Box on Two Surfaces

A rectangular box of length \(\frac{2}{3} \text{m}\) is initially traveling at \(2 \text{ m/s},\) 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:

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

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