CALC An object moving in the xy-plane is acted on by a conservative force described by the potential-energy function U(x , y) = ?[(1/x2) + (1/y2)], where ? is a positive constant. Derive an expression for the force expressed in terms of the unit vectors

Solution 36E The potential energy is, 1 1 U(x,y) = [ x2+ y ] The force is, F = ( U + U ) x y = [ 2 ] = 2[ + ] 1 x y x y = 2 i + 2 j . x y This is the force in terms of the unit vectors where 2is the x-component of the force and x 2 y is the y-component.