I had to come up with a situation where two objects undergo elastic collision. B
ID: 1780670 • Letter: I
Question
I had to come up with a situation where two objects undergo elastic collision. But I'm having trouble adjusting the outcome, so it will be inelastic and still conserve linear momentum (have to do this for another part to the question). Here is the situation I came up with: A 10kg ball is moving to the right at a velocity of 2 m/s, while a 2 kg ball is moving to the left towards the first ball at a velocity of 4 m/s. Upon collision, the heavier ball stops (0 m/s) and the smaller ball changes course and goes towards the right at 6 m/s. I found that this was elastic and conserved momentum. I just don't know how to make adjustments to the outcome to get the collision to be inelastic, while having conserved momentum. Everything I tried, for some reason didn't have conserved momentum. Basically, I need someone to change my situation to become inelastic, but only changing the outcome (final velocities?). The mass and initial velocities have to remain the same I think. Sorry for any confusion. Hopefully someone can make sense of this. Thank you for helping!
Explanation / Answer
Expression of coefficient of restitution e in terms of the velocities is e= Vfb-Vfa/Via-Vib and this should be involved here to explain.
Where Via and Vib are initial and Vfa and Vfb are final velocities of A and B respectively, towards +x direction which is rightwards.
Putting given data in above formula, we get e= 6-0/2+4= 1 , which corresponds to the case of perfectly elastic collision. A e= 0 case corresponds to perfectly inelastic collision. All other values I.e. >0 and <1 are for intermediate cases I.e. neither perfectly elastic nor inelastic. So, to convert this case to inelastic collision, put a value of e<1, say 1/2. So, 1/2 = Vfb-Vfa/Via-Vib . Or, 2(Vfb-Vfa)= (Via-Vib)= 6 Or, Vfb-Vfa=3 _____(A)
Also, momentum is conserved I.e. 10*2-2*4= 12= 2*Vfb-10*Vfa. Or, putting known values, Vfb-5Vfa=6 _____(B)
From A and B, Vfa= 0.5m/s and Vfb= 3.5m/s {where no initial velocities have been changed, and +x direction is taken as +ve everywhere} and collision is not elastic (as e<1)
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