Is Momentum Conserved in Both Collision Scenarios?

[Westin]

Homework Statement

Two identical carts A and B roll down a hill and collide as shown in the figure below.

i) A starts from rest. It rolls down and collides head-on with B which is initially at rest on the ground. The two carts stick together.

ii) A and B are at rest on opposite sides of the hill. They roll down, collide head-on and stick together.[/B]

Which statement is true about the two-cart system just after the carts collide in the two cases?

Select all that are True.
The momentum of the system is zero in case (ii).
The momentum of the system is the same in both cases (but no zero).
The momentum of the system is greater in case (ii) than in case (i).
The momentum of the system is greater in case (i) than in case (ii).

Homework Equations

Conservation of Momentum[/B]

The Attempt at a Solution

I believe the answer is #1 and #4 are true. The momentum of the system is greater in case (i) than in case (ii) because case (i) is still moving unlike case (ii).

I believe the momentum is zero in case (ii) because it started from rest ad ended at rest[/B]

 

[ehild]

It is correct in principle, but not a "case" is moving, and not the "momentum" is in rest. The momentum can have some value, zero or not zero.

 

[Westin]

It is correct in principle, but not a "case" is moving, and not the "momentum" is in rest. The momentum can have some value, zero or not zero.

So you're saying we don't know if the momentum is zero or nonzero so I'm wrong?

 

[ehild]

You know if the final momentum of the whole system is zero or not zero. The answer "#1 and #4 are true" is correct. What is wrong is "because case (i) is still moving unlike case (ii)". Use proper subject in the sentence.

 

[Westin]

Case (i) is non zero and Case (ii) is zero ?

 

[ehild]

Case (i) is non zero and Case (ii) is zero ?

What is zero? A case has no numerical value.