Couples in equilibrium

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5 years, 11 months ago

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Question statement

{applet}

Determine angle $\alpha$ knowing that the triangular plate is in equilbrium when subjected to the three couples shown.

Give any introductory information the student needs.

			Name	Type	Generated Value

alpha	integer	69
F_1	integer	350
F_2	integer	-500

			Name	Type	Generated Value

F_3	number	341.3614309077
x_max	number	-55.0079798014
roots	list	[ 69, -179.0159596029 ]

			Name	Type	Generated Value

applet	ggbapplet	HTML node
params	dict	Dictionary with 3 entries
advice	ggbapplet	HTML node
advice_params	dict	Dictionary with 3 entries

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(25..75)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

→ Used by:

F_3
params
roots

"Unnamed part" → "alpha" - Correct Angle as quantity

Parts

Gap-fill
1. Gap alpha Angle quantity
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$\alpha $ = alpha

Note: the angle is an integer between 0° and 90°.

Advice

The triangular plate is in equlibrium, so the three couple moments add to zero. Note that the length of side $d$ the triangle is not significant, only the angle $\alpha$.

\[\begin{align} \Sigma M &=0\\M_1 + M_2 + M_3 &= 0\\ \require{cancel} (\var{F_1} \cancel{d} \cos \alpha) + (\var {F_2} \cancel{d} \sin \alpha) + (\var{show(F_3)}\cancel{d} )&= 0\\ \simplify[all,!collectNumbers]{{F_1} cos(alpha)+ {F_2} sin(alpha)} &= \simplify{ - {show(F_3)}} \\ \alpha &= \var{alpha}°\end{align}\]

This equation has only one unknown, and it can be solved algebraically for $\alpha$, although it is not simple. For the method, see this example.

An easier way is simply to plot the equation: $y = \simplify[all,!collectNumbers]{{F_1} cos(alpha)+ {F_2} sin(alpha) + {show(F_3)}} $; the first positive root is the answer. A guess-and-check solution may also be used.

{advice}

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Part	Test	Passed?
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Angle quantity
Angle quantity		Hasn't run yet

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Taxonomy: mathcentre

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Checkpoint description

William Haynes 5 years, 11 months ago

William Haynes 5 years, 11 months ago

William Haynes 5 years, 11 months ago

Error in variable testing condition

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Generated value: `integer`

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Gap-fill

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Couples in equilibrium

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 5 years, 11 months ago

William Haynes 5 years, 11 months ago

William Haynes 5 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`