Show that impulse of a variable force is equal to area enclosed by for

1.	Show that impulse of a variable force is equal to area enclosed by force time curve
Answer» A\xa0variable force\xa0is a force whose magnitude or direction or both vary during the displacement of a body on which it acts or a\xa0force\xa0whose\xa0direction\xa0or\xa0magnitude\xa0or\xa0both\xa0change\xa0with\xa0time.\xa0The graphical representation is given as:Consider a small displacement element\xa0{tex}\\Delta s{/tex}\xa0under force F, which is represented by a strip KLMN. As the displacement {tex}\\Delta{/tex}s is extremely small, hence force F for entire strip KLMN may be taken as constant.Therefore,\xa0Work done during elementary expansion will be equal to{tex}\\Delta W =F\\Delta x{/tex}= area of strip KLMN ....................................(A)Total work done by the variable force can be calculated by dividing the whole path into such elementary parts and in each case the work done will be equal to area of small shaded strips like KLMN. Therefore, total work done for a given displacement is given by:W = {tex}\\sum \\Delta W=\\sum{/tex} area of various strips = total area under F-s graph .......................................(B)Thus, the work done by a variable force is given by the area under F-s curve.

Show that impulse of a variable force is equal to area enclosed by force time curve