Moment of a couple

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William Haynes

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Question statement

{applet}

{setAxisVisible(applet,false)}

Determine the moment of the couple formed by the two {F} {units[1]} forces shown. Grid units are in [{units[0]}].

Give any introductory information the student needs.

			Name	Type	Generated Value

A	vector	vector(-7,6)
B	vector	vector(-4,0)
theta	integer	165
units	list	[ "cm", "N" ]
F	integer	240

			Name	Type	Generated Value

r	vector	vector(-3,6,0)
Force	vector	Vector with 3 components
moment	number	1204.5834773824
answer	quantity	quantity(1205, "N*cm")
dperp	number	5.0190978224

			Name	Type	Generated Value

			params	dict	Dictionary with 4 entries
			applet	ggbapplet	HTML node

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
vector(random(-8..8),random(-6..6))

JME function reference

Description

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

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Generated value: `vector`

vector(-7,6)

→ Used by:

params
r

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap mag Engineering Accuracy with units
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2. Gap dir Choose one from a list
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$M$ = mag dir

Advice

The moment of a couple is found by multiplying the magnitude of force by the perpendicular distance between the lines of action of the two forces. The direction is determined by inspection. You will need to determine the perpendicular distance using the known locations of the two points, the direction of the force, geometry and trigonometry as we have done before.

$ M = F \cdot d_\perp$

$ M = (\var{F}\, \var{units[1]} ) (\var{abs(siground(moment/F,4))}\, \var{units[0]} ) = \var{siground(abs(answer),4)}$ {if(moment >0,'Counterclockwise','Clockwise')}

Alternately, you get the same result by finding the moment of one force about a point on the line of action of the other one.

So, for example, take the moment of the force at $A$ about point $B$ using Verignon's Theorem. The signs in the equation below are determined by the direction of the component moments, using the sign convention that counterclockwise moments are positive. The sign of the resulting moment indicates its direction and it should agree with your expectations from inspection of the diagram.

$ M = \pm F_x d_y \pm F_y d_x $

$ M = \pm\, ( \var{d(Force[0] )} \, \var{units[1]} ) ( \var{d(r[1])} \, \var{units[0]} ) \pm\, ( \var{d(Force[1] )} \, \var{units[1]} ) ( \var{d(r[0])} \, \var{units[0]} )$

$M = \var{siground(answer,4)}$

$M = \var{siground(abs(answer),4)} $ {if(moment >0,'Counterclockwise','Clockwise')}

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Taxonomy: mathcentre

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William Haynes 6 years, 2 months ago

William Haynes 6 years, 2 months ago

William Haynes 6 years, 2 months ago

Error in variable testing condition

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Generated value: `vector`

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Moment of a couple

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 6 years, 2 months ago

William Haynes 6 years, 2 months ago

William Haynes 6 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: vector

Parts

Gap-fill

Generated value: `vector`