Two satellites, each of mass 4000 kg and travelling in orbit in opposite directions at a speed of 8.0 km/s with respect to an earth observer, collide and stick together. Find the increase in total rest mass of the system?

Question

Two satellites, each of mass 4000 kg and travelling in orbit  in opposite directions at a speed of 8.0 km/s with respect to an earth observer, collide and stick together. Find the increase in total rest mass of the system?

anonymous · Answer

Its completely inelastic collision so both the masses are joined. And because we are assuming the impulse to be of very short time in x direction and there is no external force that is being applied on this complete system, just use simple momentum conservation
m1v1 + m2v2 = (m1+m2)v3 and find v3 win your case is 0. So now the new mass is at rest so your rest. Hope this much is hint is enough. Do mote that first you should choose a direction as positive and then see which of your velocity is positive and which is -ve as velocity is a vector quantity.

anonymous · Answer

thanks for that. However, I do realise it is the rest mass but how can V3 be 0?

anonymous · Answer

its because m1 and m2 are same and magnitude of v1 and v2 are same. Only directions are opposite. So substituting the values in that eqn, you will get the left side as 0.

anonymous · Answer

Thanks, and apologies for my naivety but that would mean there is zero net change in the rest mass of the system?

anonymous · Answer

If you see the system then its initial velocity was 0 and final also. So if you are trying to say this then its correct.

anonymous · Answer

Ok good. Are you also trying to say there is another way to view the system?