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A wedge of mass M lies on a smooth fixed wedge of inclination theta. A particle of mass m lies on the wedge of mass M in the figure. All surfaces are frictionless and the distance of the block from the fixed wedge is l. Find. (a) Normal reaction between m and M (b) the time after which the particle will hit the fixed plane. |
Answer» Solution :In the reference FRAME attachedto wedge of mass M the PARTICLE of mass m can only move horizontally.  FBD of wedge of mass M with respect to FBD of particle w.r.t. wedge of mass M ground APPLYING Newton.s `2^(nd)` law of the particle `N+ma_(WQ)SIN theta=mg "" ...(i)` `ma_(wq)cos theta=ma_(mM)""...(ii)` Applying Newton.s `2^(nd)` law for wedge of mass M `N sin theta+mg sin theta=Ma_(wq)"" ...(iii)` Solving (i), (ii) and (iii) we get `a_(wq)=((M+m)g sin theta)/(M+m sin^(2)theta)` `N=(Mmgcos^(2)theta)/((M+m sin^(2)theta))` `a_(mM)=((M+m)g sin theta cos theta)/(M+m sin^(2)theta)` |
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