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A single conservative force F(x) acts on a 1.9 kg particle that moves along an x...

A single conservative force F(x) acts on a 1.9 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is given by U(x) = -4xe-x/6 where U is in Joules and x is in meters. At x = 2 m the particle has a kinetic energy of 7.4 J. (a) What is the mechanical energy of the system? (b) What is the maximum kinetic energy of the particle and (c) the value of x at which it occurs?

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Answer #1

At , kinetic energy of particle is

a) Total mechanical energy is the sum of kinetic and potential energies.

b) The particle will have its maximum kinetic energy when its potential energy is minimum (zero).

c) For the maximum kinetic energy of particle,

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