongation in the rod. (Young’s modulus of the material of the rod is5×109N/m2 )

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