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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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