HW3 Prob2

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Vladimir Vingoradov

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Question statement

Two cables are tied together at C and are loaded as shown. Knowing that $P=\var{P}\, N$ , $\alpha=\var{a}^\circ$ and $\beta=\var{b}^\circ$ , determine the tension (in N)

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	52
b	integer	32
P	number	500.0
tBC	number	309.5
tAC	number	426.4
right_alpha	integer	38
right_beta	integer	58
alpha_beta	integer	84

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xxxxxxxxxx
 
random(20..60#2)

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Description

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Generated value: `integer`

This variable doesn't seem to be used anywhere.

Advice

Free-Body Diagram:

Force triangle:

Law of sines:

$\dfrac{T_{AC}}{\sin (90^\circ-\beta)}=\dfrac{T_{BC}}{\sin (90^\circ-\alpha)}=\dfrac{P}{\sin (\alpha+\beta)}$

$\dfrac{T_{AC}}{\sin \var{right_beta}^\circ}=\dfrac{T_{BC}}{\sin \var{right_alpha}^\circ}=\dfrac{\var{P}\,\text{N}}{\sin \var{alpha_beta}^\circ}$

(a)

$T_{AC}=\dfrac{\var{P}\,\text{N}}{\sin\var{alpha_beta}^\circ}\sin\var{right_beta}^\circ=\var{tAC}\,\text{N}\quad\blacktriangleleft$

(b)

$T_{BC}=\dfrac{\var{P}\,\text{N}}{\sin\var{alpha_beta}^\circ}\sin\var{right_alpha}^\circ=\var{tBC}\,\text{N}\quad\blacktriangleleft$

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This question is used in the following exam:

Homework 3 + Solutions by Vladimir Vingoradov in SFY0010.

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Taxonomy: mathcentre

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Vladimir Vingoradov 4 years, 5 months ago

Vladimir Vingoradov 7 years, 5 months ago

Vladimir Vingoradov 7 years, 6 months ago

Error in variable testing condition

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Generated value: `integer`

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HW3 Prob2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Vladimir Vingoradov 4 years, 5 months ago

Vladimir Vingoradov 7 years, 5 months ago

Vladimir Vingoradov 7 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Number entry

Advanced settings

Generated value: `integer`