An object is attracted toward the origin with a force given by ?Fx? = ??k?/?x?2. (Gravitational and electrical forces have this distance dependence.) (a) Calculate the work done by the force ?Fx? when the object moves in the ?x?-direction from ?x?1 to x?2. If ?x?2 > ?x?1, is the work done by ?Fx? positive or negative? (b) The only other force acting on the object is a force that you exert with your hand to move the object slowly from ?x?1 to ?x?2. How much work do you do? If ?x?2 > ?x?1, is the work you do positive or negative? (c) Explain the similarities and differences between your answers to parts (a) and (b).
Solution 71P Step 1: a) If a force “F” is applied between two positions x and x of an object, then the work 1 2 done between these points will be, x 2 W = F.dx x1 2 Provided, F = - k /x Substituting this value in the equation, x 2 2 W = (k/x ).dx x1 W = [k/x k/x ] 2 1 If x2>x1, then W will be negative as per the solution which we are getting. Step 2: 2 b) The force exerted by the hand will be, F ’ = k/x x2 2 The work done will be, W = (k/x ).dx x 1 W = [k/x k/x ], [ Integral of (k/x ) is (-k/x)] 1 2 If x2>x1, then, the work done will be positive if we are moving the object from x to x 1 2 using our hand.