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Potential Energy and Conservation of Energy

Potential Energy and Conservation of Energy - the...

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Potential Energy and Conservation of Energy In conservative systems, we can define another form of energy, based on the configuration of the parts of the system, which we call potential energy. This quantity is related to work, and thus kinetic energy, through a simple equation. Using this relation we can finally quantify all mechanical energy, and prove the conservation of mechanical energy in conservative systems. Conservation of Mechanical Energy We have just established that ΔU = - W , and we know from the Work- Energy Theorem that ΔK = W . Relating the two equations, we see that ΔU = - ΔK and thus ΔU + ΔK = 0 . Stated verbally, the sum of the change in kinetic and potential energy must always equal zero. By the associative property, we can also write that: Δ ( U + K ) = 0 Thus the sum of U and K must be a constant. This constant, denoted by E, is defined as the total mechanical energy of a conservative system. We can now generate a mathematical expression for
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Unformatted text preview: the conservation of mechanical energy: U + K = E This statement is true for all conservative systems, and thus for all systems in which U is defined. With this equation we have completed our proof of the conservation of mechanical energy within conservative systems. The relation between U, K and E is elegantly simple, and is derived from our concepts of work, kinetic energy, and conservative forces. Such a relation is also a valuable tool in solving physical problems. Given an initial state in which we know both K and U, and asked to calculate one of these quantities in some final state, we simply equate the sums at each state: U o + K o = U f + K f . Such a relation further bypasses our kinematics laws, and makes calculations in conservative systems quite simple....
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