Friday, April 4, 2014

EJS Static and Kinetic Friction on Incline Plane Model

EJS Static and Kinetic Friction on Incline Plane Model

  1. Sliding Down an Incline Plane Model by Francisco Esquembre

EJS Static and Kinetic Friction on Incline Plane Model
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} $).

changes made:

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