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Understanding Work and Energy in 3D Systems

Dive into the concept of work and energy in three-dimensional systems. Learn how force and potential energy relate, solve problems involving electrically charged particles and an air-hockey table, and derive expressions for forces in different scenarios.

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Understanding Work and Energy in 3D Systems

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  1. Work and Energy Partial Derivatives

  2. Work • The force can be three dimensional.

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

  4. Force in 3D Gradient of U

  5. 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

  6. Potential Energy for Problem 1

  7. 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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