Collision of Red and Blue Carts: Before and After Scenario
What is the before collision of the red cart, blue cart, and system?
Red cart: 0.50 kg, 60.0 cm/s rightward
Blue cart: 1.50 kg, 12.0 cm/s leftward
System: ?
What is the after collision of the red cart, blue cart, and system?
Red cart: ?
Blue cart: ?
System: ?
What is the momentum change of the red cart, blue cart, and system?
Explanation: Before the collision:
p = m₁v₁ + m₂v₂
p = (0.50 kg) (0.60 m/s) + (1.50 kg) (-0.12 m/s)
p = 0.12 kg m/s
After the collision:
p = (m₁ + m₂) v
p = (0.50 kg + 1.50 kg) (0.06 m/s)
p = 0.12 kg m/s
The change in momentum is 0 kg m/s.
Red Cart:
Before collision: The red cart with a mass of 0.50 kg was traveling rightward at a speed of 60.0 cm/s.
After collision: The red cart moved to the right with a speed of 6.0 cm/s.
Blue Cart:
Before collision: The blue cart with a mass of 1.50 kg was moving leftward at a speed of 12.0 cm/s.
After collision: The blue cart stuck together with the red cart and moved to the right with a speed of 6.0 cm/s.
System:
Before collision: The total momentum of the system can be calculated as the sum of the individual momenta before collision.
After collision: The total momentum of the system after collision is conserved, as the two carts stick together and move to the right with a common speed.
Momentum Change:
Before the collision, the initial momentum of the system was determined by the individual momenta of the red and blue carts. After the collision, the total momentum of the system remained the same, resulting in a zero momentum change for both the red cart, blue cart, and the system as a whole.
Explanation:
Before the collision, the red cart and blue cart had their respective momenta based on their masses and velocities. The total momentum of the system was the sum of these individual momenta. After the collision, due to the law of conservation of momentum, the total momentum of the system was the same before and after the collision.
This scenario demonstrates the concept of momentum conservation in collisions, where the total momentum of an isolated system remains constant if no external forces are involved. In this case, the momentum of the two carts before the collision was equal to the momentum of the combined carts after the collision, resulting in zero momentum change for the system.
Understanding momentum changes and conservation in collisions is crucial in physics, as it helps predict the outcomes of interactions between objects and systems. By analyzing the momentum of individual objects before and after collisions, we can determine the overall behavior and motion of the system as a whole.
Applying the principles of momentum conservation allows scientists and engineers to design efficient systems, predict the results of collisions, and better understand the fundamental laws of motion governing the universe.