Box on Two Surfaces

A rectangular box of length 23m\frac{2}{3} \text{m} is initially traveling at 2 m/s,2 \text{ m/s}, with its entire length over the smooth (perfectly frictionless) blue surface (shown above). The box gradually moves onto a rough surface (gray) and stops the instant that its entire length is positioned within the rough region.

Determine the coefficient of kinetic friction.

Details and Assumptions:

  • g=10 m/s2.g = 10\text{ m/s}^2.
  • The pressure at the bottom of the box is always uniform over its area.

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