Conservation of Momentum Example

Conservation of Momentum Example

Introduction

• The conservation of momentum principle can be illustrated using an example involving two model cars colliding.

Scenario

• Consider two model cars with masses:
  • Green Car (A): 1.2 kg
  • Yellow Car (B): 1.4 kg
• The cars collide at different speeds.

Total Momentum Before Collision

• To find the total momentum before the collision, we calculate the momentum of each car.
• The momentum of an object is given by the formula: Momentum (p) = Mass (m) × Velocity (v).
• In this case, the momentum of the Green car (A) is calculated as follows: Momentum of Green Car (A):
  • Mass (m1) = 1.2 kg
  • Velocity (v1) = 2.4 m/s (as given in the problem)
  • Momentum of A (p1) = m1 × v1
• The momentum of the Yellow car (B) is calculated similarly: Momentum of Yellow Car (B):
  • Mass (m2) = 1.4 kg
  • Velocity (v2) = -1.6 m/s (as it's travelling in the negative direction)
  • Momentum of B (p2) = m2 × v2
• The total momentum before the collision is the sum of these individual momenta: Total Momentum Before Collision:
  • Σp_initial = p1 + p2

Calculations

• Calculate the momenta of both cars and find the total momentum before the collision.

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Conservation of Momentum Example

Total Momentum After Collision

• If the two cars stick together after the collision and move as one, their combined mass is 2.6 kg (1.2 kg + 1.4 kg).
• The total momentum after the collision remains the same as before, which is 0.32 kg m/s.
• To find their velocity after the collision, we use the formula
  Momentum After Collision:
  • Σp_final = 0.32 kg m/s
  • Total Mass (m_total) = 2.6 kg
  • Velocity After Collision (v_final) = Σp_final / m_total

Conclusion

• The example demonstrates the conservation of momentum principle.
• The total momentum of the two cars before the collision is equal to their total momentum after the collision.
• This principle holds as long as there are no external forces acting on the system.