How is momentum conserved in an inelastic collision?

In summary: AZING, no?In summary, momentum is conserved because the force of the collision is exactly equal in magnitude but opposite in direction, so the momentum does not change.
  • #1
II Ziv II
1
0

Homework Statement


This was a test question that I got wrong and it has been bothering me so much. How is momentum conserved in an inelastic collision?


Homework Equations


p = mv
KE = (.5)m(v^2)


The Attempt at a Solution


I know that kinetic energy is not conserved because some of the energy in the collision escape as heat, sound, etc but why is momentum conserved? Shouldn't the system lose momentum because it it losing speed?
 
Physics news on Phys.org
  • #2
There are a number of ways of approaching this. It depends, among other things, on the fact that momentum is a vector while kinetic energy is a scalar.
Two identical objects with the same speed could collide head in and both come to rest and stick together.
In this case, all the kinetic energy has gone. It's also a perfectly inelastic collision.
The momentum situation is different.
The one object, moving from left to right, has momentum mv, but the other, moving right to left, has momentum -mv.
Momentum before is mv + (- mv) [the vector sum takes account of the direction]
the momentum after is zero. (both at rest)
Before = after (both zero) yet you have "lost speed".

You can also argue for conservation of momentum from Newtons 2nd and 3rd Laws.
 
  • #3
Welcome to PF!

Hi II Ziv II! Welcome to PF! :smile:
II Ziv II said:
This was a test question that I got wrong and it has been bothering me so much. How is momentum conserved in an inelastic collision?

I think the answer they want in the exam is good ol' https://www.physicsforums.com/library.php?do=view_item&itemid=26" … total force = rate of change of total momentum.

Since there are no external forces on the colliding bodies, the rate of change of total momentum is zero, ie the total momentum is constant. :wink:
 
Last edited by a moderator:
  • #4
II Ziv II said:
Shouldn't the system lose momentum because it it losing speed?

Speed? We do not work with speed in momentum, we work with velocity.
 
  • #5
II Ziv II said:

Homework Statement


This was a test question that I got wrong and it has been bothering me so much. How is momentum conserved in an inelastic collision?

Homework Equations


p = mv
KE = (.5)m(v^2)

The Attempt at a Solution


I know that kinetic energy is not conserved because some of the energy in the collision escape as heat, sound, etc but why is momentum conserved? Shouldn't the system lose momentum because it it losing speed?
In my view, the best way to explain conservation of momentum is this:

1. [itex]F = dP/dT => dP = Fdt[/itex] (definition)

2. Ball A and ball B collide. The change in momentum of A is the force of B on A multiplied by the time through which it is applied ie. time of contact (I'm over-simplifying - since the force is not constant, you have to take the integral of force x dt) .

3. The change in momentum of B is the force of A on B x time of contact.

4. BUT, the force of A on B is EXACTLY equal to the force of B on A but EXACTLY opposite in direction (Newton's 3rd law). AND, the time through which these forces last is EXACTLY the same for both. So the magnitude of the change in momentum of A is EXACTLY equal to the magnitude of the change of momentum of B and EXACTLY opposite in direction.

AM
 

1. What is momentum and how is it defined?

Momentum is a physical quantity that represents the quantity of motion an object possesses. It is defined as the product of an object's mass and its velocity. The formula for momentum is p = m * v, where p is momentum, m is mass, and v is velocity.

2. What is an inelastic collision?

An inelastic collision is a type of collision in which kinetic energy is not conserved. This means that the total energy of the system before the collision may not be equal to the total energy after the collision. In an inelastic collision, objects may stick together or deform upon impact, resulting in a loss of kinetic energy.

3. How is momentum conserved in an inelastic collision?

In an inelastic collision, momentum is still conserved. This means that the total momentum of the system before the collision is equal to the total momentum after the collision. However, unlike elastic collisions, the kinetic energy of the system is not conserved. Some of the kinetic energy is converted into other forms, such as heat or sound, during the collision.

4. What is the equation for calculating momentum in an inelastic collision?

The equation for calculating momentum in an inelastic collision is the same as the general equation for momentum, p = m * v. However, in an inelastic collision, the mass and velocity used in the equation may be different before and after the collision, as the objects involved may have different masses and velocities.

5. Can momentum be transferred between objects in an inelastic collision?

Yes, momentum can still be transferred between objects in an inelastic collision. This is because momentum is a conserved quantity and must be conserved in any type of collision. However, the amount of momentum transferred may be different from an elastic collision due to the loss of kinetic energy in an inelastic collision.

Similar threads

  • Introductory Physics Homework Help
2
Replies
47
Views
766
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
16
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
810
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
2K
Back
Top