Arailroad car of mass 2.50*10^4 kg is moving with a speed of 4.00 m/s. it collides and couples with three other coupled railroad cars, each of the same mass as the single car and moving in the same direction with an initial speed of 2.00 m/s. (a) what is the speed of the four cars after the collision? (b) how much mechanical energy is lost in the collision?

(a) 2.5 m/s

(b) 37.5 KJ

Explanation:

(a)

From the law of conservation of momentum, Initial momentum=Final momentum

and making the subject then

and since is initial velocity of car, value given as 4 m/s, is the initial velocity of the three cars stuck together, value given as 2 m/s and is the final velocity which is unknown. By substitution

(b)

Initial kinetic energy is given by

Final kinetic energy is given by

The energy lost is given by subtracting the final kinetic energy from the initial kinetic energy hence

Energy lost=350-312.5=37.5 KJ