Four railroad cars, each of mass `2.50 xx 10^4` kg, are coupled together and coasting along horizontal tracks at speed `v_(I)`towards the south. A very strong movie actor, riding on the second car, uncouples the front car and gives it a big push, increasing its speed to `4.00 m//s` southward. The remaining three cars continue moving south, now at `2.00 m//s`. (a) Find the initial speed of the cars. (b) How much work did the actor do?

Answer

`2.50m//s`, `37.5kJ`

Explanation

a. The internal forces exerted by the actor do not change the total momentum of the system of the four cars and the movie actor `(4m)v_(1)-(3m)(2.00m//s)+m(4.00m//s)`
`v_(1)=(6.00m//s+4.00m/s)/4=2.50m//s`

b. `W_(actor)=K_(f)-K_i=1/2[(3m)(2.00m//s)^(2)+m(4.00m//s^(2))]`
`-1/2(4m)(2.50m//s)^(2)`
`=((2.50xx10^(4)kg))/2 (12.0+16.0-25.0)(m//s)^(2)=37.5kJ`