Trouble applying the concept of momentum conservation

[vineroon]

I am having trouble applying the concept of momentum conservation to this problem. The particular problem I am having is in figuring out if I did part (c) correctly.

A look at Puck A:

It is evident that total the momentum is conserved before the collision because the external forces acting on the pucks (the normal force exerted by the ground on the puck and the weight of the puck) both add up to zero. Therefore, according to definition, the total momentum is conserved.

However, the specific text I am referencing for this material states that "conservation of momentum means conservation of its components." Yet, the momentum vector before collision is .400i + .300j and the momentum vector after collision is .300i + .400j. The components of these two vectors are not equal, so does that suggest that momentum ISN'T conserved?

Part (c):

Could you assume that if the total momentum is conserved, you can solve for the final velocity of Puck B by setting (m)(v_1x) = (m)(v_2x) and (m)(v_1y) = (m)(v_2y)? This would give you the exact x and y components of initial Puck B velocity, including the signs. However, the magnitude would still remain the same and agrees with the assumption.

Any help would be greatly appreciated.

 

[Rake-MC]

[...]Yet, the momentum vector before collision is .400i + .300j and the momentum vector after collision is .300i + .400j. The components of these two vectors are not equal, so does that suggest that momentum ISN'T conserved?

Momentum is conserved, it's just that some of the momentum has been passed off to the other puck. The net momentum in each dimension will always be the same (in this example).

Part (c):

Could you assume that if the total momentum is conserved, you can solve for the final velocity of Puck B by setting (m)(v_1x) = (m)(v_2x) and (m)(v_1y) = (m)(v_2y)? This would give you the exact x and y components of initial Puck B velocity, including the signs. However, the magnitude would still remain the same and agrees with the assumption.

Any help would be greatly appreciated.

So sum up the total momentum in each plane, subtract final momentum of puck A from this, you get final momentum for puck B.
Take the magnitude of this for final momentum, divide by mass for final velocity.

 

[vineroon]

Momentum is conserved, it's just that some of the momentum has been passed off to the other puck. The net momentum in each dimension will always be the same (in this example).
So sum up the total momentum in each plane, subtract final momentum of puck A from this, you get final momentum for puck B.
Take the magnitude of this for final momentum, divide by mass for final velocity.

Alright, that seems a lot more straightforward. Thanks a lot. :D

 

[Rake-MC]

Not necessarily.
Because both pucks have identical mass, it is infact possible to say that the final velocity of the system in each dimension is the same as the initial. But you cannot simply say the final velocity of each puck is the same as initial (in each dimension).