Moment of a Force: using the definition of a moment

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Created this as a copy of Moment of a Force: using Verignon's Theorem.

Name	Status	Author	Last Modified
Moment of a Force: using Verignon's Theorem	Ready to use	William Haynes	27/01/2024 15:28
Moment of a Force: using the definition of a moment	Ready to use	William Haynes	08/05/2022 02:21

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Question statement

Force $\mathbf{F}$ , which has a magnitude of {F}, acts along a line passing through points $D$ and $D'$ . The grid units are in [{units[0]}] and counter-clockwise moments are positive. Determine the moment of the force about points $A$ , and $B$ using the definition of the moment:

$M = F \cdot d_\perp$ .

{applet}

Give any introductory information the student needs.

			Name	Type	Generated Value

A	vector	vector(-5,-2)
B	vector	vector(5,-4)
C	vector	vector(6,5)
D	vector	vector(-7,3)
D'	vector	vector(8,1)
F	quantity	quantity(10, "lbs")
units	list	[ "in", "lb" ]
debug	boolean	false

			Name	Type	Generated Value

theta_A	number	60.6039471451
AD	quantity	quantity(5.385164807134504, "in")
dperp	quantity	quantity(4.691812063231134685865935936008, "in")
MA'	quantity	quantity(46.91812063231134685865935936008, "lbs*in")
test	quantity	quantity(4.692, "in")

			Name	Type	Generated Value

			Name	Type	Generated Value

ra	vector	vector(-2,5,0)
rb	vector	vector(-12,7,0)
rc	vector	vector(-13,-2,0)
force	vector	Vector with 3 components
Mx	quantity	quantity(-49.56, "in*lbs")
My	quantity	quantity(2.643, "in*lbs")
Ma	quantity	quantity(-46.918120632311371, "in*lbs")
Mb	quantity	quantity(-53.526306636862273, "in*lbs")
Mc	quantity	quantity(37.005841625485026, "in*lbs")
sum	quantity	quantity(-52.203, "in*lbs")
Fx	quantity	quantity(9.912279006826346, "lbs")
Fy	quantity	quantity(-1.32163720091018, "lbs")
dir_a	integer	-1
dir_b	integer	-1
dir_c	integer	1
dperp_a	quantity	quantity(4.691812063231, "in")
dperp_b	quantity	quantity(5.352630663686, "in")
dperp_c	quantity	quantity(3.700584162549, "in")
applet	ggbapplet	HTML node
params	dict	Dictionary with 6 entries

Automatically regenerate variables?

Name

Data type

Value

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

JME function reference

Description

point A

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

Can an exam override the value of this variable?

Generated value: `vector`

vector(-5,-2)

→ Used by:

AD
params
ra

Variable testing condition
"Geometry" - prompt

Parts

Geometry Gap-fill
$M_A$ Gap-fill
1. Gap direction Choose one from a list
  Add
2. Gap $M_A$ Engineering Accuracy with units
  Add
$M_B$ Gap-fill
1. Gap direction Choose one from a list
  Add
2. Gap $M_B$ Engineering Accuracy with units
  Add

Gap-fill

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

Find the length of the line segment from $A$ to $D$. (Or any other point on the line of action of F.)

$d$ = AD {qty(siground(abs(A-D),4),units[0]) }

Find the angle (<= 90°) between segment $\overline{AD}$ and the line of action of F.

$\theta_A =$ $θ_A$ {qty(siground(theta_A,4),'deg') }

Find the perpendicular distance between point $A$ and the line of action of force F.

$d_\perp =$ $d_⟂$ {siground(dperp,4)}

Advice

Step a) walks you through the procedure to find a moment using the definition of the moment.

An alternate approach is to use Verignon's Theorem

Verigon's theorem says that the moment of a force is the sum of the moments of its components.

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

Procedure:

Decompose force F into its x- and y-components.
Determine the horizontal and vertical distances from the moment center to a point on the line of action of F. In this problem:
1. $d_x$ is the horizontal distance from D (or D') to A, B, or C.
2. $d_y$ is the vertical distance from D (or D') to A, B, or C.
The moments of the components are $F_x d_y$ and $F_y d_x$.
The signs of these moments are determined by inspection: positive if counter-clockwise, negative if clockwise.
The total moment is the sum of the component moments.

Give a worked solution to the whole question.

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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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Moment of a Force: using the definition of a moment

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William Haynes 5 years, 7 months ago

William Haynes 5 years, 9 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, 5 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 6 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: `vector`

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Moment of a Force: using the definition of a moment

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 5 years, 7 months ago

William Haynes 5 years, 9 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, 5 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 6 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: vector

Parts

Gap-fill

Generated value: `vector`