Particle a has mass m, is initially located on the positive x axis at x = x0 and

Question

Particle a has mass m, is initially located on the positive x axis at x = x0 and is subject to a repulsive force Fx from particle b. The location of particle b is fixed at the origin. The force Fx is inversely proportional to the square of the distance x between the particles. That is, F x = A/x2, where A is a positive constant. Particle a is released from rest and allowed to move under the influence of the force. Find an expression for the work done by the force on a as a function of x. Find both the kinetic energy and speed of a as x approaches infinity.

Explanation / Answer

W = F.dx = (A/x2).dx = -A/x

integration is from x0

W = -A/x - (-A/x0) = A/x0 - A/x

K() = A/x0

v() = (2K/m) = (2A/mx0)

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