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## Work & Energy Chapters 7-8

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**Work & EnergyChapters 7-8**Work Potential Energy Kinetic Energy Conservation of Mechanical Energy**7-1 Work Done by a Constant Force**The definition of work, when the force is parallel to the displacement: (7-1) SI unit: newton-meter (N·m) = joule, J**7-1 Work Done by a Constant Force**If the force is at an angle to the displacement: (7-3)**7-1 Work Done by a Constant Force**If there is more than one force acting on an object, we can find the work done by each force, and also the work done by the net force: (7-5)**7-3 Work Done by a Variable Force**If the force is constant, we can interpret the work done graphically:**7-3 Work Done by a Variable Force**If the force takes on several successive constant values:**7-3 Work Done by a Variable Force**The force needed to stretch a spring an amount x is F = kx. Therefore, the work done in stretching the spring is (7-8)**7-2 Kinetic Energy and the Work-Energy Theorem**After algebraic manipulations of the equations of motion, we find: Therefore, we define the kinetic energy: (7-6)**7-2 Kinetic Energy and the Work-Energy Theorem**Work-Energy Theorem: The total work done on an object is equal to its change in kinetic energy. (7-7)**7-4 Power**Power is a measure of the rate at which work is done: (7-10) SI unit: J/s = watt, W 1 horsepower = 1 hp = 746 W**8-1 Conservative and Nonconservative Forces**Work done by gravity on a closed path is zero:**8-1 Conservative and Nonconservative Forces**Work done by friction on a closed path is not zero:**8-2 The Work Done by Conservative Forces**Gravitational potential energy:**8-2 The Work Done by Conservative Forces**If we pick up a ball and put it on the shelf, we have done work on the ball. We can get that energy back if the ball falls back off the shelf; in the meantime, we say the energy is stored as potential energy. (8-1)**8-2 The Work Done by Conservative Forces**(8-4) Springs:**8-3 Conservation of Mechanical Energy**Definition of mechanical energy: (8-6) Using this definition and considering only conservative forces, we find: Or equivalently: