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(iv) Tension in the string of, , a simple pendulum is always Bor., , perpendicular to the ms, , displacement of the bob so, , work done by the tension is YS), , always zero. Oey, $, , 5. 10.6 Work done by Tension, , , , 106 \, Let us consider a variable force F which is acting on a box, along the X -axis. The magnitude of force F depends on x. Due, to this force body moves from position.x, tox2. In order to find, out the work done by the force F in moving the body from.xj to, x2, we plot a graph between F and x as shown in Fig. 10.7., , , , , , , , F(x), , ‘Work, , , , , , , , °, , x %, (b), Work done by a variable force, , The total displacement from x; tox can be divided into a, large number of small equal intervals Ax. During a small, displacement Ax, the force F can be assumed to be constant., Then the work done AW will be approximately equal to the, product of F and Ax, , AW = F -Ax = Area of rectangular strip ABCD, , Adding areas of all the rectangular strips we get the total, work done as, , , , , , Physics, , , , , , , , , , s F Ax = Sum of areas of all rec, a x, from xy 10.2, , Tnthetimit when Ax -> 0, the work done, , a, W = lim Ax, A240, , Hence, for a varying force the work dor, , : i ¥, , force over the given displacen, em : A force F =(10, direction, where F is in newton and y, , this force dur, during, , definite integral of the, ag 0.50.) acts ong, , , , particle in, metre. Fine the work done by, , displacement from x = 0to.x =2m., , : Given F = (10 +0.50x), , , , , , , , , , Total work done, W=[ ~ Fax, , W =|10x +050% 102-0), * 0), , W =20+1=21 joule, , , , , , A force is said to be conservative if work done by, , against) the force in moving a body depends only upontit, , initial and final positions of the body and is independeati, , the path followed for going from initial to the final posits, _ Suppose a body moves from initial point A to the fa!, , point B through three different paths 1, 2 and 3. lf, , Conservative force acts on the body then mathematically, , W=Wy =W;, , , , , , , , Ses