00:01
Hi here in this given problem for the two steel blocks, mass of the first one means mass of block a, ma.
00:12
This is 0 .6 kilogram and mass of the second block mb, 0 .9 kilogram.
00:23
Initial speed before impact, initially speed of block a towards right, so positive, 4 meter per second.
00:34
Initial speed of block b that is towards left so we take it to be negative minus 2 meter per second final velocities of both of them means velocities after impact these are missing but this is clear that they will start moving in opposite direction so vf a it should become negative and vfp it should become positive so first of all using conservation of linear momentum initial momentum of the system means initial momentum of block a m a into v ia plus that of b mb vi b should be equal to final momentum of block a m a v f f f a plus m b v f f f f a plus m b v f f f f f f f f f f f f f f f f fb.
01:50
Plugging in all the known values here for m .a multiplied by via, 0 .6 multiplied by 4, it becomes 2 .4 plus 0 .9 multiplied by minus 2.
02:08
It becomes minus 1 .8 is equal to m .a 0 .6 but vfa is missing plus mb 0 .9 but vfb is missing.
02:21
So finally this equation takes a form 6 vfa plus 9 vfb is equal to 6 or simplifying by 3 it becomes twice of vfa plus tries of vfb is equal to 2 and that is equation number 1.
02:54
Now, coefficient of restitution, it is given to be equal to 0 .8.
03:02
And we know coefficient of restitution that is given as relative velocity of separation, vfb minus vfa, to the relative velocity of approach, via, minus via, means 0 .8 is equal to vfb, missing, vfa, missing, vfa, v i a 4 minus minus 2 so we can say minus v f a plus vf a plus vf b is equal to 4 plus 2 6 multiplied by 0 .8 4 .8 and if we multiply this equation by 2 both of the sides this is minus twice of vfa plus twice of vf b is equal to 9 .6 that is equation number two and rewriting equation one here that was twice of vfa plus thrice of vfb is equal to two that was equation number one so adding these two equations we get five times of vfb is equal to 11 .6 so finally vfb comes out to be equal to plus this is positive and 2 .32 meter per second...