Equilibrium of a particle: two suspended loads

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Question statement

{geogebra_applet('vzqtfrbq',[['a1',a1+"°"],['a2',a2+"°"],['a3',a3+"°"]])}

Two loads $W_1 = \var{w1}$ , and $W_2 = \var{w2}$ are suspended from a system of cables as shown. Determine the tensions in the cables.

Give any introductory information the student needs.

			Name	Type	Generated Value

a1	integer	15
a2	integer	25
a3	integer	45
w1	quantity	quantity(45, "lbs")
w2	quantity	quantity(25, "lbs")
units	string	lb
debug	boolean	false

			Name	Type	Generated Value

TC	quantity	quantity(67.62212203219809727560686455998895711733, "lbs")
TE	quantity	quantity(75.77122026542988309766719783688408647006, "lbs")
TD	quantity	quantity(7.708112105258691243472872062690422179501, "lbs")
TB	quantity	quantity(63.44840784429222487857176510085809535171, "lbs")

			Name	Type	Generated Value

forceB	vector	Vector with 2 components
forceC	vector	Vector with 2 components
forceE	vector	Vector with 2 components
forceD	vector	vector(7.7081121053,0)

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(10..80#5)

JME function reference

Description

angle of rope AB from horizontal, as shown on diagram.

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

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

TB
TC
forceB

This variable doesn't seem to be used anywhere.

Parts

First Particle Gap-fill
1. Gap TB Engineering Accuracy with units
  Add
2. Gap TC Engineering Accuracy with units
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Second Particle Gap-fill
1. Gap TE Engineering Accuracy with units
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2. Gap TD Engineering Accuracy with units
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Draw a free body diagram of point A and apply the equations of equilibrium to determine the tensions in cables AB and AC.

$T_{AB}$ = TB {siground(TB,4)}

$T_{AC}$ = TC {siground(TC,4)}

Advice

Begin by drawing a free body diagram of particle A, then apply the equations of equilibrium.

$\begin{align}\\ \Sigma F_x = 0 \\-{T_B}_x + {T_C}_x = 0 \end{align} \\ T_B \cos(\var{a1}°) = T_C \sin(\var{90-a2}°) \qquad(1)$

$\begin{align}\\ \Sigma F_y = 0 \\{T_B}_y + {T_C}_y - W_1 = 0 \end{align} \\ T_B \sin(\var{a1}°) + T_C \cos(\var{90-a2})° = W_1 \qquad(2)$

Solve (1) and (2) simultaneously for $T_B$ and $T_C$.

$T_B = \var{siground(TB,4)}, \quad T_C = \var{siground(TC,4)}$

With $T_C$ known, use a similar approach on particle $C$ to find $T_D$ and $T_E$.

Since cable CD is horizontal $T_D$ has no y-component, so the $\Sigma F_y = 0$ equation only has one unknown and simultaneous equations are unnecessary in this case.

$T_D = \var{siground(TD,4)}, \quad T_E = \var{siground(TE,4)}$

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This question is used in the following exams:

Chapter 03 Exercises by Michael Proudman in Engineering Statics.
06. Multiparticle Equilibrium by Michael Proudman in Engineering Statics.
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.
06. Multiparticle Equilibrium by William Haynes in Engineering Statics.

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Equilibrium of a particle: two suspended loads

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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William Haynes 5 years, 10 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 6 months ago

Error in variable testing condition

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Generated value: `integer`

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Equilibrium of a particle: two suspended loads

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 5 years, 10 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`