## Wednesday, May 7, 2014

### EJSS Object on Plane Model for Primary School Inquiry

EJSS Object on Plane Model for Primary School Inquiry showing Friction versus time

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

## The other derived and similar models

 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
}