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Tuesday, April 8, 2014

EJSS Static and Kinetic Friction on Incline Plane Model

EJSS Static and Kinetic Friction on Incline Plane Model

reference:
  1. EJS Static and Kinetic Friction on Incline Plane Model by Francisco Esquembre and lookang http://weelookang.blogspot.sg/2014/04/ejs-static-and-kinetic-friction-on.html
  2. Sliding Down an Incline Plane Model by Francisco Esquembre http://www.compadre.org/osp/items/detail.cfm?ID=9973
EJSS Static and Kinetic Friction on Incline Plane Model
http://weelookang.blogspot.sg/2014/04/ejss-static-and-kinetic-friction-on.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_friction/friction_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_friction.zip
author: Francisco Esquembre and recreated on EJSS by lookang
EJSS Static and Kinetic Friction on Incline Plane Model
http://weelookang.blogspot.sg/2014/04/ejss-static-and-kinetic-friction-on.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_friction/friction_Simulation.html
source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_friction.zip
author: Francisco Esquembre and recreated on EJSS by lookang

EJS Static and Kinetic Friction on Incline Plane Model
http://weelookang.blogspot.sg/2014/04/ejs-static-and-kinetic-friction-on.html
https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejs_model_SlidingDownAnInclinedPlanewee.jar
author: Francisco Esquembre and remixed by lookang

Model description by Paco:

Block sliding down an inclined plane

A stone block is lying on an inclined plane.

Initially, the component of gravity along the plane surface, $ mg cos (\theta ) = F_{tangent} $ , is balanced by the force caused by static friction $ f_{static} $, which is proportional to the normal to the plane, $ N $ .
The model assume the mass of the block is m = 1 kg,

$ W = mg $

where $ W $ is the weight and $ g $ is the gravitational constant of 9.81 m/s^2

In equilibrium,

$ \sum F = 0 $

$ mg sin ( \theta ) -  f_{static} = 0 $

$ mg cos ( \theta ) -  N = 0 $

In this model,

$ F_{tangent} = mg sin ( \theta ) $

$ F_{normal} = mg cos ( \theta ) $

However, the modulus of this force $ f_{static} $ cannot exceed a limit value of  $ \mu | N| $  where $ \mu_{static} $ is the static friction coefficient between the block and the plane.


$ f_{static} \leq \mu_{static}N $ in the direction negative of the velocity vector.

In this model, when velocity = 0,

$ f_{static max} = \mu_{static}N $ and

$ f_{static } = -Math.min( mg sin( \theta ), f_{static max}  ) $ 

since $ f_{static } $ cannot be greater than $ mg sin( \theta ) $ nor $ \mu_{static}N $

When the user increases the slope of the plane $ \theta $ by dragging slider of angle $ \theta $ , $ F_{tangent} $ ends up being larger than this limit and the block slides down the plane with kinetic friction present $ f_{kinetic} = \mu_{kinetic}N $ .

In this model, when velocity not equal to zero,

$ f_{kinetic} = - \mu_{kinetic}N $ .

The force caused by static friction is replaced by a (smaller) force of dynamic (or kinetic) friction $ f_{kinetic} $, given by $ \mu_{kinetic} |N| $ (where $ \mu_{kinetic} $ is the dynamic friction coefficient between the block and the plane, which is smaller then the static one, $ \mu_{static} $).

Condition for hint:

if (velocity = 0 and and only and totalForce(t,x,v) = 0), hint statetext = " in equilibrium,..."
else if (velocity = 0 and and only and totalForce(t,x,v) != 0) hint statetext = " NOT in equilibrium,..."
else if (velocity != 0) hintstatetext= " NOT in equilibrium and in motion..."

Determine direction of motion and direction of friction

if (v===0){
  directionOfMotion=0;
  }
  else if (v<0){
    directionOfMotion=-1;
    }
    else if (v>0){
    directionOfMotion=+1;
    }

Custom function:

function totalForce(time,position,velocity) {
 if (velocity!==0) return Ft+directionOfMotion*dynamicFriction; // in motion
  return Math.max(0,staticFriction+Ft); // not in motion
}

changes made:

  1. re-implemented on EJSS
  2. added a scaleforce to draw the forces to user's choice
  3. made the static and kinetic friction drawn from same vector as visible===true was buggy
  4. added more hints to make explicit in equilibrium and not in equilibrium when net force.
  5. made the color dynamic with change in static to kinetic
  6. added paco as co-author as the EJS codes came from the man :)




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