Moment of a force about a point

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6 years, 5 months ago

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William Haynes commented 1 year, 1 month ago

Minor changes only: added diagram to advice, removed preamble script, replaced with a function. Minor rewording to advice.

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William Haynes 1 year, 1 month ago

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William Haynes 2 years, 10 months ago

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Revised advice to show appropriate diagram for both solution methods.

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William Haynes 6 years, 5 months ago

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William Haynes 6 years, 7 months ago

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William Haynes 6 years, 8 months ago

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Question statement

{applet}

A $\var{scalar(f)}$ lb force $\mathbf{F}$ is applied to the control rod $AB$ as shown. Knowing that the length of the rod is $\var{d}$ and that $\alpha$ is {alpha}°, determine the component of $\mathbf{F}$ perpendicular to rod $AB$ and the magnitude of the moment produced.

A $\var{scalar(f)}$ lb force $\mathbf{F}$ is applied to the control rod $AB$ as shown. Knowing that the length of the rod is $\var{d}$ and that $\alpha$ is {alpha}°, determine the perpendicular distance from the line of action of force $\mathbf{F}$ to point $B$, and the magnitude of the moment produced.

Force $\mathbf{F}$ is applied to the $\var{d}$ long control rod $AB$ at angle $\alpha$ = {alpha}° as shown. Knowing that it creates a {siground(scalar(M),4)} in lb {direction} moment about point B, determine the perpendicular distance from the line of action of force $\mathbf{F}$ to point $B$, and the magnitude of force $\mathbf{F}$.

A {scalar(f)} lb force $\mathbf{F}$ is applied to control rod $AB$ at angle $\alpha$ = {alpha}° as shown. Knowing that it creates a {siground(scalar(M),4)} in lb {direction} moment about point $B$ , determine the length of the control rod, and the component of $\mathbf{F}$ in a direction perpendicular to $AB$ .

A {scalar(f)} lb force $\mathbf{F}$ is applied to the {scalar(d)} inch long control rod $AB$ as shown. Knowing that it creates a {siground(scalar(M),4)} in lb {direction} moment about point $B$ , determine angle $\alpha$ and the perpendicular distance between the line of action of force $\mathbf{F}$ and point $B$ .

F: {F} D:{D} $\alpha$: {alpha} $F_\perp$: {fperp} $d_\perp$: {dperp} M: {M}

Give any introductory information the student needs.

			Name	Type	Generated Value

beta'	integer	30
alpha'	integer	30
D	quantity	quantity(30, "in")
F	quantity	quantity(2.2, "lbs")

			Name	Type	Generated Value

M	quantity	quantity(33, "lbs*in")
Fperp	quantity	quantity(1.1, "lbs")
Dperp	quantity	quantity(15, "in")
direction	string	clockwise

			Name	Type	Generated Value

alpha	number	30
beta	integer	30
version	integer	0
answers	list	Nested 5×4 list
debug	boolean	false

			Name	Type	Generated Value

applet	ggbapplet	HTML node
params	dict	Dictionary with 4 entries
advice	ggbapplet	HTML node

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(20..160#10 except 90)

JME function reference

Description

angle of bar from positive x axis

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:

beta
params

This variable doesn't seem to be used anywhere.

Parts

Answers Gap-fill
1. Gap Gap 0. Engineering Accuracy with units
  Add
2. Gap Gap 1. Engineering Accuracy with units
  Add

Gap-fill

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

{answers[version][0]} = Gap 0. $\qquad$ {answers[version][2]} = Gap 1.

{answers[version][1]}

{answers[version][3]}

Advice

{advice}

Method 1

Draw the line of action of the force.
Make a triangle including the perpendicular distance $d_\perp.$
Use geometry to find an angle in the triangle.
Use trig to find the value of the perpendicular distance.
Apply equation $M=F d_\perp = F(d sin \alpha) $ to solve for the unknown quantity.

Method 2

Use geometry to find the angle between the force and the control rod.
Identify and solve for the component of force $F$ perpendicular to the control rod, $F_\perp$ .
Apply equation $M = F_\perp d = (F sin \alpha) d $ to solve for the unknown quantity.

Give a worked solution to the whole question.

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Part	Test	Passed?
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Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
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This question is used in the following exams:

Chapter 04 Exercises by Michael Proudman in Engineering Statics.
07. Moment of a Force by Michael Proudman in Engineering Statics.
Studio 4 - Chapter 4 Exercises by Jay McCormack in studio 4.
Chapter 4 Exercises for studio 4 by Jay McCormack in 23-24 Studio 4 Statics Practice.
Chapter 4 Exercises by William Haynes in Engineering Statics.
07. Moment of a Force by William Haynes in Engineering Statics.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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William Haynes commented 1 year, 1 month ago

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William Haynes 6 years, 5 months ago

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William Haynes 6 years, 8 months ago

Error in variable testing condition

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Generated value: `integer`

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Moment of a force about a point

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes commented 1 year, 1 month ago

William Haynes 1 year, 1 month ago

William Haynes 2 years, 10 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 7 months ago

William Haynes 6 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`