A particle moving along the x axis is acted upon by a single force F = F₀e^-^kx, where F₀ and k are constants. The particle is released from rest at x = 0. It will attain a maximum kinetic energy of:

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Quizplus · Accepted Answer

To find the maximum kinetic energy, we need to find the maximum work done by the force on the particle. This occurs when the force is in the same direction as the displacement of the particle. In this case, the force is given by F = -kx, which is a simple harmonic force with a frequency of w = sqrt(k). Thus, the maximum displacement of the particle is x = A, where A is the amplitude of oscillation. The potential energy of the particle is given by U(x) = (1/2)kx^2, and the initial potential energy is zero since the particle is released from rest at x = 0. At the maximum displacement, the potential energy is U(A) = (1/2)kA^2, and the kinetic energy is K(A) = U(0) - U(A) = (1/2)kA^2. Therefore, the maximum kinetic energy is K(max) = (1/2)kA^2. Since A = F₀/k, we have K(max) = (1/2)k(F₀/k)^2 = F₀/k.

A Particle Moving Along the X Axis Is Acted Upon