Lecture on Momentum

Key Concepts

Definition of Momentum

• Momentum: Property of all moving objects
• Calculated as: momentum (p) = mass (m) \times velocity (v)

Examples

• Dinosaur: Mass = 4500 kg, Velocity = 12 m/s
  • Momentum: 4500 \times 12 = 54000 kg m/s
• Car: Mass = 1200 kg, Velocity = 25 m/s
  • Momentum: 1200 \times 25 = 30000 kg m/s

Characteristics of Momentum

• Vector Quantity
  • Has both magnitude and direction
  • Example: Forward (right) = positive, Backward (left) = negative

Conservation of Momentum

Principle

• Total momentum in a closed system before an event and after the event remains the same.

Example: Collision

• Scenario: Dinosaur and car collide and move together at same speed
• Before Collision:
  • Dinosaur momentum: 54000 kg m/s (right)
  • Car momentum: -30000 kg m/s (left)
  • Total momentum: 54000 + (-30000) = 24000 kg m/s (right)

Calculation After Collision

1. Total momentum remains 24000 kg m/s to the right
2. Combine masses: Dinosaur (4500 kg) + Car (1200 kg) = 5700 kg
3. Velocity after collision = Total momentum / Combined mass = 24000 / 5700 = 4.4 m/s (right)

Zero Initial Momentum

Stationary Objects

• No initial momentum as they are not moving
• Total momentum after event must also be zero

Example: Firing a Gun

• Initial momentum = 0 (gun is stationary)
• Bullet gains forward momentum, gun recoils backward to keep total momentum zero
• Calculations:
  1. Bullet mass = 0.005 kg, Velocity = 120 m/s
  2. Bullet momentum: 0.005 \times 120 = 0.6 kg m/s
  3. Gun mass = 2 kg, Gun momentum = 2v (where v is gun's recoil velocity)
  4. Total momentum equation: 2v + 0.6 = 0
  5. Solve for v:
     • 2v = -0.6
     • v = -0.3 m/s (backward recoil velocity)

Symbol for Momentum

• Symbol: p (Rho)
• Momentum equation: p = m \times v

Conclusion

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