Momentum

• Calculating Momentum

  • A moving object has momentum which is defined by the equation:

  p = mv

  • Where:
  • p = momentum in kilogram metre per second (kg m/s)
  • m = mass in kilograms (kg)
  • v = velocity in metres per second (m/s)
• • An object at rest (i.e v = 0) has no momentum
  • Momentum keeps an object moving in the same direction, making it difficult to change the direction of an object with a large momentum
  • Since velocity is a vector this means that the momentum of an object also depends on its direction of travel
  • This means that momentum can be either positive or negative
  • Right= positive
  • Left= negative
• The momentum of an object will change if:

  • The object accelerates (speeds up) or decelerates (slows down)
  • Changes direction
  • Its mass changes
• Examples of Momentum

  • Examples of momentum in an event are collisions
  • Objects will either:
  • Collide and move in opposite directions - this is an elastic colision
  • Collide and move in the same direction together - this is an inelastic collision
  • When the objects move in opposite directions:
  • Each object will have a different velocity depending on its mass and initial momentum of the system
  • When the objects move in the same direction together:
  • They will have a combined mass and velocity
  • Momentum is always conserved in a collision
• Conservation of Momentum

  • The principle of conservation of momentum states that:In a closed system, the total momentum before an event is equal to the total momentum after the event
  • A closed system means the energy within the system is constant and there is an absence of external forces (e.g. friction)
• The total momentum before a collision = The total momentum after a collision

  • A system is a certain number of objects under consideration
  • This can be just one object or multiple objects
  • Since momentum is a vector quantity, a system of objects moving in opposite directions (e.g. towards each other) at the same speed will have an overall momentum of 0 since they will cancel out
  • Momentum is always conserved over time
• Newton's Third Law & Momentum

  • Newton’s third law of motion states:Whenever two bodies interact, the forces they exert on each other are equal and opposite
  • This means:
  • When one object exerts a force on another object, the second object will exert an equal force on the first object in the opposite direction
  • When two objects collide, both objects will react, generally causing one object to speed up (gain momentum) and the other object to slow down (lose momentum)
• Newton's third law can be applied to collisions

  • Consider the collision between two trolleys, A and B:
  • When trolley A exerts a force on trolley B, trolley B will exert an equal force on trolley A in the opposite direction

  
• FB–A = –FA–B

  • While the forces are equal in magnitude and opposite in direction, the accelerations of the objects are not necessarily equal in magnitude
  • From Newton's second law, acceleration depends upon both force and mass, this means:
  • For objects of equal mass, they will have equal accelerations
  • For objects of unequal mass, they will have unequal accelerations
• Force & Momentum

  • When a force acts on an object that is moving, or able to move, the object will accelerate (or decelerate)
  • This causes a change in momentum
  • More specifically, the force is the rate of change in momentum