Velocity when two object collide in an elastic collision

[mahela007]

When two objects collide in an elastic collision, aren't there an infinite number of possible velocities that the objects can gain? Let's consider two objects each of mass 1kg. One of them is moving at 1 ms-1 and the other is stationary.
After the collision, the first object (the one which was moving) could come to rest and the other object could start moving at 1 ms-1.
That's one scenario in which the 1st object transfers all it's kinetic energy to the other object.

Couldn't the first object keep some of it's energy and only transfer a fraction of it's total KE to the other object? (In which case both objects would be moving after the collision). If that happens, then couldn't there be a several pairs of values for the velocity of Object 1 and object 2 which would comply with the conservation of momentum and the conservation of kinetic energy? How can we determine which one of these combinations of velocities will occur ?

 

[tiny-tim]

Hi mahela007!

… If that happens, then couldn't there be a several pairs of values for the velocity of Object 1 and object 2 which would comply with the conservation of momentum and the conservation of kinetic energy? How can we determine which one of these combinations of velocities will occur ?

No, conservation of both energy and momentum always gives a unique answer.

Try it and see.

 

[Saw]

We have been discussing more or less about this in the thread "Acceleration in an elastic collision", which you may want to look at for more detail. Conservation of momentum alone does allow for many final velocities. But, as tiny-tim implied, if you stipulate that the collision is perfectly elastic, that is to say, if all kinetic energy is conserved in the system, then there is only one possible solution. In particular, it's one complying with the requirement that the relative velocity of approach (before collision) = the relative velocity of separation (after collision).

 

[mahela007]

Hm... Ok.. I'll check that and post back.

 

[PJC01]

Yes, in an elastic collision, there are an infinite number of possible velocities that the objects can gain. This is because the total kinetic energy of the system is conserved, meaning that the sum of the kinetic energies of the two objects before and after the collision must be equal. However, the specific velocities that the objects will gain depend on the details of the collision, such as the masses and initial velocities of the objects, as well as the angle and location of the collision.

In the scenario described, where one object is moving at 1 ms-1 and the other is stationary, it is possible for the first object to transfer all of its kinetic energy to the second object, resulting in the first object coming to rest and the second object moving at 1 ms-1. However, it is also possible for the first object to transfer only a fraction of its kinetic energy to the second object, resulting in both objects moving after the collision. In this case, there are multiple combinations of velocities that would comply with the conservation of momentum and kinetic energy.

To determine which combination of velocities will occur in a specific elastic collision, we would need to know the specific details of the collision and use the principles of conservation of momentum and kinetic energy to solve for the velocities. This would involve using equations such as the law of conservation of momentum (p1 + p2 = p'1 + p'2) and the law of conservation of kinetic energy (1/2m1v1^2 + 1/2m2v2^2 = 1/2m1v'1^2 + 1/2m2v'2^2). By plugging in the known values and solving for the unknown velocities, we can determine the specific velocities that the objects will have after the collision.

In summary, in an elastic collision, there are an infinite number of possible velocities that the objects can gain, but the specific velocities that will occur depend on the details of the collision and can be determined using the principles of conservation of momentum and kinetic energy.