Conservation of Linear Momentum problem help

[wsender]

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.

 

[cupid.callin]

i got the same problem few days back ...
check this: https://www.physicsforums.com/showthread.php?t=479966

 

[Doc Al]

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.

 

[wsender]

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?

 

[Doc Al]

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.

 

[wsender]

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.

 

[Doc Al]

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.