Friction: block on block 1

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William Haynes

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William Haynes 2 years, 1 month ago

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William Haynes 2 years, 1 month ago

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William Haynes 2 years, 1 month ago

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William Haynes 2 years, 4 months ago

Created this as a copy of HW5 Prob4.

Name	Status	Author	Last Modified
HW5 Prob4	Ready to use	Vladimir Vingoradov	06/12/2022 18:15
HW5 Prob5	Ready to use	Vladimir Vingoradov	06/12/2022 18:16
Friction: block on block 2	Ready to use	William Haynes	07/05/2023 14:10
Friction: block on block 1	Ready to use	William Haynes	07/05/2023 14:08

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Question statement

The coefficient of friction is $\mu_s=\var{mu_s}$ between all surfaces of contact. Knowing that $M_1=\var{M1}$ kg and $M_2=\var{M2}$ kg, determine the smallest force $P$ required to start the block $M_2$ moving.

Give any introductory information the student needs.

			Name	Type	Generated Value

mu_s	number	0.4
M1	integer	20
M2	integer	30
P1	number	353.16
P2	number	196.2

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Generated value: `number`

0.4

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Parts

Part a) Gap-fill
1. Gap P1 Engineering Accuracy with units
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Part b) Gap-fill
1. Gap P2 Engineering Accuracy with units
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Gap-fill

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cable AB is connected.

$P$ = P1

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(a)

Free body: $\var{M1}$-kg block

$W_1=M_1 g=\var{m1}\times 9.81=\var{m1*9.81}\,\text{N}$

$+\!\!\uparrow\sum F_y=0:\quad N_1=W_1$

$F_1=\mu_s N_1=\var{mu_s}\times\var{m1*9.81}=\var{mu_s*m1*9.81}\,\text{N}$

$\overset{+}{\rightarrow}\sum F_x=0:\quad T-F_1=0,\quad T=F_1=\var{mu_s*m1*9.81}\,\text{N}$

Free body: $\var{M2}$-kg block

$W_2=M_2g=\var{M2}\times 9.81=\var{m2*9.81}\,\text{N}$

$+\!\!\uparrow\sum F_y=0: $

$N_2-N_1-W_2=0,$

$N_2=W_1+W_2=\var{(m1+m2)*9.81}\,\text{N}$

$F_2=\mu_s N_2=\var{mu_s}\times\var{(m1+m2)*9.81}=\var{mu_s*(m1+m2)*9.81}\,\text{N}$

$\overset{+}{\rightarrow}\sum F_x=0: -P+F_1+F_2+T=0$

\[P=F_1+F_2+T=\var{P1}\,\text{N}\quad\blacktriangleleft\]

(b)

Blocks move together

$W=(M_1+M_2)g=\var{(m1+m2)*9.81}\,\text{N}$

$\overset{+}{\rightarrow}\sum F_x=0:$

$P-\mu_s N=0$

$P=\mu_s N=\mu_s W=\var{mu_s}\times\var{(m1+m2)*9.81}=\var{P2}\,\text{N}$

\[P=\var{P2}\,\text{N}\quad\blacktriangleleft\]

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William Haynes 2 years, 1 month ago

William Haynes 2 years, 1 month ago

William Haynes 2 years, 1 month ago

William Haynes 2 years, 4 months ago

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Generated value: `number`

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Friction: block on block 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 2 years, 1 month ago

William Haynes 2 years, 1 month ago

William Haynes 2 years, 1 month ago

William Haynes 2 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`