Laws of motion & momentum

• Newton's 1st law of motion --> An object will remain at rest or continue to move with constant velocity unless acted upon by a resultant force
• Newton's 3rd law of motion --> When two objects interact, they exert equal & opposite forces on each other
• • When two objects interact, the pair of forces produced will always be equal & opposite
  • The forces acting in the interacting objects are always of the same type
  • Momentum = mass x velocity
• • A group of interacting objects is referred to as a closed system
  • For a system of interacting objects, the total momentum in a specified direction remains constant, as long as no external forces act on the system
  • The total momentum before & after the collision is the same
• Investigating momentum:

  • A linear air track is ideal because a cushion of air minimises the friction between the gliders & track, but trolleys & a horizontal runway also work
  • The velocity of each object is determined with a motion sensor & a laptop, light gates & a digital timer, ticker timers, or simply a stopwatch to measure the time taken to cover a known distance.
• Elastic collisions:

  • Momentum is conserved
  • Total energy is conserved
  • Total kinetic energy is conserved
• Inelastic collisions:

  • Momentum is conserved
  • Total energy is conserved
  • Total kinetic energy is not conserved
• Newton's 2nd law of motion --> The net (resultant) force acting on an object is directly proportional to the rate of change of its momentum, and is in the same direction
• Conserving momentum in collisions:

  • The net force acting on the objects in this closed system is zero
  • According to Newton's 2nd law rate of change of momentum/ change in time = 0
  • The change in momentum of both objects must be zero therefore the total momentum of the objects doesn't change
  • Momentum is always conserved
• • net force = rate of change of momentum
  • The product of force & time is equal to the change in momentum
• Impulse of a force --> the product of force and the time for which this force acts on an object

  • impulse of a force = change in momentum
• Force-time graphs:

  • the area under the graph is equal to Ft, which is the impulse of the force or the change in momentum of the object
  • the area under a force-time graph is always equal to the change in momentum, even when the force is changing
• Adding momentum:

  • An object A moving to the right with momentum p, it collides with a stationary object B
  • After the collision, A & B move off in different directions with momenta p1 & p2 respectively
  • Since linear momentum must be conserved, the vector sum p1 & p2 (total final momentum) must be equal to p (initial momentum)
• Resolving momentum:

  • The momentum in any direction must be conserved. In this case the momentum must remain the same in the x direction & y direction
  • x direction : total initial momentum = total final momentum
  • m1v0 = m1v1 x cos theta + m2v2 x cos theta
  • y direction : total initial momentum = total final momentum
  • 0 = m1v1 x sin theta + m2v2 x sin theta