Vectors 4 with solution

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Vladimir Vingoradov

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Created this as a copy of Vectors 4.

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Question statement

The cable stays AB and AD help support pole AC. Knowing that the tension is {tAB}N in AB and {tAD}N in AD,

Give any introductory information the student needs.

			Name	Type	Generated Value

tAB	integer	94
tAD	integer	56
R	number	125.1
gammaAB	number	38.66
gammaAD	number	30.96
a	number	24.81

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$\tan \alpha=\frac{8}{10}\quad\Rightarrow\quad \alpha=\var{gammaAB}^\circ$

$\tan \beta=\frac{6}{10}\quad\Rightarrow\quad \beta=\var{gammaAD}^\circ$

(a) Using the triangle rule

$\alpha+\beta+\psi=180^\circ$

$\psi=180^\circ-\var{gammaAB}^\circ-\var{gammaAD}^\circ=110.38^\circ$

Using the rule of cosines

$R^2=T_{AB}^2+T_{AD}^2-2T_{AB}T_{AD}\cos\psi$

$R^2=\var{tAB}^2+\var{tAD}^2-2(\var{tAB})(\var{tAD})\cos 110.38^\circ$

$R=\var{R}\,\text{N}$ ◀

(b) Use the rule of sines

$\dfrac{\sin \gamma}{T_{AD}}=\dfrac{\sin \psi}{R}$

$\dfrac{\sin \gamma}{\var{tAD}\,\text{N}}=\dfrac{\sin 110.38^\circ}{\var{R}\,\text{N}}$

$\gamma=\var{a}^\circ$ ◀

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This question is used in the following exams:

Homework 1 + Solutions by Vladimir Vingoradov in SFY0010.
NCM4 FE-F2022 UNIT 8 All by Terry Young in NCM4 FINAL EXAM Fall 2022.
All the good stuff by Chris Templet in Chris's workspace.

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Vladimir Vingoradov 4 years, 5 months ago

Vladimir Vingoradov 7 years, 7 months ago

Vladimir Vingoradov 7 years, 7 months ago

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Vectors 4 with solution

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Comment

Checkpoint description

Vladimir Vingoradov 4 years, 5 months ago

Vladimir Vingoradov 7 years, 7 months ago

Vladimir Vingoradov 7 years, 7 months ago

Error in variable testing condition

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Warning

Generated value: integer

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Number entry

Advanced settings

Generated value: `integer`