Is Momentum Conserved in Both Collision Scenarios?

• Westin
In summary: Case (i) and Case (ii) are situations.In summary, the two-cart system has a greater momentum in case (i) than in case (ii) and the momentum of the system is zero in case (ii). This is determined by the fact that in case (i), the system is still moving after the collision, while in case (ii), the system comes to a complete stop. This is in accordance with the law of conservation of momentum.
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]

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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.

ehild said:
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?

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.

Last edited:
Case (i) is non zero and Case (ii) is zero ?

Westin said:
Case (i) is non zero and Case (ii) is zero ?

What is zero? A case has no numerical value.

1. What is momentum?

Momentum is a measure of an object's motion, specifically its mass and velocity. It is calculated by multiplying an object's mass by its velocity.

2. How is momentum related to the motion of two carts?

In the context of two carts, momentum refers to the combined momentum of both carts together. This can be calculated by adding the individual momentums of each cart.

3. What is the law of conservation of momentum?

The law of conservation of momentum states that the total momentum of a closed system remains constant. This means that in the absence of external forces, the momentum of the system before and after an interaction will be the same.

4. How does the mass and velocity of each cart affect their momentum?

The mass of an object has a direct relationship with its momentum - the more mass an object has, the more momentum it will have. The velocity of an object also affects its momentum, as momentum increases with an increase in velocity.

5. How can the momentum of two carts be changed?

The momentum of two carts can be changed by applying external forces, such as pushing or pulling on one of the carts. This can change the velocity and therefore the momentum of the carts.

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