# Simple physics question but is driving me crazy.

Discussion in 'Physics' started by Mvjhoda, Jul 21, 2011.

1. ### Mvjhoda Thread Starter New Member

Jul 13, 2011
4
2
Why is momentum conserved in a one dimentional collision of two objects that lose energy after the collision?
Kinetic energy gets lost because of a loss of velocity, and momentum is proportional to velocity.

2. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
789
I guess it depends on whether you accept conservation of momentum (within a given frame of reference) as fundamental or not.

Jul 7, 2009
1,585
142
For one of the best reasons we know of: it is observed experimentally. Energy is also conserved, but in inelastic collisions you just have to widen your definition of energy a bit and include the internal energies of the bodies when you have deformations.

As to why this is true, nobody knows. It happens to be the way our universe appears to work. If you go on in studying technical stuff, you might get exposed to a beautiful mathematical theorem relating symmetries to conservation laws (also called invariances) called Noether's Theorem. You'll find that linear momentum conservation is associated with an invariance with respect to where things happen in space. If Moe smacks Curly's head in Cleveland, it recoils in exactly the same fashion as if he had done it in Canberra. Or, for that matter, in a galaxy 1e25 m thataway, at least as far as we can tell. This seems to be a property of the universe we live in and the mathematics we use to describe it. Does this give any deeper insights? I dunno -- I studied this stuff as an undergrad a long time ago and no doubt some theoreticians have managed to confangle it up even more cryptically in dense 75 page journal articles, but I'm unaware of any really new physical insights, correspondences, or ramifications.

4. ### samuelsun New Member

Nov 3, 2010
10
0
Hi, look at law of conservation of momentum...

5. ### Tesla23 Senior Member

May 10, 2009
359
78
Conservation of momentum of a system of objects in the absence of an external force is a simple consequence of Newton's third law.

The momentum of a system of objects is:

$\mathbf{p}= \sum_{i = 1}^n m_i \mathbf{v}_i = m_1 \mathbf{v}_1 + m_2 \mathbf{v}_2 + m_3 \mathbf{v}_3 + \cdots + m_n \mathbf{v}_n\,,$

$\frac{\delta \mathbf{p}}{\delta t}= \sum_{i = 1}^n m_i \frac{\delta \mathbf{v}_i}{\delta t} = \sum_{i = 1}^n m_i \mathbf{a}_i = \sum_{i = 1}^n \mathbf{F}_i = 0$

As there are no external forces, the internal forces may be broken down into in equal and opposite pairs (for every action there is an equal and opposite reaction), and so the internal forces sum to zero. Hence momentum is conserved.