Relationship between momentum,KE and internal energy

[something_about]

hello

I just realized I'm having some trouble figuring out the relationship between conservation of momentum and kinetic energy and internal energy in isolated system.

We learned that total momentum gets conserved if two object collide in isolated system.

But when learning about energies they tell you that if collision is not elastic then part of kinetic energy will get transformed into internal energy. So if collision is elastic, then first object will give certain amount of its energy via work to second object

before

KE of O1= 10
KE of O2= 4
total KE = 14

and after collision

KE of O1 = 8
KE of O2 =6
total KE =14

But if collision is not elastic then KE transformed into internal energy is for example W(internal)=2

If that is the case then total KE available to objects O1 and O2 in isolated system is merely KE - W(internal)=12.

So how can momentum get conserved?

thank you

 

[Astronuc]

In elastic collisions, both momentum and kinetic energy are conserved.

In inelastic collisions, momentum is conserved, but not kinetic energy, because some kinetic energy becomes internal energy.

See - http://hyperphysics.phy-astr.gsu.edu/hbase/inecol.html#c1
and - http://hyperphysics.phy-astr.gsu.edu/hbase/elacol.html#c4

I believe by isolated, one is referring to the fact that dispersive agents, e.g. friction, are not involved.

 

[kyle8921]

for your question! The relationship between momentum, kinetic energy, and internal energy can be a bit confusing, but it all comes down to the conservation of energy and momentum in an isolated system. In an isolated system, the total amount of energy (including both kinetic and internal energy) and momentum must remain constant.

When two objects collide, their total momentum must be conserved. This means that the sum of their individual momentums before the collision must be equal to the sum of their individual momentums after the collision. This is true for both elastic and inelastic collisions.

In an elastic collision, the total kinetic energy of the system is conserved. This means that the sum of the individual kinetic energies of the objects before the collision must be equal to the sum of their individual kinetic energies after the collision. In your example, the total kinetic energy of the system remains at 14 before and after the collision, even though the individual kinetic energies of the objects have changed.

In an inelastic collision, some of the kinetic energy is converted into internal energy, as you mentioned. This means that the total kinetic energy of the system decreases, but the total energy (including internal energy) remains constant. In your example, the total kinetic energy decreases from 14 to 12, but the total energy remains at 14.

So, in an isolated system, the conservation of momentum and energy are both important. Even though the total kinetic energy may change in an inelastic collision, the total energy (including both kinetic and internal energy) remains constant. This allows for the conservation of momentum to still hold true. I hope this helps clarify the relationship between momentum, kinetic energy, and internal energy in an isolated system.