Two cars intially at rest are free to move in the `x` direction. Car `A` has mass 4 kg and car `B` has mass 2kg. They are tied together, compressing a spring in between them. When the string holding them together is burned, car `A` moves off with a speed of `2//s`
(a) with what speed does car `B` leave.
(b) how much energy was stored in the spring before the string was burned.

Answer

4m/s, 24J

Explanation

(a) `m_(A)v_(A)+m_(B)+v_(B)=0` [Initially both of them were at rest]
`rArrv_(B)=-(m_(A)v_(A))/(m_(B))=-((4)(2))/((2))=-4m//s`
(b) `E=(1)/(2)m_(A)v_(B)^(2)+(1)/(2)m_(B)v_(B)^(2)`
`rArrE=(1)/(2)(4)(2)^(2)+(1)/(2)(2)(-4)^(2)=24J`