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

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

Infinity Learn · Accepted Answer

See fig.For vertical $$equilibriumR=Fcos$$⁡θ$$+mg$$   …(i)For$$ horizontal motion,Fsin⁡θ−μ$$R=maFsin$$⁡θ$$=$$μR  ...$$(ii)Substituting$$ the value of R from eq. $$(i) in eq. (ii), we get Fsin⁡θ$$=$$μ[Fcos⁡θ$$+mg$$]or Fsin⁡θ$$+$$μFcos⁡θ$$=$$μmg∴ $$F=$$μ$$mg($$$$sin$$⁡θ$$+$$μ$$cos$$⁡θ$$)$$.

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

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