Stuck on this problem:
A train car (mass 15,000 kg) moving right with a velocity of 4.0 m/s collides with a train car (mass 14,000 kg) moving right with a velocity of 0.5m/s. They couple or get stuck together. What is the final velocity
To find the final velocity of the two train cars after they collide and get stuck together, we can use the principle of conservation of momentum.
The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act upon it. In this case, the two train cars form an isolated system, as no external forces are acting on them after the collision.
The formula for momentum is given by momentum (p) = mass (m) × velocity (v). Therefore, the initial momentum of the first train car is 15,000 kg × 4.0 m/s = 60,000 kg·m/s, and the initial momentum of the second train car is 14,000 kg × 0.5 m/s = 7,000 kg·m/s.
Since the train cars get stuck together, their final mass is the sum of their masses, which is 15,000 kg + 14,000 kg = 29,000 kg. Let's denote the final velocity of the two cars after the collision as V.
By applying the principle of conservation of momentum, the total initial momentum of the system is equal to the total final momentum of the system. Therefore, we can write the equation:
(initial momentum of first train car) + (initial momentum of second train car) = (final momentum)
60,000 kg·m/s + 7,000 kg·m/s = (29,000 kg) × V
Simplifying, we have:
67,000 kg·m/s = 29,000 kg × V
Now, divide both sides of the equation by 29,000 kg:
V = 67,000 kg·m/s ÷ 29,000 kg
V ≈ 2.31 m/s
Therefore, the final velocity of the two train cars after the collision and getting stuck together is approximately 2.31 m/s in the right direction.
momentum is conserved
(m1 * v1) + (m2 * v2) = (m1 + m2) * v3