Mechanics, collisions help
Hi, not been online in some time but back again now with some more probably simple questions ;)
I can't get my head around this question involving collisions, it's a bit wordy to please bear with me.
Obviously the final velocity of B needs to be greater than 2, but I'm having trouble making this into an equation?
3 smooth identical spheres each of mas 1kg move on a straight line on a smooth horizontal floor. B lies between A and C.
Spheres A and B are projected towards each other with speeds 3 m/s and 2 m/s respectivly, and C is projected away from sphere A at a speed of 2m/s.
The coefficient of restitution between any two spheres is e
, show that sphere B will only collide with C if e
Thanks in advance
Coefficient of Restitution
There are two principles involved here. They are momentum and restitution. In the equations that follow, I am taking the direction as positive, and I'm assuming that the velocities of and are and respectively, after the impact. So:
1 The momentum of the system is conserved at the impact. So (noting that the masses are all 1 kg):
2 The restitution equation is: the velocity of separation = -e times the velocity of approach.
In other words, the (velocity of velocity of ) after impact (velocity of velocity of ) before impact. So (remembering that we are taking as the positive direction):
Add (1) and (2):
and if collides with