Two railway trucks of masses m and 3m move towards each other in opposite directions with speeds 2v and v respectively. These trucks collide and stick together. What is the speed of the trucks after the collision?

Explanation

This is a case of inelastic collision. Let us consider the truck with mass 'm' is coming from the left with velocity '2v' ⇒ The momentum of the truck coming from left = m × 2v = 2mv Let us consider the truck with mass '3m' is coming from the right side with veloctiy 'v' ⇒ The momentum of the truck coming from right = 3m × (-v) The negative sign should be considered because the truck coming from the right is moving in the opposite direction to that of truck coming from the left. Total momentum of Railway truck system before collision = 2mv - 3mv = -mv Now let us calculate the momentum of this system after the collision : As both the truck's stick together after the collision, the total mass of the Railway truck system = m + 3m = 4m But we don't know the velocity with which this combined truck system is moving. Let us consider the velocity of the combined truck system as : v(don't know) Momentum of this combined truck system = 4m × v(don't know) Momentum before collision = Momentum after collision ⇒ mv = 4m × v(don't know) ⇒ v(don't know) = v/4 = 0.25v Hence the speed of the combined truck system after collison = 0.25v = 1/4v = v/4