Conservation of momentum in one dimension - Momentum

Conservation of momentum in one dimension

Lessons

Notes:

In this lesson, we will learn:

  • Meaning of conservation of momentum
  • Deriving conservation of momentum from Newton's third law
  • Meaning of closed/open systems and identifying conservation of momentum problems
  • Problem solving with conservation of momentum in 1 dimension

Notes:

  • Momentum is a conserved quantity: the total momentum of a set of objects before an event (like a collision or explosion) is equal to total momentum after.
  • Conservation of momentum (pi=pf\sum\vec{p}_i = \sum\vec{p}_f)is a result of Newton's 3rd
  • Law (FA=FB\vec{F}_A = -\vec{F}_B).
  • When talking about conservation of momentum, system is a name given to an object or set of objects that are being examined.
    • A closed system is an object or set of objects that are not affected by external forces (i.e. their motion is not changing due to forces from outside the system). Momentum is conserved in a closed system.
      • A system can have external forces acting on it while still being closed, as long as those forces are balanced. A ball rolling across a frictionless table would be considered a closed system even though gravity and normal force act on the ball. Gravity and normal force are balanced, so they are not causing the ball to accelerate, and momentum is conserved.
    • An open system is an object or set of objects that are affected by external forces (i.e. their motion does change due to forces from outside the system). Momentum is not conserved in an open system.
      • If the ball from the earlier example rolls off the edge of the frictionless table and is accelerated by gravity towards the earth, then it is no longer considered a closed system. The system is open and gaining momentum from the acceleration due to gravity.

Momentum

p=mv:\vec{p} = m \vec{v}: momentum, in kilogram meters per second (kg∙m/s)

m:m: mass, in kilograms (kg)

v:\vec{v}: velocity, in meters per second (m/s)


Conservation of Momentum

pi=pf\sum\vec{p}_i = \sum\vec{p}_f

pi:\vec{p}_i: initial momentum, in kilogram meters per second (kg·m/s)

pf:\vec{p}_f: final momentum, in kilogram meters per second (kg·m/s)


Impulse

J=FΔt=Δp=m(vfvi\vec{J} = \vec{F} \Delta t = \Delta \vec{p} = m( \vec{v}_f - \vec{v}_i)

J:\vec{J}: impulse, in newton seconds (N∙s)

F:\vec{F}: net force acting on an object, in newtons (N)

Δt:\Delta t: the length of time for which the force acts, in seconds (s)

Δp:\Delta \vec{p}: change in momentum of an object, in kilgram meters per second (kg∙m/s)

  • Intro Lesson
    Introduction to conservation of momentum in one dimension:
  • 1.
    pi=pf:\bold{\sum\vec{p}_i = \sum\vec{p}_f}: Objects that bounce apart after collision
  • 2.
    pi=pf:\bold{\sum\vec{p}_i = \sum\vec{p}_f}: Objects that stick together after collision
  • 3.
    pi=pf:\bold{\sum\vec{p}_i = \sum\vec{p}_f}: Objects that explode apart
Teacher pug

Conservation of momentum in one dimension

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