Three carts move on a frictionless track with inertias and velocities as shown. The carts collide and stick together after successive collision.
(a) Find loss of mechanical energy when `B` & `C` stick together.
(b) Find magnitude of impulse experienced by `A` when it sticks to combined mass `(B" & "C)`.

Answer

(a)3 J, (b) `(12)/(5)N.s`

Explanation

conservation of momentum `=1(1)-2(2)=-3v`
Loss in energy `=[(1)/(2)(1)(1)^(2)+(1)/(2)(2)(2)^(2)]-[(1)/(2)(3)(v)^(2)]`
`=(1)/(2)+4-(3)/(2)=3J`

conservation of momentum `=(2)(1)-3(1)=-5v'`
`v'=(1)/(5)m//s`
Impulse on `A=2(-(1)/(5))-2(1)=(-12)/(5)kgm//s.=-(12)/(5)Ns.`