Conservation of Linear Momentum problem help

AI Thread Summary
The discussion revolves around solving a conservation of linear momentum problem involving a block on a wedge. The user struggles with applying the center of mass (COM) approach due to confusion about momentum conservation in vertical and horizontal directions. It is clarified that momentum can be conserved in one direction while not in another, specifically that horizontal momentum is conserved in this scenario. The user questions their professor's assertion about the necessity of conservation in both directions, which is confirmed to be incorrect. The conversation emphasizes the importance of understanding the conditions under which momentum conservation applies in physics problems.
wsender
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Homework Statement


Having a little trouble with this problem. I've tried a few different manipulations using COM & COE and wasn't able to get it to fit the form.

"A block of mass m rests on a wedge of mass M which, in turn, rest on a horizontal table as shown in the figure. All surfaces are frictionless. If the system starts at rest with point P of the block a distance h above the table, find the velocity of the wedge the instant point P touches the table."



Homework Equations



KE+PE+W=KE+PE

P1=P2

See attached image file for solution and diagram.


The Attempt at a Solution



Tried using COM to solve this but ran into issues in the y direction regarding preservation.
 

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wsender said:
Tried using COM to solve this but ran into issues in the y direction regarding preservation.
If your y direction is vertical, momentum is not conserved in the y direction. (The floor exerts a force.) But the horizontal component of momentum is conserved.
 
Doc,

I worked that out as well and my Professor said that you can't use COM for any parts of the equation if either the X or Y component isn't conserved, is it true?
 
wsender said:
Doc,

I worked that out as well and my Professor said that you can't use COM for any parts of the equation if either the X or Y component isn't conserved, is it true?
No, that's not true. (Perhaps you misheard him.) Momentum is a vector and it can be conserved in one direction but not another, which is the case here. There are no external horizontal forces on the system, so the horizontal component of momentum will be conserved.
 
Doc Al said:
No, that's not true. (Perhaps you misheard him.) Momentum is a vector and it can be conserved in one direction but not another, which is the case here. There are no external horizontal forces on the system, so the horizontal component of momentum will be conserved.

No I definitely didn't mishear him. I brought up this exact point in class and he dispelled is validity. Thank you for confirming my suspicions.
 
You don't have to assume conservation of momentum, it will automatically fall out of the equations from Newton's laws. Give it a shot.
 

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