HW5 Prob3

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Vladimir Vingoradov

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7 years, 4 months ago

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Vladimir Vingoradov 4 years, 4 months ago

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Vladimir Vingoradov 7 years, 4 months ago

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Vladimir Vingoradov 7 years, 5 months ago

Created this as a copy of HW5 Prob3.

Name	Status	Author	Last Modified
HW5 Prob3	Ready to use	Vladimir Vingoradov	06/12/2022 18:15
Friction: Range of values 2	Ready to use	William Haynes	23/02/2024 20:39

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Question statement

The coefficient of friction between the block and the rail is $\mu_s=\var{mu_s}$ . Knowing that $\theta=\var{th}^\circ$ , determine the smallest value of P (in N) required

Give any introductory information the student needs.

			Name	Type	Generated Value

mu_s	number	0.35
th	integer	80
Pmin	number	312.1
Pmax	number	450.6

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Generated value: `number`

0.35

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Pmax
Pmin

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$+\!\!\nwarrow\sum F_y=0,\quad\implies\quad N-500 \cos 35^\circ+P\sin(\theta-35^\circ)=0$

$N=500 \cos 35^\circ-P\sin( \var{th-35}^\circ),$

$F_m=\mu_s N$

To start moving the block up the incline:

$+\!\!\swarrow\sum F_x=0,\quad\implies\quad \mu_s N-P\cos(\theta-35^\circ)+500\sin 35^\circ=0$

$\mu_s (500 \cos 35^\circ-P\sin \var{th-35}^\circ)-P\cos \var{th-35}^\circ+500\sin 35^\circ=0$

$P=\dfrac{500\,(\sin 35^\circ+\mu_s\cos 35^\circ)}{\cos \var{th-35}^\circ+\mu_s \sin \var{th-35}^\circ}=\var{Pmax}\,\text{N}\quad\blacktriangleleft$

To prevent the block from moving down:

$+\!\!\swarrow\sum F_x=0,\quad\implies\quad -\mu_s N-P\cos(\theta-35^\circ)+500\sin 35^\circ=0$

$-\mu_s (500 \cos 35^\circ-P\sin \var{th-35}^\circ)-P\cos \var{th-35}^\circ+500\sin 35^\circ=0$

$P=\dfrac{500\,(\sin 35^\circ-\mu_s\cos 35^\circ)}{\cos\var{th-35}^\circ-\mu_s \sin \var{th-35}^\circ}=\var{Pmin}\,\text{N}\quad\blacktriangleleft$

$\var{Pmin}\,\text{N} \le P \le \var{Pmax}\,\text{N}\quad\blacktriangleleft$

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This question is used in the following exams:

Homework 5 Friction + Solutions by Vladimir Vingoradov in SFY0010.
tutorial: fiction by Vladimir Vingoradov in ENG1507 Mechanics 1.

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Vladimir Vingoradov 4 years, 4 months ago

Vladimir Vingoradov 7 years, 4 months ago

Vladimir Vingoradov 7 years, 5 months ago

Error in variable testing condition

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Generated value: `number`

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HW5 Prob3

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Vladimir Vingoradov 4 years, 4 months ago

Vladimir Vingoradov 7 years, 4 months ago

Vladimir Vingoradov 7 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Number entry

Advanced settings

Generated value: `number`