Thursday, December 19, 2013

Sliding Block Model

to learn, is to inquiry about it yourself. enjoy!

Sliding Block Model by Fu-Kwun Hwang

this version on the blog is only slightly edited by lookang.
Ejs Open Source Frictional Mass Block moving on Horizontal Plane Java Applet by Fu-Kwun Hwang, remixed by lookang
author:Fu-Kwun Hwang, remixed by lookang

to help in activity real life problem question by
Activity 4 - Consolidation
Real life problem

Alan has been asking Jenny what her mass is, but Jenny refuses to tell him.
Alan came up with a plan to try to measure Jenny’s mass without her knowing.
One day, Alan asks Jenny out to a ice skating ring.
He has a super duper iPhone app that can measure both the force and acceleration.
Once Jenny steps into the ring, Alan gave Jenny a push and activated his iPhone to measure the force he applied and the acceleration of Jenny.
The result is as follow:
Force = 135N
Acceleration = 3m/s2
Alan concluded that the mass of Jenny is 45kg.
Jenny laughed and said: “ I am not so heavy”.
Q1. Work with your group members to determine who is right and explain.

Q2. If Jenny's mass is only 40 kg, what is the size of the frictional force?

Do some research on the internet if you need to.

as part of the review process in ICT connection lesson submission, officers in MOEHQ-ETD would value add during the peer review process by creating computer models to support student's inquiry.  enjoy!
this model is made by Fu-Kwun Hwang and Loo Kang Lawrence Wee
 — with Albert Teo and 2 others.

Sliding Block Model by Fu-Kwun Hwang

The Sliding Block model displays the dynamics of a block being push along by an external force.. When the block is sliding, Newton's law for motion for a mass m moving along the horizontal plane can be written as

$m\frac{d^{2}x}{dt^{2}} = -  \mu_{k}mg $

where $\mu_{k}$ is the kinetic (sliding) coefficient of friction,  and g is the acceleration of gravity in m/s^2. The - sign is because the friction oppose the +x direction.

In this model the static friction force prevents motion until some limit where motion occurs. It is characterized by a static coefficient of friction $\mu_{s}$ and is equal and opposite to the net applied force less than a maximum value.

The dry friction resists relative lateral motion of two solid surfaces in contact.The two regimes of dry friction are 'static friction' ("stiction") between non-moving surfaces, and kinetic friction (sometimes called sliding friction or dynamic friction) between moving surfaces.
For simplicity, we assume  

Coulomb friction, named after Charles-Augustin de Coulomb, is an approximate model used to calculate the force of dry friction. It is governed by the model:
$ |\ f | \le -\mu_{s} N = -\mu_{s} mg $
is the force of friction exerted by each surface on the other. It is parallel to the surface, in a direction opposite to the net applied force.
$\mu_{s}$ is the coefficient of friction, which is an empirical property of the contacting materials,
N is the normal force exerted by each surface on the other, directed perpendicular (normal) to the surface.

The Coulomb friction f may take any value from zero up to $\mu_{s} N$, and the direction of the frictional force against a surface is opposite to the motion that surface would experience in the absence of friction. Thus, in the static case, the frictional force is exactly what it must be in order to prevent motion between the surfaces; it balances the net force tending to cause such motion. In this case, rather than providing an estimate of the actual frictional force, the Coulomb approximation provides a threshold value for this force, above which motion would commence. This maximum force is known as traction.

The force of friction is always exerted in a direction that opposes movement (for kinetic friction) or potential movement (for static friction) between the two surfaces.

$\ frictionForce = Math.signum(v) \mu_{k}mg $