Momentum Notes

Momentum

• Momentum is the product of mass and velocity.
• $Momentum = mass \times velocity$
• A stationary object has 0 momentum because its velocity is 0.
• Momentum increases as mass or velocity increases.

Learning Intentions

• Understand that momentum is the product of the mass and velocity of an object.
  • $p = mv$ where:
    • $p$ is momentum
    • $m$ is mass
    • $v$ is velocity
• Understand the law of conservation of momentum.
  • In an isolated system, the total momentum remains constant during a collision.

Success Criteria

• Understanding momentum as the product of mass and velocity ($p=mv$).
• Understanding the law of conservation of momentum.

Glossary Terms

• Momentum: The product of an object's mass and velocity.
• Law of Conservation of Momentum: In an isolated system, the total momentum does not change during a collision.

Momentum Explained

• All moving objects possess 'mass in motion' or momentum.
• Momentum is not a form of energy.
• The faster an object travels, the more momentum it has.
• A cricket ball is harder to stop than a tennis ball traveling at the same speed because the cricket ball has more mass.
• Objects with more mass have more momentum if they are traveling at the same velocity.

Momentum Triangle

• A momentum triangle can be used to calculate momentum, mass or velocity.
• To calculate a value, cover the desired quantity, and the other two will form the formula.

Law of Conservation of Momentum

• In an isolated system, momentum is transferred between objects during a collision, but the total momentum remains constant.
• The initial momentum before the collision equals the final momentum of all objects after the collision.
• This is similar to the law of conservation of energy.

Worked Example 8.7A: Calculating Initial Momentum

• Scenario: Head-on collision between two dodgem cars.

  • Green Car:
    • Velocity: $0.8 m/s$
    • Mass: $701 kg$
    • Initial Momentum: $p = m \times v = 701 kg \times 0.8 m/s = 561 kg \cdot m/s$
  • Purple Car:
    • Velocity: $-0.7 m/s$ (negative because it's moving in the opposite direction)
    • Mass: $660 kg$
    • Initial Momentum: $p = m \times v = 660 kg \times -0.7 m/s = -462 kg \cdot m/s$
  • Total Initial Momentum:
    • $561 kg \cdot m/s + (-462 kg \cdot m/s) = 99 kg \cdot m/s$
    • The positive number indicates the total momentum is to the right.

Worked Example 8.7B: Calculating Momentum After Collision

• The total momentum before the crash was $99 kg \cdot m/s$ to the right.
• Because momentum is conserved, the total momentum after the crash is also $99 kg \cdot m/s$ to the right.
• If the green car is not moving after the collision, it has no momentum.
• Therefore, the momentum of the purple car after the collision is $99 kg \cdot m/s$ to the right.

Remember and Understand

1. Identify the units of momentum.
2. Describe the law of conservation of momentum.

Apply and Analyze

3. Use the momentum triangle to calculate the three different formulas.
4. Explain why it is harder to stop a cricket ball than a tennis ball traveling at the same velocity. (Cricket ball has more mass)
5. Explain why it is harder to stop a fast-moving tennis ball than a slow-moving tennis ball. (Faster tennis ball has greater velocity, thus greater momentum).
6. Calculate the momentum of a $600 kg$ golf cart that is traveling at $0.8 m/s$. ($p = 600 kg \times 0.8 m/s = 480 kg \cdot m/s$)

Evaluate and Create

7. Use your understanding of momentum to evaluate which would cause the greatest damage: colliding with a truck or colliding with a car. (Truck has much greater mass.)