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Question

In the situation shown in figure, a wedge of mass m is placed on a rough surface, on which a block of equal mass is placed on the inclined plane of wedge. The friction coefficient between the wedge and the block and also between the ground and the wedge is μ. An external force F is applied horizontally on the wedge towards the right, assuming block does not slide on the wedge. Find the minimum value of Force F at which the block will start slipping.

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Solution

N1=mg+mg=2mg N2=mgcosθ+masinθHere, f1 and f2 are the frictional force and force masinθ is pseudo force and acceleration of the system is a F−f1=(m+m)aa=F−2μmg2mIf block start slipping thenmacosθ=mgsinθ+f2macosθ=mgsinθ+μ(mgcosθ+masinθ)a(cosθ−μsinθ)=g(sinθ+μcosθ)a=g(sinθ+μcosθ)(cosθ−μsinθ)F−2μmg2m=g(sinθ+μcosθ)(cosθ−μsinθ)F=2m[μg+g(sinθ+μcosθ)(cosθ−μsinθ)]

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