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jehwig0107

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Moved from a technical forum, no template.

I have a problem in mechanics.

On the wedge and block only the gravisational force (mg) is exerted (and there is no friction in this system).

What is asked in the question is the final velocities of the wedge and the block (vB, vK). The velocity of the block is conserved when it reaches at the ground.

Do I need to solve this question with the conservation of momentum and conservation of energy? (this is what the solution tolds me) It seems to me that it is absurd, because if the momentum is conserved, then the total energy is encreased.

When we compare two energies:

1) E just before the separation : 0.5*(mB * vB^2 + mK * vK'^2) = mB * g * h

And when the momentum for horizontal direction is conserved : mB * vB'x - mK * vK' = mB * vB - mK * vK = 0

(vB' is the velocity of Block just before the seperation, and its magnitude is same with vB, the final velocity. vB'x is the horizontal component of vB')

vK is thus greater than vK' (because vB is greater than vB'x)

2) E after the separation : 0.5*(mB * vB^2 + mK * vK^2) > mB * g * h (1)

Therefore the total energy is not conserved if the horizontal momentum is conserved.

Am I wrong?