Question

Two train carts are colliding with each other. Train cart A moves east at 5 m/s.

Train cart B moves west at 10 m/s. Train cart A is full with a mass of 2000 kg.
Train cart B is empty with a mass of 500 kg. After the collision, the train cars stick
together. What is their speed after the collision?

A) 5 m/s to the east
B) 2 m/s to the east
C) 10 m/s to the west
D) 15 m/s to the west

Answer 1

In this inelastic collision, the two train carts stick together post-collision. Using the conservation of momentum, we calculate that the combined carts move at 2 m/s to the east after collision.

Step-by-step explanation:

The question involves a collision in which two train carts stick together after impacting. This is an example of an inelastic collision, where momentum is conserved but kinetic energy is not necessarily conserved. To find the speed of the train carts after the collision, we can use the principle of conservation of linear momentum:

Momentum before collision = Momentum after collision
(mass of cart A × velocity of cart A) + (mass of cart B × velocity of cart B) = (total mass) × (velocity after collision)

Since Train cart A moves east and Train cart B moves west, we'll consider east as the positive direction and west as the negative direction. Substituting the given values:

(2000 kg × 5 m/s) + (500 kg × -10 m/s) = (2000 kg + 500 kg) × (velocity after collision)
10000 kg·m/s - 5000 kg·m/s = 2500 kg × (velocity after collision)
5000 kg·m/s = 2500 kg × (velocity after collision)

Solving for the velocity after collision gives:

velocity after collision = 5000 kg·m/s / 2500 kg = 2 m/s

The velocity is positive, which means that the direction is to the east. Therefore, the correct answer is B) 2 m/s to the east.