Forces acting at a point
Introduction
This software has been designed to provide visual representations of the addition of
vectors and can be used to show the concept of a polygon of forces. It allows
vectors to be manipulated on-screen, so that they can be added together and the
resultant seen both graphically and numerically.
This guide aims to introduce teachers and lecturers to the software and to provide
some possible lesson ideas. There are a number of files that go with this booklet that
can be loaded rather than using the random generation of vectors that are a feature
of the software.
MEI has been responsible for the development of the software and would be
interested to receive feedback from teachers and lecturers who use the software.
To start the resource, open Forces acting at a point.html in your web browser.
Screen layout
The general screen layout is shown below.
Change the problem
options.
Force vectors. These can act from
the origin, or the end of another
vector.
Controls to predict the
direction of the resultant
force vector.
Customise, save or load a custom
problem configuration.
Generate a
new problem.
Zoom display in.
Currently shows the
magnitude and
direction of each
individual force.
Zoom display out.
Display area. Click and
drag to move.
Click here to change the
display to show the
resolved horizontal and
vertical components of
each force.
Show/hide force
vectors.
Click on a row here to
highlight the vector in the
display area.
Show previous layout of the
forces. This allows you to show
that the resultant is the same
regardless of the order that the
forces are examined.
Reset the forces
to their original
layout.
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Origin.
Details of connected
force vector.
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Main features
Clicking the options button gives, for example:
The options are:
Option
Description
Number of forces
Selects the number of forces in the problem.
Selecting “Random” will generate between 2 and
5. A new problem will be generated if the number
of forces is changed.
Defines the resultant force of new problems.
Problem resultant
Always zero:
The combined vertical and
horizontal components of all
the force vectors will be zero.
Never zero:
The magnitude of the
resultant force vector will be
non-zero.
Random:
The force vectors will be
defined at random.
Defines when the resultant sum will be displayed
in the bottom panel.
Resultant sum
Show:
The bottom panel displays
the resultant force of the
connected force vectors.
Hide:
The bottom panel Never
displays the resultant force in
the bottom panel.
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Option
Description
On complete:
Grid lines
Arrow position
Show components
The bottom panel only
displays the resultant force
once all of the forces have
been connected.
Show/hide grid lines.
Change the position of the arrow on the force
vectors. They can be positioned at the end or in
the middle of the vector.
Choose whether or not to display the vertical and
horizontal components of the vectors.
If you are using the resource online and your browser allows cookies then any
update to the options will be saved. If you have downloaded the resource and are
running it locally then the options will also be saved.
Examples
A set of example problems is included with this resource. To open an example, select
Custom in the top right of the window, and then select Open in the bottom left.
Navigate to the resource’s directory. Load the file First Example. Your window
should now look like this:
You have now opened a custom configuration. In the resource directory, there are a
number of examples that you can open and use. See the Appendix for pictures of
each one.
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HV Forces: These examples contain only horizontal and vertical force vectors, and
are a good starting point.
Students should try and identify whether they are in equilibrium, and if not, what the
resultant force is equal to.
Can Equilibrium: Students may be posed the question: Can two non-zero vertical
vectors and one non-zero horizontal vector ever be in equilibrium?
These examples give students a visual aid to help answer this.
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Force Angles: These examples contain forces at angles. Students may be asked to
predict whether or not the forces are at equilibrium.
Generating your own examples
You can also press New at any time to generate a new random configuration,
according to the options you have set.
Information panels
Once you have generated a problem, whether by loading a custom one or generating
a random one, there are a few panels that give you information about it.
The left hand panel can be set to describe the force vectors in terms of their
magnitude and direction, or in terms of their x and y components. So for the First
Example configuration, these would show:
On either of these views, you may click on a row to see the corresponding vector
highlighted in the display area. Likewise, clicking on a vector in the display area will
highlight the corresponding row in the information panel.
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The bottom panel of the window gives you the equivalent information about the
resultant of the connected vectors. Depending on how you have set your options this
may show at different times or not at all (see the options section above):
It is important to note that this panel will only ever show the details of connected
vectors, regardless of your settings. We will see how to connect vectors below.
Predictions
Before solving a problem, students can be asked to predict the direction of the
resultant force vector. You can use the
buttons in the top panel to choose the
direction that you think the resultant will point, or press the
resultant will be zero.
button if you think the
After making a prediction, you can check to see if it is correct by dragging all of the
forces end to end, to create a single resultant force, as shown below.
If you need more room, drag the display or zoom in/out.
Now compare your prediction to the actual resultant (shown by the light blue arrow).
When you have finished building the force vector, you will see the
symbol
appear in the bottom left of the display area. Click this repeatedly to see the force
vector built out of its individual horizontal and vertical components.
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Show Last Function
This resource also contains a function that allows you to rearrange the forces whilst
displaying your previous arrangement, to demonstrate that vectors will give the same
result, regardless of which order they are added.
After arranging the forces in one way, click Reset and then Show Last. You may
then rearrange the forces in another way to prove that the end point will be the same,
as shown below:
Custom Configurations
Using the Custom button you can create, save and load your own examples. After
pressing Custom, the bottom panel should look like this:
This indicates that you have entered custom mode.
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While in custom mode, you can edit the direction and length of the force vectors by
clicking and dragging the ends.
Clicking on OK returns you to the mode where you can drag vectors. You cannot add
or remove vectors. To increase or decrease the number of vectors, go to Options,
and choose a number between 2 and 5.
If you want to save a configuration click Save and provide a suitable filename.
To load previously saved problems click Load and select the file. Note that this may
change the number of vectors.
Once you have finished creating your custom configuration, select Save, and give
your configuration a name. It is important that you save the file in the same folder as
the resource. You need to be running the resource locally to do this.
This configuration can now be opened and used whenever it is needed.
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Appendix
Examples:
Below are some reference sheets for the example configurations contained in the
resource directory.
HV Forces 1:
HV Forces 2:
HV Forces 3:
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HV Forces 4:
Can Equilibrium 1:
Can Equilibrium 2:
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Can Equilibrium 3:
Force Angles 1:
Force Angles 2:
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Force Angles 3:
Force Angles 4:
Force Angles 5:
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Force Angles 6:
Force Angles 7:
Force Angles 8:
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