Inclined Plane

A cubical block of mass m m is released from rest at a height h h on a frictionless surface of a movable wedge of mass M M , which in turn is placed on a horizontal frictionless surface as shown in the figure.

The magnitude of velocity of the triangular block when the smaller block reaches the bottom is

v=[ambghcoscθ(m+M)(M+msindθ)]e\large v = { \left [ \dfrac{a m^b g h \cos ^{ c }{ \theta } }{( m + M)( M + m\sin ^{ d }{ \theta } )} \right]}^{ e }

Enter your answer as a+b+c+d+e a + b + c + d + e.

DetailsDetails andand AssumptionsAssumptions:

  • aa,bb,cc,dd are positive integers and ee is a positive rational number

  • Velocity is asked when the block reaches the bottom of the incline ( not the horizontal surface).

  • All surfaces of contacts are frictionless.

  • Size of block is negligible compared to size of the incline.

This is a part of my set Aniket's Mechanics Challenges.

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