Saturday, December 11, 2010


Newton's Three Laws are:

  1. The law of Inertia.  Objects will continue to be in motion or stationary unless it is affected by another force against it.
  2. Force=mass . acceleration.  Force is directly proportional to mass times acceleration. Mass and acceleration however share an inverse relationship.
  3. For every action force, there is and equal and opposite reaction force. (However it is possible for the reaction force to act in the same direction as the action force. For example if a person with skates is standing constant on ice, and another person skating bumps into the stationary person, the reaction force will send the stationary person in the same direction as the skating person was traveling.)
Four types of problems involving Newton's Three Laws:
1. Equilibrium
Equilibrium is when the object remains static.  These are the assumptions made when solving equilibrium problems:
  • there is no friction
  • there is no acceleration
  • the net force is 0
2. Inclined Planes
There are incline problems can be solved in two ways. (Those involving a static Mk and those involving a  kinetic Mk.) Incline plane problems involves friction because the object is sliding down a slope (hence the name inclined plane). The object has a friction because since the surface is slanted there is a force applied in the x-axis. Friction resists the force. Assumptions to be made when solving incline plane problems are:
For static:
  • there is no acceleration
  • the positive axes is the direction of acceleration on the surface
  • there is no air resistance
  • Mu is static if the object is not moving at first
  • the normal force is perpendicular to the surface
For kinetic:
  • The normal force is perpendicular to the surface
  • there is acceleration
  • there is no air resistance
  • Positive axes are in the direction of acceleration and surface
  • Mu is kinetic if the object is moving
When solving incline questions FBDs can be really helpful.  Gravity is always pointing down.  Gravity should be broken down using x and y components.
3. Pulleys
The assumptions when solving pulley problems are:
  • the pulley has no friction
  • the rope is frictionless
  • there is no air resistance
  • there are 2 FBDs (one for each load)
  • tension for both systems is equal
  • Acceleration of the 2 systems is the same
  • Positive axes are the direction of the acceleration of each load
4. Trains
Assumptions for train questions:
  • there is no air resistance
  • there is the same acceleration throughout the whole system
  • the y component is in equilibrium (no acceleration) 
  • FBDs one for each of the masses
  • The cables that connect the masses are weightless
  • Positive axis is in the direction of  the acceleration
There are also tension forces connecting the carts. For example the tension force pulling cart 3 forwards is the same as the tension force pulling cart 2 backwards.

Assumptions are very important to include when solving the four types of problems, because it is necessary to specify the conditions concerning a problem in order to find a way to solve it.

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