Pushing force making an angle $$0$$ to the horizontal is applied on a block of weight W placed on a horizontal table. If the angle of friction is ϕ the magnitude of force required to move the body is equal to

Question

Pushing force making an angle $$0$$ to the horizontal is applied on a block of weight W placed on a horizontal table. If the angle of friction is ϕ the magnitude of force required to move the body is equal to

Infinity Learn · Accepted Answer

The situation is shown in fig.From figure, $$tan$$⁡ϕ$$=fRor$$ $$f=Rsin$$⁡ϕ   …(1)The$$ condition for the block $$(just) to move is Fcos⁡θ$$=f=Rtan$$⁡ϕ   …(2)and$$ Fsin⁡θ$$+R=Wor$$ $$R=W$$−Fsin⁡θ   …$$(3)From$$ eqs. $$(2) and (3)Fcos$$⁡θ$$=(W$$−Fsin⁡θ$$)$$tan$$⁡ϕ $$=Wtan$$⁡ϕ−Fsin⁡θ$$tan$$⁡ϕor Fcos⁡θ$$+Fsin$$⁡θ$$sin$$⁡ϕ$$cos$$⁡ϕ$$=Wsin$$⁡ϕ$$cos$$⁡ϕMultiplying by $$cos$$ ϕ, we getFcos⁡θ$$cos$$⁡ϕ$$+Fsin$$⁡θ$$sin$$⁡ϕ$$=Wsin$$⁡ϕFcos⁡$$($$θ−ϕ$$)=Wsin$$⁡ϕ$$F=Wsin$$⁡ϕ$$cos$$⁡$$($$θ−ϕ$$)$$

Pushing force making an angle 0 to the horizontal is applied on a block of weight W placed on a horizontal table. If the angle of friction is $ϕ$ the magnitude of force required to move the body is equal to

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Pushing force making an angle 0 to the horizontal is applied on a block of weight W placed on a horizontal table. If the angle of friction is ϕ the magnitude of force required to move the body is equal to

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Pushing force making an angle 0 to the horizontal is applied on a block of weight W placed on a horizontal table. If the angle of friction is $ϕ$ the magnitude of force required to move the body is equal to