Thursday, 14 February 2013

Modelling mechanics in software

Mechanics is more than just an application of algebra and geometry, it is the primary application of geometry and algebra.  Newton’s development of calculus was to answer problems in what we would now call mechanics and much of his work was geometrical in nature.  However, students study less geometry than they use to and this, along with difficulties in algebra, can result in issues when they start studying mechanics.

As a remedy to this software that links geometry and algebra is perfect tool in which students can practise modelling situations in mechanics.  This can complement their studies in mechanics and enhance their skills.

In particular two main methods that lend themselves well to being represented in software are interactive force diagrams and animations of position.

Interactive force diagrams

Interactive force diagrams can be created where the vectors for the forces acting on an object are represented dynamically.

The diagram below shows the forces acting on a block when there is a pulling force at some angle to the upwards vertical.

Animations of position

Many other situations in mechanics are about describing how objects move and this movement is often defined as function as time.  This may be something as straightforward as the position being given as a linear function of the time (in the case of constant velocity) or more completed examples where the velocity, acceleration or force are given as functions of the time.

Most graph-plotters and dynamic geometry software allow for a function, or the coordinates of a point, to be defined in terms of a parameter, t.  This means that if you know the x and y-position of a particle as a function of the time these can be entered to give the path of the particle.

To further enhance this a slider can be added for t and the both the position of the particle and vectors for velocity (and acceleration) can be shown.  In Geogebra once a slider has been added this can be animated. 

The example below shows the position, velocity and speed for a particle where these are functions of time.

Further examples

A full A level Mechanics 1 paper converted to dynamic Geogebra files can be found at:

1 comment:

  1. I read it thoroughly and found out lot of new things to learn. You have done very good work. Keep it up ! Have a nice day !!

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