Conservation of energy In some cases, Newtons second law
Chapter , Problem 69(choose chapter or problem)
Conservation of energy In some cases, Newtons second law can be written mx_1t2 = F 1x2, where the force F depends only on the position x, and there is a function w (called a potential) such that w_1x2 = -F 1x2. Systems with this property obey an energy conservation law. a. Multiply the equation of motion by x_1t2 and show that the equation can be written d dt c 1 2 m1x_1t222 + w1x2 d = d dt c 1 2 mv2 + w1x2 d = 0. b. Define the energy of the system to be E1t2 = 1 2 mv2 + w (the sum of kinetic and potential energy) and show that E1t2 is constant in time.
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