Collision, Momentum, Impulse

• Collision


  Interaction of two (2) or more objects, whose momenta (singular, momentum) are conserved
• Impulse (J)


  An object's force being transferred at a certain rate. It is the product of an object's average force and time.
• Momentum (p)


  An object moving at a certain velocity. It is the product of an object's mass (or center of mass) and its velocity. Momentum is a vector quantity, hence its direction is always the same as the direction of the velocity.
• Center of mass


  • The focal point within an object or body whose entire mass rests on. For most simple objects, their centers of mass are located at its center.
  • Mathematically represented as 1/M ∫x dm for a single object, and (Σmixi)/M for multiple objects
• Calculating center of mass

  1. Pick a reference point

  2. Use the formula (Σmixi)/M
• Velocity of the center of mass (VCOM)

  1/M Σmivi
• Acceleration of the center of mass (aCOM)

  1/M Σmiai
• Impulse-Momentum Theorem


  Describes how an object in motion dictates how much force it will deliver in a certain time. The longer the time, the weaker the impulse despite a strong force, reducing the velocity of the moving mass.
• Applications of Impulse-Momentum Theorem

  • Crumpling of cars during accidents to prolong force delivery
  • Use of airbags in cars to extend time to stop momentum
• Solving Impulse-Momentum Theorem sample problem

  1. Given: 20-kg stroller, 15-kg toddler, push speed of 1 m/s, initially at rest

  2. Find: Average force required to push for 5 seconds
• Collision

  Transfer of momentum, relies on restitution coefficient (e) for verification. Has two types: elastic and inelastic
• Elastic collision


  e = 1 (perfect elastic), 0 < e < 1 (inelastic)
• Inelastic collision


  e = 0 (perfect inelastic)
• Momentum transfer during collision

  Elastic, single projectile: P10 = (P1 + P2)f

  Elastic, multiple projectiles: (P1 + P2)0 = (P1 + P2)f

  Inelastic: P1 + P2 = (m1 + m2)vf
• Cases of single projectile elastic collision

  • m1 = m2: A stops, B gets A's velocity

  m1 > m2: B moves almost twice as fast as A

  m1 < m2: A moves in opposite direction at almost same velocity
• Linear Momentum Conservation Law
• Only external forces can change the momentum of a system