reference:

- 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 $

$ 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} $).

## changes made:

- re-position to the hint texts
- made the hint "change the angle of the slope and click play" to appear once only and playing and paused as other hints
- re layout the model with my usual slider design and colored background
- added stroke line to be dashed to represent components of gravity forces
- made the auto-scale of y to allow angle up to 90 degrees.
- added a scaleforce to draw the forces to user's choice
- made the view xmin,xmax, ymin,ymax to increase by 1 if object over move
- fix a bug on the visual of vector of kinetic friction to be directionOfMotion*dynamicFriction