Conserved kinetic energy in collisions in different frames

In summary, to show that in the non-relativistic case, if kinetic energy is conserved in a collision as viewed in one frame, then it is conserved in all other frames moving with constant velocity, one can start by stating the equation for conservation of momentum as observed from a stationary frame. This can then be modified to represent conservation of momentum from the perspective of a moving frame. By expanding the terms on both sides and using simple algebra, one can see that the equation for conservation of momentum in the new frame is m1u1'+m2u2' = m1v1'+m2v2'. To show conservation of energy, one can substitute u1'+Vcm into the energy equation and expand.
  • #1
bon
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Homework Statement



How do you show that in the non-relativistic case, if KE is conserved in a collision as viewed in one frame, then it is conserved in all other frames moving with constant velocity?



Homework Equations





The Attempt at a Solution



Not sure what to do...

thanks
 
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  • #2


bon said:
Not sure what to do...
thanks

Perhaps start by stating the equation for (non-relativistic) conservation of momentum as observed from a stationary frame. Then modify that equation such that it represents conservation of momentum from the perspective of a (non-relativistic) moving frame.

Then a little algebra will show you to the light. :cool:
 
  • #3


Hmm so m1(u1' + Vcm) + m2(u2' + Vcm) = m1(v1' + Vcm) + m2(v2' + Vcm)

How does this help?

thanks
 
  • #4


Hello bon,

bon said:
Hmm so m1(u1' + Vcm) + m2(u2' + Vcm) = m1(v1' + Vcm) + m2(v2' + Vcm)

How does this help?

thanks

That's a great start! :approve:

Now is where the simple algebra fits in. Multiply m1 and m2 through their factors, and you should see what I mean.

[Edit: What I mean by that is expand the terms on both sides of the equation. See what cancels out.]
 
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  • #5


Ok cool so i see m1u1'+m2u2' = m1v1'+m2v2'

i.e. consv of momentum in new frame...Now need to get consv. of energy..

should i subsstitute u1'+Vcm into energy equn and expand?
 
  • #6


edit: yes that works!
 

FAQ: Conserved kinetic energy in collisions in different frames

What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is a scalar quantity and is dependent on an object's mass and velocity.

What is conserved kinetic energy in collisions?

Conserved kinetic energy in collisions refers to the principle that in an isolated system, the total kinetic energy of the system remains constant before and after a collision between objects. This means that the kinetic energy lost by one object in the collision will be gained by the other object involved.

How does kinetic energy change in different frames of reference?

In an isolated system, the total kinetic energy remains constant in any frame of reference. This means that if one observer measures a certain amount of kinetic energy before a collision, another observer in a different frame of reference will measure the same amount after the collision.

What factors affect the conservation of kinetic energy in collisions?

The conservation of kinetic energy is affected by the type of collision, the masses and velocities of the objects involved, and the presence of external forces such as friction. Inelastic collisions, where kinetic energy is not conserved, occur when some of the energy is converted into other forms, such as heat or sound.

Why is the conservation of kinetic energy important in collisions?

The conservation of kinetic energy is important because it allows us to predict the outcomes of collisions and understand the behavior of objects in motion. It also follows the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted into different forms.

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