MATH 1152 Kwantlen Polytechnic University Algebra Question

MATH 1152 Maple Assignment 2Due: 11:59PM, March 25
Assignment Requirements
• Your assignment must be as a Worksheet, not a Document, and commands must be in Maple notation,
not 2-D Display. To ensure that all execution groups use Maple notation, from the “Tools” menu,
select “Options.” Click on the “Display” tab in the pop-up window that appears, click on “Maple
Notation” for the “Input Display,” and click on the “Apply Globally” button at the bottom.
• Your assignment must have a properly-formatted title identifying the assignment number and course.
There must be an “author.”
• Load all packages at the top of the worksheet, just below the title. Syntax is “with(package name ).”
• Your assignment must include text and must include material entered as math within that text.
• If you use an object more than once, make sure to give it a name. You name objects in Maple with
“:=”. The names should be descriptive and more than one character. For example, “x” is a very bad
name (can you see why?), and A1, A2, etc. do not make debugging or understanding your work any
easier.
• Type in all commands you use. Selecting commands from tooltips etc. is easy, but Maple sometimes
forgets what you have done when you re-execute a worksheet, and it makes editing commands harder.
• When you have finished the assignment, clean up your worksheet. Eliminate unnecessary lines (Ctrldelete), and suppress printing of output you do not want to see by ending those lines with a “:”
• Object names must be descriptive. “f1” is a very bad choice for an object name, especially if you define
many functions.
• Late assignments lose 10% per day.
• All graphs must be black-and-white. If they have more than one plot, different line styles must be
used to distinguish the plots, there must be a legend, and there must be title. Graphs must not cross
vertical asymptotes, though you can add a dashed line to indicate a vertical asymptote (you will have
to figure out how to do so).
Useful Maple Facts
• Load packages using “with(package name )”. When handing in, make sure to end this line with a
“:”. Should you so desire, you can load individual commands from a package.
• When you re-open a worksheet, none of the commands have been executed (despite their results
showing). Re-execute the worksheet by clicking on the triple exclamation mark in the toolbar.
• Eliminate unnecessary lines with ctrl-delete
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• To start a Text group below the cursor, click on “T” in the toolbar. To add math within a text group,
click on “non-executable math” just above the window. To return to text, move the cursor to the end
of the math, and click on “text” just above the window. The style menu will help with formatting.
• The ln function is known as log, with log[10] being log base 10. The exponential function is known
as exp, so exp(2) is e2 .
• A list in Maple is a comma-separated list enclosed in square brackets. A set is a comma-separated list
enclosed in braces. Lists have an order and allow repeats, sets have no order and repeats are ignored.
• A range of values is given by a..b where a is the left endpoint, and b the right.
• Commands you may find useful are eval, evalf, LinearSolve, GaussianElimination, and BackwardSubstitute.
Multiplication of matrices and matrices, matrices and vectors, or the dot product of vectors is with “.”
Maple guesses at the intended multiplication, so you may need to be more specific using MatrixMatrixMultiply,
MatrixVectorMultiply, or DotProduct. All but eval and evalf are in the LinearAlgebra package.
Assignment
Purpose
In this assignment you will analyze the truss above using Maple. The truss is anchored at A, and all
horizontal and vertical forces are absorbed there. The truss is further anchored at F so that all horizontal
(but no vertical) forces at B are absorbed. The truss makes an angle of α with the horizontal, and a weight,
W hangs off the end. The Ti are the magnitudes of the stresses in the corresponding members.
π
1. For α =
set up the statics equations at each of the nodes B, C, D, E in Maple and solve for
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T1 , T2 , · · · , T7 . Assume each Ti is a stress, that is, the forces at each node point along the relevant
member, and the member is pushing the node away. Which members are under stress? Which are
under tension? Which member is under the greatest stress? Which is under the grestest tension?
π
2. We now want to see how the forces change as α varies between 0 and . Set up the statics equations
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for an arbitrary α, and solve for T1 , T2 , · · · , T7 . As for question 1, assume all forces are stresses.
(a) Plot the forces against θ on a single graph. Make sure your graph is in black-and-white, that the
forces are distinguished by different line styles, and that your graph has a legend. Note that if V
is a Vector, the command convert(V, list) will convert V into a list.
(b) Are there members that are under stress for some angles, and under tension for others? Which
members are under the highest stress? For which angles? Which are under the highest tension?
For which angles?
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Notes
• The solution is rather sensitive to errors, so double check your statics equations.
• I find it easiest to assemble the equations by assuming the forces are vectors, and concatenating them
to produce the matrix equation. Note that there, then, 4 directions, including the zero vector.
• I found it easiest to use the standard horizontal and vertical axes, but feel free to tilt yours!
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