EJSS Static and Kinetic Friction on Incline Plane Model

EJSS Static and Kinetic Friction on Incline Plane Model

reference:

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
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

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,

mgcos(θ)=Ftangent , is balanced by the force caused by static friction

fstatic, 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,

∑F=0

mgsin(θ)−fstatic=0

mgcos(θ)−N=0

In this model,

Ftangent=mgsin(θ)

Fnormal=mgcos(θ)

However, the modulus of this force

fstatic cannot exceed a limit value of

μ|N| where

μstatic is the static friction coefficient between the block and the plane.

fstatic≤μstaticN in the direction negative of the velocity vector.

In this model, when velocity = 0,

fstaticmax=μstaticN and

fstatic=−Math.min(mgsin(θ),fstaticmax)

since

fstatic cannot be greater than

mgsin(θ) nor

μstaticN

When the user increases the slope of the plane

θ by dragging slider of angle

θ ,

Ftangent ends up being larger than this limit and the block slides down the plane with kinetic friction present

fkinetic=μkineticN .

In this model, when velocity not equal to zero,

fkinetic=−μkineticN .

The force caused by static friction is replaced by a (smaller) force of dynamic (or kinetic) friction

fkinetic, given by

μkinetic|N| (where

μkinetic is the dynamic friction coefficient between the block and the plane, which is smaller then the static one,

μstatic).

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:

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