Conservation of Linear Momentum and Inelastic Collisons

[1MileCrash]

I don't understand how inelastic collisions still conserve momentum.

If kinetic energy is not conserved, velocity must change, and the mass obviously doesn't change, how can momentum be conserved? It makes no sense to me at all.

 

[emailanmol]

During collisions (where mass is constant) velocity generally changes .However it changes such that momentum is conserved i.e if one body gains momemtum(increase in velocity along initial direction) the other loses momentum(loss in velocity along initial direction)

So mu+MV is constant where m, M are mass and u and V are velocity vectors at any instance.

During collision u and V can change however the sum mu+MV muat remain constant.

This in no way implies that mu^2/2 +MV*2/2 is constant.

So sum of kinetic energy may or may not remain constant.

For eg: take m =1 M =5
And u1 =3 and V1= 4 (all in SI units)
after collision suppose u2=-2
So V2 has to become 5.

So not only is individual kinetic energy of bodies changing after collisions, the sum of kinetic energies is also changing.

 

[Nugatory]

I don't understand how inelastic collisions still conserve momentum.

If kinetic energy is not conserved, velocity must change, and the mass obviously doesn't change, how can momentum be conserved? It makes no sense to me at all.

Suppose I have two objects, same mass, both at rest. Momentum and kinetic energy is zero.

Now consider the same two objects, but one is moving left at speed u, the other is moving right at speed u. Momentum is still zero (mu + -mu = 0) but the kinetic energy is not zero.

If they collide head-on and stick together (completely inelastic collision) they end up both at rest. Momentum is conserved because it's zero either way. Kinetic energy isn't conserved, but the total energy is conserved; all the pre-collision kinetic energy has turned into heat.

 

[chingel]

Momentum is conserved because of Newton's law, every force has an equal and opposite force. If one object pushes the other for some time with an average force of F, it feel on itself in the other direction the same force F for the same time. Since force is proportional to mass and acceleration, if one is twice the mass of the other, it feels half the acceleration, four times then one fourth etc. Since the acceleration lasts the same time, the velocity times mass stays the same if you consider both of them (eg a five times heavier object's velocity changes five times less, while a five times lighter objects velocity changes five times more, if you multiply momentums together and add them up, they stay the same before and after the collision).

The energy might not be conserved, because as one object collides into the other, it causes deformation and depending on whether the deformation pushes back or stays deformed (increasing heat) the kinetic energy is conserved or not. The momentum is still conserved, because the force needed to cause the deformation is still felt by both of the objects for the same time, but if the deformation is not elastic it uses up some of the potential to do work.

 

[PJC01]

Dear fellow scientist,

I understand your confusion about the concept of conservation of linear momentum in inelastic collisions. However, it is important to note that inelastic collisions do still conserve momentum, even though kinetic energy is not conserved.

In an inelastic collision, the objects involved stick together or deform upon impact, resulting in a loss of kinetic energy. This loss of kinetic energy is typically converted into other forms of energy, such as heat or sound.

While the objects may have different velocities before and after the collision, the total momentum of the system remains constant. This is because momentum is a vector quantity that takes into account both the mass and velocity of an object. So, even though the velocity may change, the mass of the objects remains the same, resulting in a conservation of momentum.

One way to think about it is to consider the law of conservation of energy. In an inelastic collision, the total energy of the system is still conserved, but it is just converted into a different form. Similarly, in an inelastic collision, the total momentum of the system is still conserved, but it is just distributed differently among the objects involved.

I hope this helps to clarify the concept of conservation of linear momentum in inelastic collisions. Please feel free to reach out if you have any further questions or concerns.

Best,