In this case, the gradient of work yields WU(Ux, Uy,Uz)F,displaystyle nabla W-nabla U-left(frac partial Upartial x,frac partial Upartial y,frac partial Upartial zright)mathbf F, and the force F is said to be "derivable from a potential." 8 Because the potential U defines a force.This force does zero work because it is perpendicular to the velocity of the ball.
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Just get ready for.Let the mass m move at the velocity v then the work of gravity on this mass as it moves from position r ( t 1) to r ( t 2) is given by W-int _mathbf r (t_1)mathbf r (t_2)frac GMmr3mathbf r cdot dmathbf.The time derivative of the integral for work yields the instantaneous power, dWdtP(t)Fv.