Question

a 0.20 kg model railroad car moving with a horizontal velocity of 0.24 m/sec is truck from behind by a 0.42 kg car traveling at 0.45 m/sec. if the two cars stick together when they collide, what will their final velocity be?

Answer 1

Using the conservation of momentum, the final velocity of the two model railroad cars that collide and stick together is calculated to be 0.3576 m/s. This example demonstrates how to apply the momentum conservation principle to solve collision problems.

Step-by-step explanation:

The student's question involves applying the principle of conservation of momentum to a scenario where two model railroad cars collide and stick together. In physics, conservation of momentum states that the total momentum of a system remains constant if no external forces are acting on it. We use this principle to solve the mathematical problem completely. Here, the system is composed of two cars, one with a mass of 0.20 kg moving at 0.24 m/s, and the other with a mass of 0.42 kg moving at 0.45 m/s.

To find the final velocity after the collision, we set up the momentum conservation equation as follows:

• The total momentum before collision is the sum of the momenta of both cars.
• The total momentum after collision is the mass of both cars combined times their final velocity (since they stick together).

Mathematically: (0.20 kg × 0.24 m/s) + (0.42 kg × 0.45 m/s) = (0.20 kg + 0.42 kg) × final velocity

After calculations, the final velocity comes out to be:

final velocity = ((0.20 × 0.24) + (0.42 × 0.45)) / (0.20 + 0.42)

final velocity = 0.3576 m/s

Therefore, the final velocity of the two cars sticking together is 0.3576 m/s. This answer helps the student understand how to apply conservation of momentum in collisions where the objects stick together post-collision.