Would you mind elaborating on the center of mass frame?
BTW, Doc Al, I have been discussing this topic for nearly 24 hours online in different forums. Your explanation is the most satisfying thus far.
So given
m1=10 kg v1i= 10 m/s
m2=10 kg v2i = 0
pi = 100 kg m/s = pf = (10+10)*vf -> vf = 5 m/s (perfectly inelastic)
Now from Energy's point of view.
KEi = (1/2)(10)(10)^2 = 500 J
KEf = (1/2)(20)(5)^2 = 250 J
so KEi > KEf
You are saying that the decrease in KE is totally due to heat?
So for a mathematical model, how can you defend supporting a perfect inelastic collision from the point of view of momentum, but not from the point of view of Energy?
m1*vi=(m1+m2)*vf only works perfectly if there is no heat/vibration and is a purely mathematical model.
Given the same...
Would you agree that if there were any vibration/heat/deformation in the collision under discussion that vf would be less than predicted given m1vi=(m1+m2)vf?
The question posed is entirely theoretical, and I posed it to figure out mathematically how in a perfectly inelastic collision KEi>KEf. The constraints of the problem as I have posed them permit an accurate discussion of the mathematical assumptions, though most contributed to the discussion are...
The two masses stick together. There is no intrinsic means of expressing lost due to deformation or heating assuming a perfectly inelastic collision considering the view conservation of momentum. Therefore, given the same collision (perfectly inelastic) considering conservation of energy, there...
Heat or deformation cannot contribute to velocity here, as per the view of conservation on momentum. So how is it that momentum is conserved but kinetic energy is not given a perfectly inelastic collision?
The two masses stick together.
There is no intrinsic means of expressing lost due to...