Question

A right triangular wedge of mass M and inclination angle θ , supporting a small block of mass m on its side, rests on a horizontal frictionless table, as shown in figure. Assuming all surfaces are frictionless, What horizontal force F must be applied to the system to achieve this result?

Answer 1

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(M+m)gtanθ(M+m)gtan⁡θIn this case M and m are moving with the same acceleration a. Note that a is along x-direction onlyFor M and m :F−N2sinθ=MaF−N2sin⁡θ=Ma--------(1)mg−N2cosθ=0mg−N2cos⁡θ=0⇒N2=mgcosθ⇒N2=mgcos⁡θ------(2)N2sinθ=maN2sin⁡θ=ma------(3)From (2) and (3),a=gtanθa=gtan⁡θSubstitute (3) into (1) obtainsF=(M+m)aF=(M+m)a=(M+m)gtanθ