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Work and Energy Partial Derivatives

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Work The force can be three dimensional.

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Force and Potential Energy Force is the negative of the slope of the potential energy versus position graph.

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Force in 3D Gradient of U

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Problem 1 An electrically charged particle is held at rest at the point x=0, while a second particle with an equal charge is free to move along the positive x- axis. The potential energy of the system is as follows where C is a positive constant that depends on the magnitude of the charges. Derive an expression for the x-component of force acting on the movable charge, as a function of it position

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Potential Energy for Problem 1

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Problem 2 A puck slides on a level, frictionless air-hockey table. The coordinates of the puck are x and y. It is acted on by a conservative force described by the potential-energy function that follows. Derive an expression for the force acting on the puck.

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