A ball is thrown up into the air; at the highest point the po- tential energy U is a maximum. Is the derivative of U zero at the highest point? If so, what does this say about the force on the ball at the highest point? If not, then how is U a maxi- mum?
Yes the derivative of U zero at the highest point .In one dimensional conservative system ,the relation between the potential energy and force F is given by
F= -dU/dx
at a point where U has a maximum value the slope of U vs x will be zero so the force will be zero .this implies that a particle at rest will remain at rest but when it is slightly displaced from its equilibrium point the force will tend to push it from equilibrium position and it will be in conservative in nature
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