Arailroad car of mass 3.05 ✕ 104 kg moving at 2.60 m/s collides and couples with two coupled railroad cars, each of the same mass as the single car and moving in the same direction at 1.20 m/s. (a) what is the speed of the three coupled cars after the collision? m/s (b) how much kinetic energy is lost in the collision? j

(a) 1.67 m/s

For the purpose of the problem, we can consider the two coupled railroad cars has a single car, having a total mass of

Initially moving at

v1 = 1.20 m/s

The first car instead has mass

and velocity

v2 = 2.60 m/s

The law of conservation of momentum states that the total initial momentum of the system must be equal to the total momentum after the collision. So we can write

where v is the velocity at which the three cars move together after the collision.

Solving the equation for v, we find:

(b)

The kinetic energy is given by

where m is the mass of the object and v is the speed.

The total kinetic energy before the collision is

While the total kinetic energy after the collision is

So the kinetic energy lost is