![Modellu
Modellus 4
2008 http://m de
http:// odellus.fct.unl.pt
http://modellus.fct.unl.pt
/ ct t
5
1 How to build a Once the Vector representing
the initial velocity is defined,
using its components, the tip of
model? the Vector may be dragged to
Start by defining the functions that describe one or
5 attribute adequate values to the
components of the initial velocity.
several properties/quantities of the phenomenon or
mathematical object under study… 1 Alternatively, these values may
be directly introduced in the
For example, the equations highlighted in the figure
Mathematical Model window or in
refer to the motion of a projectile when air resistance
the Parameters ribbon.
is negligible.
2 6
It is possible to create
objects in the workspace to
represent the variables of the The Play / Pause button starts the simulation of
model, either using the icons the projectile motion. The domain and step of the
or the right button of the independent variable t are defined in the Independent
mouse.
2 Variable ribbon: by default, the domain is [0; 50] and
the step is 0.1. These values may be changed.
For example, a Particle may
be created to represent the 6 In this example the motion was interrupted when
projectile. t = 7.90…
3 7 7
3
To each object of In the example shown in the figure, it was also created
the workspace it is a Pen to trace the graph of y as a function of t in the
possible to assign workspace.
defining properties.
For example, x and Each object in the workspace may have its own scale,
y are associated to independently of the other objects, as well as other
the Particle as the features (colour, etc.). The Autoscale button may be
particle coordinates. used to adjust a scale that is a function of the minimum
and maximum values of the quantities defining each
object.
4 8 8
Since in the model Each model may have as many objects as necessary
the components of to better visualize the phenomenon, the physical
the initial velocity are quantities involved or the corresponding mathematical
indicated by v0x and objects.
v0y, it is possible to
4 represent the initial To the projectile model were added functions describing
velocity by a Vector. the potential energy, the kinetic energy, etc, as
functions of time, as well as the velocity and the
acceleration in each instant.
Modellu
Modellus 4
2008 http://m de
http:// odellus.fct.unl.pt
http://modellus.fct.unl.pt
/ ct t](https://image.slidesharecdn.com/2008modellus4-01flyeruk-120207144426-phpapp02/85/kimika-2-320.jpg)
kimika
- 1. Four examples... Modellus 4 2008 http://modellus.fct.unl.pt The Dino starts moving to the right with acceleration pointing to the left… Before starting the motion, it is possible to define the initial position, the initial velocity and the acceleration, Interactive Modelling with Mathematics dragging the corresponding Vectors. In the graphs drawn, the second graph represents the derivative of the first and the third graph represents the derivative of the second… Modellus is designed to introduce students and teachers in scientific computation, namely through the analysis and exploration of mathematical models based on functions, iterations and differential equations. For example, it allows the construction and analysis of models illustrating Newton’s reasoning when comparing the motion of A stroboscopic photo of a collision was placed as a a projectile and the motion of a satellite. background in the workspace... The development of Modellus 4 is being done with generous support from the Portu- guese Ministry of Education (DGIDC), the Portuguese Foundation for Science and Three Vectors were created to measure, in an arbitrary Technology (FCT), the European Community, the Institute of Physics (UK) and the scale, the linear momentum of each object, before and research unit UIED-FCTUNL. after the collision… Dragging the Vectors it is easy to check the conservation of the linear momentum... The Modellus installation program includes many examples and others are regularly added to the web site http://modellus.fct.unl.pt. Besides the Modellus files, the web site also contains several documents for students and teachers from basic learning levels to higher education. These The side of a square was defined… documents are regularly updated. The area and the perimeter were calculated… The square was represented by Geometrical Objects In the figure, an example that illustrates the use of (Segments), which may be linked in succession… sinusoidal functions in an oscilloscope. With this model Several Pens were created to represent relations it is possible to analyse the frequency, the amplitude between area and perimeter, etc… and other aspects of periodic sinusoidal signals. Model of the motion of a bouncing ball: the vertical A model was created using a system of ordinary trajectory of the ball and several graphs for physical differential equations (which represent the instantaneous quantities as functions of time may be visualised rate of change of products and reactants…). simultaneously. It is also possible to attribute a certain The model assumes plausible reaction velocities… initial velocity to the ball and to study the ideal case Several Level Indicators (Bars) and Pens were created to when there is no energy dissipation. represent parameters and initial values… Play / Pause executes the model… Using the mouse it is possible to dynamically change the concentration values and observe how the system behaves when there is a change in the concentration of Modellu Modellus 4 the chemical species… 2008 http://m de http:// odellus.fct.unl.pt http://modellus.fct.unl.pt / ct t
- 2. Modellu Modellus 4 2008 http://m de http:// odellus.fct.unl.pt http://modellus.fct.unl.pt / ct t 5 1 How to build a Once the Vector representing the initial velocity is defined, using its components, the tip of model? the Vector may be dragged to Start by defining the functions that describe one or 5 attribute adequate values to the components of the initial velocity. several properties/quantities of the phenomenon or mathematical object under study… 1 Alternatively, these values may be directly introduced in the For example, the equations highlighted in the figure Mathematical Model window or in refer to the motion of a projectile when air resistance the Parameters ribbon. is negligible. 2 6 It is possible to create objects in the workspace to represent the variables of the The Play / Pause button starts the simulation of model, either using the icons the projectile motion. The domain and step of the or the right button of the independent variable t are defined in the Independent mouse. 2 Variable ribbon: by default, the domain is [0; 50] and the step is 0.1. These values may be changed. For example, a Particle may be created to represent the 6 In this example the motion was interrupted when projectile. t = 7.90… 3 7 7 3 To each object of In the example shown in the figure, it was also created the workspace it is a Pen to trace the graph of y as a function of t in the possible to assign workspace. defining properties. For example, x and Each object in the workspace may have its own scale, y are associated to independently of the other objects, as well as other the Particle as the features (colour, etc.). The Autoscale button may be particle coordinates. used to adjust a scale that is a function of the minimum and maximum values of the quantities defining each object. 4 8 8 Since in the model Each model may have as many objects as necessary the components of to better visualize the phenomenon, the physical the initial velocity are quantities involved or the corresponding mathematical indicated by v0x and objects. v0y, it is possible to 4 represent the initial To the projectile model were added functions describing velocity by a Vector. the potential energy, the kinetic energy, etc, as functions of time, as well as the velocity and the acceleration in each instant. Modellu Modellus 4 2008 http://m de http:// odellus.fct.unl.pt http://modellus.fct.unl.pt / ct t