Two small spheres A and B of equal radius but different masses of 3m and 2m are moving towards each other and impinge directly. The speeds of A and B before collision are, respectively, 4u and u. The collision is such that B experiences an impulse of magnitude 6mcu, where c is a constant. Determine a. the coefficient of restitution, b. the limits for the value of c for which such collision is possible.

Two small spheres A and B of equal radius but different masses of 3m a

1.	Two small spheres A and B of equal radius but different masses of 3m and 2m are moving towards each other and impinge directly. The speeds of A and B before collision are, respectively, 4u and u. The collision is such that B experiences an impulse of magnitude 6mcu, where c is a constant. Determine a. the coefficient of restitution, b. the limits for the value of c for which such collision is possible.
Answer» Solution :Using CONSERVATION of momentum `m_(1)u_(1)+m_(2)u_(2)=m_(1)v_(1)+m_(2)v_(2)` Putting the values we get `(3m)(4u)-(2m)u=3mv_(1)+2mv_(2)` `implies 3v_(1)+2v_(2)=10u`……..i Using equation of restitution `v_(2)-v_(1)=5ue` ..........ii From i and ii `v_(2)=2u+3eu` Now impulse on `m_(2)`: `J=2mv_(2)-(-2MU)` Put the value of `J` and `v_(2)` to get `e=c-1` As `0leele1implies1lecle2`