Equilibrium of a particle - equilibrium equation method

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William Haynes

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William Haynes commented 1 year, 2 months ago

Cleaned up advice and latex.

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William Haynes 6 years ago

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Question statement

{geogebra_applet('uwmn9de6',[['alpha', alpha+'°'],['theta', theta+'°']])}

Three forces act on particle $A$ as shown. Use the equations of equilibrium to determine the magnitudes of $B$ and $C$ when load $W =$ {qty(W,unit)}.

Give any introductory information the student needs.

			Name	Type	Generated Value

B	number	122.787803969
C	number	405.5797876726
K_1	number	0.3027
K_2	number	1.2328

			Name	Type	Generated Value

unit	string	kN
W	integer	500
alpha	integer	35
theta	integer	80

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
W cos(radians(theta))/sin(radians(90-alpha+theta))

JME function reference

Description

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

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Generated value: `number`

122.787803969

← Depends on:

alpha
theta
W

→ Used by:

Advice
"Unnamed part" → "Force B" - Correct Quantity.

Parts

Gap-fill
1. Gap Force B Engineering Accuracy with units
  Add
2. Gap Force C Engineering Accuracy with units
  Add

Gap-fill

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$B$ = Force B

$C$ = Force C

Advice

Knowns:

$W = \var{qty(W,unit)}$, $\alpha = \var{alpha}°$ and $\theta=\var{theta}°$.

Apply equations of equilibrium

$\begin{align}
\Sigma F_x &= 0 & \Sigma F_y &= 0 \\-B_x + C_x &= 0 & B_y + C_y -W &= 0\\
B \sin\alpha & = C \cos\theta & B \cos\alpha + C \sin\theta & = W \\
B &= C \left(\frac{\cos\theta}{\sin\alpha}\right)\\
B &= \var{K_1}\, C\\
&&(\var{K_1}\, C) \cos\alpha + C \sin\theta & = W \\
&& \var{K_2}\, C&= \var{qty(W,unit)} \\
&&C &= \var{qty(siground(W/K_2,4),unit)} \\
B &= \var{K_1}\, (\var{qty(siground(W/K_2,4),unit)})\\
B&=\var{qty(siground(B,4),unit)}
\end{align}$

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This question is used in the following exams:

Exam 1 - three versions of Q2 by William Haynes in Online Exams.
Chapter 03 Exercises by Michael Proudman in Engineering Statics.
05. Equilibrium of a Particle by Michael Proudman in Engineering Statics.
Statics - Equilibrium by Robert Birch in Robert's workspace.
Statics - Chapter 3 Exercises by Jay McCormack in studio 4.
Chapter 3 Exercises for studio 4 by Jay McCormack in 23-24 Studio 4 Statics Practice.
Chapter 3 Exercises by William Haynes in Engineering Statics.
Homework #2 by Mallory Barkdull in Mallory's workspace.
05. Equilibrium of a Particle by William Haynes in Engineering Statics.

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Equilibrium of a particle - equilibrium equation method

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William Haynes commented 1 year, 2 months ago

William Haynes 6 years ago

William Haynes 6 years ago

William Haynes 6 years ago

Error in variable testing condition

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Generated value: `number`

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Equilibrium of a particle - equilibrium equation method

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes commented 1 year, 2 months ago

William Haynes 6 years ago

William Haynes 6 years ago

William Haynes 6 years ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`