momentum

Momentum

Definition of Momentum

  • Momentum combines the concepts of mass and velocity of an object.

  • It is defined as the quantity of motion that an object possesses.

  • Momentum can be described as a measurement of mass in motion: how much mass is in how much motion.

Stopping Momentum

  • To bring an object to a complete stop, its momentum must be decreased to 0.

Calculation of Momentum

Basic Equations

  • Momentum, denoted by P, is calculated using the formula: P = mv Where:

    • P = momentum (measured in kg•m/s or Newton-seconds, N•s)

    • m = mass (measured in kg)

    • v = velocity (measured in m/s)

Example Calculations

Train Momentum Calculation

  1. For a 100,000 kg train moving at 5.0 m/s:

    • Calculation:
      P = (100,000 ext{ kg})(5.0 ext{ m/s})
      = 500,000 ext{ kg•m/s} or N-s.

  2. For a 100 kg train moving at 5.0 m/s:

    • Calculation:
      P = (100 ext{ kg})(5.0 ext{ m/s})
      = 500 ext{ kg•m/s} or N-s.

Toy Car Momentum Calculation

  1. For a 10 kg toy car moving at 5 m/s:

    • Calculation:
      P = (10 ext{ kg})(5 ext{ m/s})
      = 50 ext{ kg•m/s} or N-s.

  2. For a 10 kg toy car moving at 10 m/s:

    • Calculation:
      P = (10 ext{ kg})(10 ext{ m/s})
      = 100 ext{ kg•m/s} or N-s.

Cart Momentum Calculation

  1. Cart 1 (3.00 kg cart moving at 30 m/s North):

    • Calculation:
      P = (3.00 ext{ kg})(30 ext{ m/s})
      = 90 ext{ kg•m/s} or N-s.

  2. Cart 2 (2.00 kg cart moving at 45.0 m/s South):

    • Calculation:
      P = (2.00 ext{ kg})(45.0 ext{ m/s})
      = 90 ext{ kg•m/s} or N-s.

    • Analysis: Both carts have the same momentum in magnitude but different directions.

Momentum Insights Recap

  • The relationship between velocity and momentum:

    • If velocity increases, momentum increases at the same rate.

    • If velocity decreases, momentum decreases at the same rate.

    • If mass increases, momentum increases at the same rate.

    • If mass decreases, momentum decreases at the same rate.

    • Heavier objects moving at the same velocity will have more momentum than lighter objects.

    • Faster-moving objects at the same mass will have more momentum than slower ones.

Conservation of Momentum

Fundamental Principle

  • According to Sir Isaac Newton, when measuring the momentum of colliding objects before and after an event:

    • The total momentum of any isolated system remains constant. Mathematically:
      P{ ext{total before collision}} = P{ ext{total after collision}}
      or
      mv{ ext{total before}} = mv{ ext{total after}}

Example of Collision

  • In the scenario of a school bus colliding with a car:

    • The total momentum before the collision equals the total momentum after the collision, assuming no net external force acts on the system.

Types of Collisions

  1. Completely Inelastic Collision:

    • When two objects collide and stick together, their combined momentum after the collision:

    • ext{Momentum of bus (before)} + ext{Momentum of car (before)} = ext{Momentum of bus/car (after)}

    • Equation:
      (mv){ ext{bus}} + (mv){ ext{car}} = (mv)_{ ext{bus/car}}

  2. Elastic Collision:

    • In this type, the momentum conservation equation can be expressed as:

    • (mv){ ext{bus1}} + (mv){ ext{car1}} = (mv){ ext{bus2}} + (mv){ ext{car2}}

    • This highlights how momentum is distributed among separate wrecks post-collision.

Activity Understanding and Practice

Activity #1 - Momentum Questions

  1. Calculate the final momentum when a 4000 kg bus travelling at 80 km/h collides with a car weighing 1000 kg moving at 60 km/h.

  2. If a bicycle has a momentum of 24 kg•m/s, determine the new momentum when:

    • it has three times the mass and is moving at half the speed.

Impulse

Definition of Impulse

  • Impulse is defined as the force acting on an object multiplied by the time interval that the force is exerted.

  • It is a vector quantity, represented mathematically as: I = F imes t Where:

    • I = Impulse (measured in N•s)

    • F = Force (measured in N)

    • t = Time (measured in s)

Application of Impulse

  • To reduce an object's momentum to zero, an impulse must be applied.

  • Impulse influences momentum change; increasing force or time results in greater impulse.

    • Two strategies for increasing impulse include:

    1. Increase the force applied.

    2. Increase the duration the force is applied.

Observations from Practical Examples

Example: Using a Bedsheet for an Egg Drop

  • Using a bedsheet to catch an egg allows the force of the egg to distribute over a wider area and a longer time:

    • This reduces the average force exerted on the egg.

    • Similar concepts apply to vehicle safety designs, such as airbags, which extend the time of impact and reduce force, enhancing safety.

Impulse in Sports

Improving Sports Performance

Volleyball Spike Example

  • To improve your spike in volleyball, the impulse can be increased by:

    1. Strength training (building up strength increases the force applied).

    2. Following through on the hit (this increases contact time with the ball).

Impulse Versus Momentum Relationship

  • Impulse is also defined as change in momentum:

    • I = ext{Change in momentum} = \Delta P = m \Delta v = m(v2 - v1)