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Homework Statement
A block of mass ##m## slides down a wedge of mass ##M## and inclination ##\theta## whose surfaces are all frictionless. Find the velocity of the block when it just reaches the bottom of the wedge.
Homework Equations
The Attempt at a Solution
I was told that to solve this problem, we have to apply the concepts of Relative Velocity (between the block and the wedge), Conservation of Mechanical Energy, and Conservation of Linear Momentum. However, I've got a few doubts regarding the conservation of Linear Momentum.
I know that we can conserve Linear Momentum in any direction as long as the net external force is ##0## in that direction. Now, the given method states that for the system ##Earth+Block+Wedge## I can conserve Linear Momentum in the ##X## direction ONLY. However, I fail to understand why we cannot conserve Linear Momentum in the ##Y## direction too. As per the FBD's I've made, the forces acting on the Wedge are the Normal force ##N_1## due to the Earth, and the Normal force ##N_2## due to the block. Also, the forces acting on the block are ##N_2## due to the wedge. The reaction force acting on the Earth is ##N_3## due to the wedge.
Thus, the forces operating on the system ##Earth+Wedge+Block## are Internal Forces. Hence the Net External Force is ##0##.
Thus, can't we apply Conservation of Linear Momentum in the ##Y## direction too? If so, could somebody kindly show me how to? Many thanks in advance!
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