## Friday, April 4, 2014

### EJS Static and Kinetic Friction on Incline Plane Model

EJS Static and Kinetic Friction on Incline Plane Model

reference:
1. Sliding Down an Incline Plane Model by Francisco Esquembre http://www.compadre.org/osp/items/detail.cfm?ID=9973

 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, $N$ .

In equilibrium,

$\sum F = 0$

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

$mg cos ( \theta ) - N = 0$

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.

$f_{static} \leq \mu_{static}N$

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

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

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, $\mu_{static}$).