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:  http://www.mei.org.uk/?section=resources&page=ict#geogebra

Comments

  1. Holton25 June 2014 at 05:33

    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 !!

    digital certificate

    ReplyDelete
  2. Unknown21 October 2017 at 16:22

    this is really nice to read..informative post is very good to read..thanks a lot! digital signage cloud

    ReplyDelete

Post a Comment

Popular posts from this blog

Maths GIFs: parabolas

Image
One of the fantastic features of dynamic graphing software is that you can animate how a graph changes as some aspect of it is varied. I'm particularly keen on making short GIFs of animated graphs that demonstrate interesting properties.  One advantage of animated GIFs is that they are really easy to distribute via Twitter. There are loads of them if you have a look at the hashtag #mathgif .  Parabolas I've been posting animated Maths GIFs to Twitter for quite a while now. Here are some of my favourites featuring parabolas: The midpoint of the points of intersection of y  =  x ² and y  = mx  + c lies on the line x = m /2. The tangent at point P to a parabola with vertex Q can be constructed by finding R, the point of intersection of the vertical through P and the horizontal through Q, finding the midpoint, M, of QR and then drawing the line through P and M. If the tangents at two points A and B on a parabola are perpendicular then the line AB goes through the focus and the tang
Read more

The problem with Powerpoint for teaching maths

There are a lot places on the internet where the are negative opinions about Powerpoint.  I don't want to repeat these arguments here, instead I wish highlight particular problems relating to the use of Powerpoint in the teaching and learning of mathematics.  These are that: It reinforces a view of mathematics that it is a series of algorithms to be rote-learned; It can reduce the amount of student-centred use of ICT in learning mathematics; It is usually a static form of mathematics and there are many easy tools for creating equivalent dynamic forms of mathematics. Reinforcing a limited perception of mathematics Many Powerpoint presentations for mathematics feature a question with the stages of a solution presented.  This can have a negative impact of students' perceptions of mathematics.  There is a link between students' perception of mathematics and how successful they are.  Students who perceive maths a series of unrelated recipes for solving problems are less
Read more

Desmos Classroom Activities: An ideal tool for remote/blended learning

Image
The past few months have been a very chaotic time for teachers and students. Many schools and colleges are now back to teaching full time but this year is likely to be very challenging and teachers want to know that they can provide opportunities for students to learn, even if the normal day-to-day routines are disrupted. For me, one tool stands out as particularly effective in ensuring that students have interesting and engaging activities that will develop their mathematical understanding: Desmos Classroom. Desmos Classroom Activities  Desmos Classroom activities are collections of screens that provide students with the opportunity to interact and respond to mathematical questions. They can feature text answers, mathematical answers, graphical features, multi-choice, card sorts and many other types of elements.  There is a large selection of pre-made activities and it's really easy to adapt these or create your own. These activities are great for supporting students in thinking d
Read more