First slide
Friction on horizontal surface
Question

A block placed on a horizontal surface is being pushed by a force F making an angle θ with the vertical. The coefficient of friction between block and surface is μ. The force required to slide the block with uniform velocity on the floor is:

Moderate
Solution

For vertical equilibrium of the block:

  R = F cos θ + mg-------------(i)

While for horizontal:

    F sin θ = μR-----------(ii)

From (i) and (ii),

F sin θ = μ(F cos θ + mg)

or F = μmg(sin θ - μ cos θ)

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