(455) Momentum [IB Physics SL/HL]

Introduction to Momentum

  • Momentum (P): Defined as the product of mass and velocity.

  • Equation: P = MV

    • Where:

      • P = momentum

      • M = mass (kg)

      • V = velocity (m/s)

  • Units of momentum: kilograms meters per second (kg·m/s)

Importance of Momentum

  • Momentum is conserved in a closed system, meaning total momentum before an event equals total momentum after the event.

  • Useful for predictions in various physics problems.

  • Conservation laws apply to momentum analogous to other physical quantities like mass.

Collision Example: Skier and Snowboarder

  • Scenario: An elastic collision between a skier (55 kg) and a snowboarder (70 kg).

  • Initial Velocities:

    • Skier: 20 m/s East

    • Snowboarder: 30 m/s West

  • Inelastic Collision: They stick together after collision.

Calculating Momentum

  1. Momentum of Skier:[ P_{skier} = 55 ext{ kg} \times 20 ext{ m/s} = 1100 ext{ kg·m/s} ext{ (East)} ]

  2. Momentum of Snowboarder:[ P_{snowboarder} = 70 ext{ kg} \times 30 ext{ m/s} = 2100 ext{ kg·m/s} ext{ (West)} ]

  3. Total Momentum:

    • Total momentum = P_{snowboarder} - P_{skier}

    • [ P_{total} = 2100 - 1100 = 1000 ext{ kg·m/s} ext{ (West)} ]

Final Velocity Calculation

  • Combined Mass:

    • Total mass = 55 kg + 70 kg = 125 kg

  • Using Total Momentum to find Final Velocity (V_f):[ P_{total} = (M_{1}+M_{2}) \times V_f ]

    • [ 1000 = 125 \times V_f ]

    • [ V_f = \frac{1000}{125} = 8 ext{ m/s (West)} ]

Conclusion

  • The skier and snowboarder will move together at a final velocity of 8 m/s towards the West after the inelastic collision.