Momentum Conservation in Collisions: Equal Mass Carts

Click For Summary

Homework Help Overview

The discussion revolves around the conservation of momentum in collisions, specifically focusing on two carts of equal mass. The original poster questions the implications of equal mass on individual momenta during and after a collision, expressing confusion about the dynamics involved during the collision itself.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the concept of momentum conservation at different stages of a collision, questioning what happens to individual momenta during the collision and whether the carts exchange velocities after the collision.

Discussion Status

Some participants provide insights into the principles of momentum conservation, referencing Newton's laws to support their reasoning. There is an ongoing exploration of conditions under which the carts might exchange velocities, with no explicit consensus reached on the implications of the collision type.

Contextual Notes

The original poster expresses uncertainty about the typical focus on pre- and post-collision scenarios, indicating a potential gap in understanding the dynamics during the collision phase. The discussion also touches on the nature of the collision (elastic vs. inelastic) as a factor in the outcome.

nietzsche
Messages
185
Reaction score
0

Homework Statement



When two carts collide, is momentum conserved at each instant before, during and after the collision? If the carts are of equal mass what happens to their individual momenta during and after the collision?

Homework Equations


The Attempt at a Solution



I'm actually unsure of what the question means. "If the carts are of equal mass what happens to their individual momenta during and after the collision?" During the collision? I'm confused because we normally just consider before the collision and after the collision, leaving out the complex in-between stuff.

As for after the collision, I think the answer is this. If cart 1 is moving at a velocity v relative to cart 2, and cart 2 is at rest, then after the collision, cart 1 will have 0 final momentum relative to cart 2, and cart 2 will have the same initial momentum that cart 1 had. Please correct me if I'm wrong.
 
Physics news on Phys.org
Momentum is conserved at each instant before, during and after a collision. This is why,

1. Before and after a collision Newton's 1st Law holds, "An object will maintain its state of motion unless an unbalanced force acts on it." Each cart experiences no unbalanced force.

2. During the collision momentum is conserved because of Newton's 2nd and 3rd Laws. Cart 1 experiences a force due to Cart 2 and exerts an equal and opposite force on Cart 2 (Newton's 3rd Law.) Now from Newton's 2nd Law, momentum change (impulse) is force times time interval over which the force acts. Since the forces that the carts exert on one another are equal and opposite and act for the same time (as long as the carts are in contact), then the changes in momentum are equal and opposite. This means that their sum is zero, i.e. momentum is conserved. The masses of the carts are irrelevant.
 
Thank you.

So does this necessarily mean that cart 1 will end up with cart 2's initial velocity, and cart 2 will end up with cart 1's initial velocity?
 
No it does not necessarily mean that. The two carts will exchange velocities if (a) the masses are equal and (b) the collision is perfectly elastic.
 
Ah thank you. Makes sense.
 

Similar threads

Momentum: why don't the two carts become one?
  • · Replies 32 ·
2
Replies
32
Views
2K
Explosion of 2 Carts on a Platform (Momentum)
  • · Replies 40 ·
2
Replies
40
Views
5K
Cart/putty collision question (conservation of momentum)
  • · Replies 6 ·
Replies
6
Views
7K
A cart collides with a bumper -- Find the final displacements, etc.
  • · Replies 15 ·
Replies
15
Views
2K
Why Is Momentum Conserved in a Variable Mass System Like a Sand-Laden Cart?
  • · Replies 5 ·
Replies
5
Views
2K
Ambiguous question on momentum and how it works...
  • · Replies 13 ·
Replies
13
Views
1K
Calculate the final velocity of each cart after a collision
  • · Replies 8 ·
Replies
8
Views
5K
Coefficient of Restitution for a Hypothetical Collision where masses are not equal after the collision compared to before the collision
  • · Replies 6 ·
Replies
6
Views
1K
Convert to Center of Mass Reference Frame
  • · Replies 9 ·
Replies
9
Views
1K
Momentum with Two Carts on a Low-Friction Track
  • · Replies 3 ·
Replies
3
Views
5K