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A wedge of mass *M* rests on a horizontal frictionless surface. A point mass *m* is placed on the wedge, whose surface is also frictionless. Find the horizontal acceleration *a* of the wedge.

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Answer

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Let *N* be the normal reaction force, then the Newton equation for the wedge projected on the horizontal axis gives

Consider now the motion of the small mass. Its acceleration is $\bold{a_\perp} + \bold{a_{||}}$. The second term $\bold{a_{||}}$ is along the incline, and so it vanishes if projected on the direction normal to the incline. The corresponding Newton law reads:

(3)Substituting *N* from the first equation and solving for *a*, we get

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