Momentum Calculations

Momentum

• Momentum is a quantity relating to a moving object, calculated by multiplying mass and velocity.
• Momentum is a vector quantity, meaning it has both magnitude and direction.
• An object at rest has zero momentum.
• Momentum increases with increasing velocity.
• Momentum can be thought of as a combination of mass and velocity.
• Momentum helps explain some of the most important interactions in nature.
• The total momentum before an event equals the total momentum after the event (conservation of momentum).
• A closed system is not affected by external forces.
• Momentum is conserved in collisions and explosions.
• Conservation of momentum explains recoil in guns/cannons.
• Force is related to the rate of change of momentum (force = rate of change of momentum).

Calculating Momentum

• Momentum (p) = mass (m) × velocity (v)
• Units: kg m/s (kilograms meters per second)

Example Calculations

• Lorry:

  • Mass = 7,500 kg
  • Velocity = 25 m/s (south)
  • Momentum = 7,500 kg × 25 m/s = 187,500 kg m/s (south)

• Ice Skater:

  • Mass = 60 kg
  • Velocity = 15 m/s
  • Momentum = 60 kg × 15 m/s = 900 kg m/s

Conservation of Momentum

• The total momentum of a system remains the same.

Collisions

• When two objects meet and interact.
• During a collision there is a change in momentum; the force of the collision is related to the rate of change of momentum.

Explosions

• When parts of a system separate and move apart.

Example: Cannon & Cannonball

• Before firing (event), total momentum = 0 kg m/s (neither moving).
• After firing,total momentum = 0 kg m/s (momentum of cannon and cannon ball in opposite directions).

Example Calculations: Trolleys/ Explosions ( using conservation of momentum)

• Momentum is calculated for trolleys/ cannon and cannon ball before and after collision/ explosion.
• The velocity of the combined trolleys/cannon ball and cannon after collision can be calculated using conservation of momentum.
• Positive values for velocity indicate direction.
• A cannon ball of mass 4.0 kg is fired from a stationary 96 kg cannon at 120 m/s.
• The velocity of the cannon immediately after firing can be calculated using conservation of momentum.

Force and Momentum

• Force = mass × acceleration
• Force is equivalent to the rate of change of momentum
• Car safety features (seatbelts, airbags, crumple zones) increase the time taken for a collision, decreasing the rate of change of momentum and the force of the collision.
• Crumple zones are areas of a car designed to deform upon impact.

Example Calculation: Car Acceleration

• Mass = 1,500 kg
• Initial velocity = 0 m/s
• Final velocity = 30 m/s
• Time taken = 20 seconds
• Calculate the force acting on the car using the relationship force = mass × change in velocity / time taken