# Impulse and Momentum Conservation for a Frictionless Cart

• Nelson2436
In summary, the wall has no velocity and no momentum, unless the vibrations caused by the collision are considered.
Nelson2436

## Homework Statement

A 2 kg frictionless cart with a velocity of 6 m/s hits a wall and rebounds with a velocity of 4 m/s. What is the impulse on the cart by the wall? Is momentum conserved?

J = Δp

## The Attempt at a Solution

J = Δp = pf-pi = mvf-mvi = 2kg (-4m/s -6m/s) = -20 kgm/s

I think I solved the part for the impulse correctly but needed some help with the reasoning for the second part of the question. I think that the momentum would not be conserved in this case because there is an impulse so there's a net force on the system. On the other hand the system is not defined so the momentum can be conserved if the system is considered to be both the cart and the wall, since the wall would experience an impulse from the cart. Which line of reasoning is correct?[/B]

You are correct. The system is not defined so both arguments you make are valid. Who knows what the question setter intended.

Nelson2436
Nelson2436 said:
On the other hand the system is not defined so the momentum can be conserved if the system is considered to be both the cart and the wall, since the wall would experience an impulse from the cart.
Okay, what is the velocity of the wall? What is the momentum of the wall?

Nelson2436
insightful said:
Okay, what is the velocity of the wall? What is the momentum of the wall?
The wall has no velocity and no momentum, unless the vibrations caused by the collision are considered. So does that mean that momentum is not conserved because there's an impulse?

Nelson2436 said:
The wall has no velocity and no momentum, unless the vibrations caused by the collision are considered. So does that mean that momentum is not conserved because there's an impulse?

To have conservation of momentum, you must take into acccount not just the wall but what it is attached to - probably the Earth.

These questions that ask whether momentum is conserved make no sense. Momentum is always conserved in a collision, as long as you consider all objects involved. It would be better to ask "discuss conservation of momentum in this case".

Nelson2436
PeroK said:
These questions that ask whether momentum is conserved make no sense. Momentum is always conserved in a collision, as long as you consider all objects involved. It would be better to ask "discuss conservation of momentum in this case".
I would suggest that one does not tell a teacher or professor that their question makes no sense. Many times it is the solver's job to make sense of the problem. Otherwise agree.

OP, you need to convince yourself that the momentum of the wall and therefore the Earth changes in this problem.

Nelson2436

## 1. What is impulse and momentum conservation?

Impulse and momentum conservation is a fundamental principle in physics that states that the total momentum of a system remains constant unless acted upon by an external force. This means that in a closed system, the total momentum before a collision or interaction will be equal to the total momentum after the collision or interaction.

## 2. How does a frictionless cart affect impulse and momentum conservation?

A frictionless cart is a simplified scenario in which the effects of friction are not present. In this scenario, the only external forces acting on the cart are the initial and final impulses, making it easier to observe the conservation of momentum. Since there is no loss of energy due to friction, the total momentum of the cart will remain constant throughout its motion.

## 3. What factors affect impulse and momentum conservation in a frictionless cart?

The key factors that affect impulse and momentum conservation in a frictionless cart include the mass of the cart, the velocity of the cart, and the initial and final impulses acting on the cart. These factors determine the total momentum of the cart and how it changes during collisions or interactions with other objects.

## 4. How is impulse and momentum conservation applied in real-world situations?

Impulse and momentum conservation is applied in various real-world situations, such as in sports, car crashes, and rocket launches. In sports, players use the principle to gain momentum and change directions while running or throwing objects. In car crashes, the conservation of momentum helps engineers design safety features to minimize the impact of collisions. In rocket launches, the conservation of momentum is crucial in achieving the desired velocity and trajectory.

## 5. What are some limitations of using the frictionless cart model?

While the frictionless cart model is a useful tool for understanding impulse and momentum conservation, it is important to note that it does not accurately represent real-world scenarios. In reality, friction is always present, and other external forces such as air resistance and gravity can also affect the motion of objects. Therefore, the results obtained from the frictionless cart model may not be entirely accurate in real-life situations.

• Introductory Physics Homework Help
Replies
1
Views
815
• Introductory Physics Homework Help
Replies
40
Views
3K
• Introductory Physics Homework Help
Replies
24
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
20
Views
2K
• Introductory Physics Homework Help
Replies
19
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
7
Views
1K
• Introductory Physics Homework Help
Replies
8
Views
2K