Resultant of a force-couple system

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Question statement

Replace the force-couple system acting at the origin with a single force which has the same effect. Specify the magnitude and direction of the resultant force and the coordinate $x_A$ $y_A$ of the point on the $x$ -axis $y$ -axis through which the line of action of this force passes.

{applet}

F: {F} Fx: {Fx} Fy: {Fy}

M: {M} $x_A$ : {dx} $y_A$ : {dy}

Give any introductory information the student needs.

			Name	Type	Generated Value

			applet	ggbapplet	HTML node
			params	dict	Dictionary with 5 entries

			Name	Type	Generated Value

F	quantity	quantity(30, "lbs")
M	quantity	quantity(102, "lbs*in")
alpha	integer	310
units	list	[ "lb", "in" ]
Fx	quantity	quantity(19.28362829059617, "lbs")
Fy	quantity	quantity(-22.98133329356934, "lbs")
dx	quantity	quantity(-4.44, "in")
dy	quantity	quantity(-5.29, "in")
version	integer	0
debug	boolean	false

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
geogebra_applet('xfrg2ewr',params)

JME function reference

This variable is an interactive HTML node. Interactive HTML nodes can not be relied upon to work correctly when resuming a session - for example, attached event callbacks will be lost, and mathematical notation will likely also break.

If this causes problems, try to create HTML nodes where you use them in content areas, instead of storing them in variables.

Description

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

Can an exam override the value of this variable?

Generated value: `ggbapplet`

GeoGebra applet loading...

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Solution Gap-fill

Gap-fill

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The force and couple above can be replace with a single force with mangntude

$F$ = F

acting at an angle of Angle measured sign from the ref,

and passing through the $x$-axis $y$-axis at $x_A$ $y_A$ = Intercept.

Advice

The equivalent force has the same magnitude and direction as the original force, but its line of action must be changed in such a way as to produce the same moment about A with the same direction as the original moment M. You may move the force horizontally to $x_A$ where $F_y x_A = M$ or vertically to $y_A$ where $F_y y_A = M$.

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Part	Test	Passed?
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Angle quantity 2020
Angle quantity 2020		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.
16. Equivalent Systems, Resultants by Michael Proudman in Engineering Statics.
Studio 4 - Chapter 4 Exercises by Jay McCormack in studio 4.
Chapter 4 Exercises by William Haynes in Engineering Statics.
16. Equivalent Systems, Resultants by William Haynes in Engineering Statics.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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William Haynes 4 years, 2 months ago

William Haynes 4 years, 6 months ago

William Haynes 4 years, 6 months ago

William Haynes 4 years, 6 months ago

William Haynes 5 years, 9 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 7 months ago

Error in variable testing condition

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Warning

Generated value: `ggbapplet`

Parts

Gap-fill

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Resultant of a force-couple system

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 4 years, 2 months ago

William Haynes 4 years, 6 months ago

William Haynes 4 years, 6 months ago

William Haynes 4 years, 6 months ago

William Haynes 5 years, 9 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: ggbapplet

Parts

Gap-fill

Generated value: `ggbapplet`