First slide
Friction on horizontal surface
Question

A block of mass m, 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 the surface is µ. The force required to slide the block with uniform velocity on the floor is

Easy
Solution

See fig.

For vertical equilibrium

R=Fcosθ+mg   …(i)

For horizontal motion,

FsinθμR=maFsinθ=μR  ...(ii)

Substituting the value of R from eq. (i) in eq. (ii), we get

 Fsinθ=μ[Fcosθ+mg]or Fsinθ+μFcosθ=μmg F=μmg(sinθ+μcosθ).

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