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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
(1)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
(4)
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