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6. Let F : Rn → Rn, n 1, 2, 3, , be a conservative force. Suppose that a mass m is moving in Rn under the influence of F according to Newtons second law of motion, F ma. Show that the total mechanical energy of the mass, E(t), is constant in time over its trajectory x(t). (You will, of course, have to define Et),) Be sure that you denote all vector quantities as vectors, e-g, or z, and dot products appropriately, e.g., u.v.
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