Same old block on the floor problem

A block of mass \(m\) is placed on a rough horizontal floor at position \(A\). This block is to be moved to position \(B\) under the application of a force of constant magnitude \(F\), acting on the block. Find the minimum time (in seconds) for which this force should act on the block so that it just reaches \(B\). Round your answer to the nearest integer.

Details and Assumptions

  • Consider the block as a point object and it is always in contact with the floor.
  • \(m=5 \text{ kg}\), \(F=100 \text{ N}\), \(\overline{AB}=l=1900 \text{ m}\).
  • Acceleration due to gravity: \(g=10\text{ m/s}^{2}\).
  • Coefficient of friction: \(\mu = 0.5\).

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