Question

Two carts with masses of 4.68 kg and 2.44 kg move toward each other on a frictionless track with speeds of 4.78 m/s and 3.80 m/s respectively. The carts stick together after colliding head-on. Find the final speed.

Answer 1

The final velocity of the two carts, after colliding head-on and sticking together, is 0.211 m/s.

Step-by-step explanation:

The final speed of the two carts after the collision can be calculated using the law of conservation of momentum. The law states that the total momentum before the collision is equal to the total momentum after the collision. In this case, since the carts stick together, the final velocity can be calculated by adding up the products of mass and initial velocity of each cart, and dividing by the total mass of the system.

1. Find the total mass of the system by adding the masses of the two carts: 4.68 kg + 2.44 kg = 7.12 kg.
2. Calculate the total initial momentum of the system by multiplying the mass and initial velocity of each cart, and summing them up: (4.68 kg * 4.78 m/s) + (2.44 kg * -3.80 m/s) = 1.50 kg m/s.
3. Divide the total initial momentum by the total mass of the system to find the final velocity: 1.50 kg m/s / 7.12 kg = 0.211 m/s.

Therefore, the final velocity of the two carts after colliding head-on and sticking together is 0.211 m/s.