Final answer:
The collision described is a perfectly inelastic collision because momentum is conserved while kinetic energy is not, as evidenced by the orange car stopping and the yellow car moving with a velocity that conserves the system's total momentum.
Step-by-step explanation:
Understanding the Type of Collision
The type of collision described in the student's question is a perfectly inelastic collision. This is determined by the fact that after the collision the orange bumper car comes to a stop while the yellow bumper car moves to the right. In a perfectly inelastic collision, momentum is conserved but kinetic energy is not, which means some kinetic energy is transformed into other forms of energy, like heat or sound, during the collision.
Conservation of Momentum
In the perfectly inelastic collision scenario provided, the conservation of momentum can be represented as:
- Initial momentum of orange car = (10 kg)(10 m/s) = 100 kg·m/s to the right
- Initial momentum of yellow car = (20 kg)(0 m/s) = 0 kg·m/s
- Total initial momentum = 100 kg·m/s to the right
- Final momentum of orange car = (10 kg)(0 m/s) = 0 kg·m/s
- Final momentum of yellow car = Total initial momentum
- Thus, the yellow car's final momentum = 100 kg·m/s to the right
Therefore, after the collision, the yellow car must be moving with a velocity that keeps the total system momentum unchanged.
Type of Collision Based on Energy
In an elastic collision, both momentum and kinetic energy are conserved. Since kinetic energy is not conserved in this scenario (the orange car has lost all of its kinetic energy), we can confirm that the collision is not elastic, but rather perfectly inelastic because the momentum is conserved while kinetic energy is not.