Three masses elastic collision

[luckis11]

Elastic collision. I cannot find the after collision velocities (quantity and direction), when 2 spheres strike an immobile sphere. All three of them have the same shape and volume, and the same mass (say e.g. 1 kg each). The two moving ones move parallel to each other with the same velocity u, and during their movement their center is on the same axis, vertical to the axis of their velocity. So at the first moment of the collision, the centres of the three spheres form an equilateral tringle. A link would be very helpful too.

 

[Bob_for_short]

Elastic collision. I cannot find the after collision velocities (quantity and direction), when 2 spheres strike an immobile sphere. All three of them have the same shape and volume, and the same mass (say e.g. 1 kg each). The two moving ones move parallel to each other with the same velocity u, and during their movement their center is on the same axis, vertical to the axis of their velocity. So at the first moment of the collision, the centres of the three spheres form an equilateral triangle. A link would be very helpful too.

I think that the energy-mimentum conservation laws are insufficient to determine the final vectors in general case. In your case you can add the equations of symmetry: the still sphere should move along one axis, so the other velocity components are zero. The bounced spheres should have equal velocity modules after collision. Maybe these additional equations will fix the liberty in your variables and lead to an unambiguous answer. It concerns the problem in the laboratory reference frame.

In the center of inertia frame everything is much simpler: the initial and final energies are equal, and the velocities change simply their signs.

Bob.

 

[tiny-tim]

In the center of inertia frame everything is much simpler: the initial and final energies are equal, and the velocities change simply their signs.

Yes, do it in the centre of mass frame

 

[Cantab Morgan]

I don't see how the center of mass idea helps here. If the third sphere is immobile, then it's easiest to do it in the frame where that sphere has no velocity.

 

[Cantab Morgan]

Oh, wait, does immobile here not mean "unable to move"? Does it mean simply "initially motionless"?

I'd normally think of an immobile sphere as having infinite mass, but the problem statement says all three spheres have the same mass. So, if that's the case, then yeah, center of mass makes sense to me now. Can you clarify a bit what you mean by "immobile," luckis11?

 

[luckis11]

By "immobile" I meant that its velocity was zero before the collision.