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Island Physics

linear momentum

Bermuda Motorcross Racing (Photo: Takara Dill)
Home >> AP Physics I >> Linear Momentum >> Conservation of Momentum
Types of Collision >>

6.2 - Conservation of Momentum

  • To understand that in the absence of an external force, the total momentum of a system is conserved.
  • To know that this is a consequence of Newton's First Law of Motion
In any closed system, if there is no external force acting on it, the overall momentum is conserved.  This is a direct consequence of Newton's First Law of Motion.  I will discuss what a closed system is later - it is a key concept at AP.  Generally the law of conservation of momentum is used for collisions and explosions.  Drawing a pair of well-labelled diagrams to show the 'before' and 'after' situation of the event is extremely useful and is actively encouraged.

Collisions

There are a couple of common situations:  an object runs into another head on a collide or it bounces off.  Note the before and after on all of the diagrams!

Picture
The overall momentum before the collision is the sum of the two momenta, with the \(2 \,\text{kg}\) cart being negative as it is moving to the left.
\[​p_{before}= p_{1}+p_{2}= \left ( 4\times 15 \right )+\left ( 2\times -3 \right )=54\, \text{kgm/s}\]
​Therefore, the total momentum of the coupled carts after must also equal \(56 \,\text{kgm/s}\).
\[p_{after}= 54 \,\text{kgm/s}= (6\, \text{kg}\times v)\]
\[v = \frac{54}{6}=9 \,\text{m/s}\]

The interesting thing about the above example is that if you think about it really carefully you can see that the centre of mass of the system continues to move at a constant speed to the right.  This is Newton's First Law.  Our previous version of it assumed that we were dealing with ONE object whose mass is constant.  But really we should consider a more general version of it.  

In the absence of an external resultant force the motion of a closed system remains constant.  The motion is defined by momentum as it involves not only the velocity but the mass as well.   The situation above is such a closed system.  Now if an external force such as friction or due to a gradient was involved the momentum would not be conserved.  We analyse it further by saying that the centre of mass will accelerate.  But that is beyond the scope of this sub-topic.
​


Types of Collision >>

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PhET SImulation: Collision Lab
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    • Solids, Liquids and Gases
    • Waves
    • Astrophysics
    • Electricity
    • Magnetism
    • Nuclear Physics
    • IGCSE revision
  • Physics I
    • Kinematics >
      • Variables and Units
      • Describing Motion
      • Equations of Motion
      • Problem Solving
      • Projectiles
      • Kinematics Animations
    • Dynamics >
      • Forces
      • Static Equilibrium
      • Newton's Laws
      • Friction
      • Advanced Problems
    • Gravitation and Orbits >
      • Circular Motion
      • Vertical Circles
      • Universal Gravitation
      • Orbits
      • Circular Motion Animation
    • Energy >
      • Work
      • Springs
      • PE and KE
      • Conservation of Energy
      • Work-Energy Theorem
    • Linear Momentum >
      • Impulse
      • Conservation of Momentum
      • Types of Collision
      • 2-D Collisions
    • Simple Harmonic Motion >
      • Mass on Spring
      • Pendulums
      • SHM Animations
    • Rotational Mechanics >
      • Torque
      • Rotational Kinematics
      • Rotational Dynamics
      • Angular Momentum
      • Rotational Energy
    • Mechanical Waves >
      • Waves on a String
      • Sound
    • AP-1 Revision
    • AP Physics C (Mechanics)
  • Physics II
    • Fluid Mechanics
    • Thermal Physics
    • Electrostatics
    • Magnetic Fields >
      • EM Induction
    • Interference and Diffraction
    • Optics
    • Modern Physics
    • AP 2 Revision
  • OCEANOGRAPHY
    • The World Ocean >
      • What is Oceanography
      • History
      • Lat and Long
      • Size and Origin
      • Plate Tectonics
    • Seawater >
      • A Salty Sea
      • Measuring Salinity
      • Thermal Properties
      • Density Profiles
      • Drinking Seawater
    • Circulation and Climate >
      • Global Heating
      • Coriolis Effect
      • Surface Currents
      • Vertical Motion
      • Thermohaline Circulation
      • El Nino
      • Carbon Cycle
    • Waves and Tides >
      • Wave Motion
      • Formation of Waves
      • Beaches
      • Tsunamis
      • Tides
    • Observation Systems >
      • Challenges
      • The CTD
      • Moorings
      • Sound Waves
      • Robotics
      • Satellites
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      • Weather Systems
      • Weather Forecasting
      • Hurricanes
      • Navigation
      • Life at Sea
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