Force & Momentum (HL IB Physics)

• The resultant force on a body is the rate of change of momentum
• The change in momentum is defined as:

• Where:
  • Δp = change in momentum (kg m s^–1)
  • p_f = final momentum (kg m s^–1)
  • p_i = initial momentum (kg m s^–1)
• These can be expressed as follows:

• Where:
  • F = resultant force (N)
  • Δt = change in time (s)
• This equation can be used in situations where the mass of the body is not constant

• It should be noted that the force in this situation is equivalent to Newton's second law:

• This equation can only be used when the mass is constant

• The force and momentum equation can be derived from Newton's second law and the definition of acceleration

Direction of Forces

• Force and momentum are vector quantities with both magnitude and direction 
• The force that is equal to the rate of change of momentum is still the resultant force
• The positive direction is taken to be the direction of the initial motion; therefore:
  • a force on an object will be negative if the force opposes its initial velocity
  • the opposing force is exerted by the object it has collided with 
  • the forces will be of equal magnitude and opposite in direction, in accordance with Newton's Third Law

The car exerts a force on the wall of  300 N, and due to Newton's third law, the wall exerts a force of -300N on the car