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a particle located at the same physical location in a closed loop must have the same kinetic energy

# A particle located at the same physical location in a closed loop must have the same kinetic energy

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a particle located at the same physical location in a closed loop must have the same kinetic energy at all times if it is within a conservative system. This fact is the fundamental definition of a conservative force. Though we will derive other properties of conservative forces from this statement, it remains the most important one to keep in mind. Since the work over a closed loop must be zero for conservative forces, what other properties can we state? Let's break the path of a closed loop into two separate paths: Figure %: a) A closed loop, split into 2 segments. b) Two different paths from point A to point B. Since the path in part a) is a closed loop, we know that the total work around the loop must be zero if the force in question is conservative: W

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Unformatted text preview: 1 + W 2 = 0 . Now compare the two different paths taken from A to B in part b). The work on the first path is the same as part a), simply W 1 . The direction of travel on the second path is reversed in b), implying that the work done over the path is negated, or equal to - W 2 . But we know from a) that - W 2 = W 1 . Thus the work done over path 1 and path 2 in part b) is the same! This concept, called path independence, is incredibly useful, as we will soon see. Stated verbally: The work done by a conservative force in moving a body from an initial location to a final location is independent of the path taken between the two points...
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A particle located at the same physical location in a closed loop must have the same kinetic energy

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