Vector addition: tip-to-tail method

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Name	Status	Author	Last Modified
Vector addition: tip-to-tail method	Ready to use	William Haynes	20/01/2024 02:43
Ann's copy of Vector addition: tip-to-tail method	draft	Ann Smith	02/11/2018 17:06
Josh's copy of Vector addition: tip-to-tail method	draft	Josh Lim	01/07/2019 11:59
Vector Tip-Toe Method Addtion	draft	Johnny Yi	13/12/2018 00:45
Timur's copy of Vector addition: tip-to-tail method	draft	Timur Zaripov	03/04/2019 11:23
John's furious copy of Vector addition: tip-to-tail method	draft	John Wick	29/04/2019 12:13
Maria's copy of Vector Tip-Toe Method Addtion	draft	Maria Aneiros	24/05/2019 00:47
Maria's copy of Vector addition: tip-to-tail method	draft	Maria Aneiros	24/05/2019 07:15
Maria's copy of John's furious copy of Vector addition: tip-to-tail method	draft	Maria Aneiros	25/05/2019 02:21
Vector addition: tip-to-tail method	draft	Xiaodan Leng	10/07/2019 22:05

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Question statement

{geogebra_applet('jwussezq', [['f_a', forceA],['f_b', forceB],['f_c', forceC]])}

Three forces act on point A: $A$ = {FA} {units[1]} at {alpha}°, $B$ = {FB} {units[1]} at {beta}° and, $C$ = {FC} {units[1]} at {gamma}°.

Estimate the magnitude and direction of the resultant force $R$ using the tip-to-tail method.

Force A: {fa} {units[1]} at {alpha} = {forceA}

Force B: {fb} {units[1]} at {beta} = {forceB}

Force C: {fc}{units[1]} at {gamma} = {forceC}

Resultant: {R}{units[1]} at {rho} = {forceR}

Move the tips of forces $A$ , $B$ , and $C$ in this diagram to the correct magnitudes and directions. When this has been done correctly the dotted vector will become solid.
Pick up vectors $A$ , and by their tails, and move them into a tip to tail arrangement. When this has been correctly done the resultant force $R$ will appear.

Based on this diagram, estimate the magnitude and direction of the resultant.

Give any introductory information the student needs.

			Name	Type	Generated Value

alpha	integer	-30
gamma	integer	180
beta	integer	-150
FA	integer	50
FB	integer	30
FC	integer	45
units	list	[ "in", "lb" ]
debug	boolean	false

			Name	Type	Generated Value

ForceA	vector	vector(43.3012701892,-25)
ForceB	vector	vector(-25.9807621135,-15)
ForceC	vector	Vector with 2 components
ForceR	vector	vector(-27.6794919243,-40)
rho	number	-124.6827421793
R	number	48.6431318193

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
(random(-180..180#15))
​

JME function reference

Description

direction of force 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: `integer`

-30

This variable doesn't seem to be used anywhere.

Parts

Magnitude Gap-fill
1. Gap Magnitude Engineering Accuracy with units
  Add
Direction Gap-fill
1. Gap Direction Angle quantity 2020
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2. Gap sign Choose one from a list
  Add
3. Gap ref Choose one from a list
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Gap-fill

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

$R$ = Magnitude

Advice

Vector Addition:

When the forces have been moved to a tip-to=tail arrangement, the magnitude and direction can be read off the polar diagram.

$\Sigma F_x = R_x \qquad R=\sqrt{R_x^2 + R_y^2}\\\\ \Sigma F_y = R_y \qquad \theta = \tan^{-1}\left(\left|\frac{R_y}{R_x}\right| \right)$

Give a worked solution to the whole question.

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Angle quantity 2020
Angle quantity 2020		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet

This question is used in the following exams:

PreCal CW Vectors by Terry Young in NC PreCalculus.
PRACTICE Vectors by Terry Young in NCDCS Unit 1 Intro to Matrices & Vectors.
REVIEW UNIT 1 Intro to Matrices and Vectors by Terry Young in NCDCS Unit 1 Intro to Matrices & Vectors.
TEST UNIT 1 Intro to Matrices and Vectors by Terry Young in NCDCS Unit 1 Intro to Matrices & Vectors.
Michael's copy of 03. Vector Addition Trig Methods by Michael Proudman in .Vectors.
Chapter 02 Exercises by Michael Proudman in Engineering Statics.
03. Vector Addition Trig Methods by Michael Proudman in Engineering Statics.
vector new by abc temp in abc's workspace.
NCM4 FE-F2022 UNIT 8 All by Terry Young in NCM4 FINAL EXAM Fall 2022.
NCM4 FE-F2022 UNIT 8 Vectors by Terry Young in NCM4 FINAL EXAM Fall 2022.
NCM4 PRACTICE Adding Subtracting Resultant Vectors by Terry Young in NC Math 4.
03. Vector Addition Trig Methods by Sarah Sojka in Statics at Randolph College.
EGR 260 Exam 1 by Sean Higgins in Sean's workspace.
Andrew's copy of Chapter 2 Exercises by Andrew Burkert in Andrew's workspace.
Chapter 2 Exercises for studio 4 by Jay McCormack in 23-24 Studio 4 Statics Practice.
Vector Additions by Deactivated user in Deactivated user's workspace.
Algebra and Geometry by Deactivated user in Deactivated user's workspace.
My First Exam by Thales Peixoto in Thales's workspace.
Habeeba's copy of Chapter 2 Exercises by Habeeba Ahmed in Habeeba's workspace.
03. Vector Addition Trig Methods by William Haynes in Engineering Statics.
Chapter 2 Exercises by William Haynes in Engineering Statics.
Ch. 2 Homework by Megan Voss in ENGR 212 Spring 2025.

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William Haynes 4 years, 8 months ago

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William Haynes 6 years, 9 months ago

William Haynes 6 years, 9 months ago

Error in variable testing condition

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Generated value: `integer`

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Vector addition: tip-to-tail method

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 1 year, 3 months ago

William Haynes 2 years, 4 months ago

William Haynes 4 years, 3 months ago

William Haynes 4 years, 8 months ago

William Haynes 4 years, 8 months ago

William Haynes 4 years, 8 months ago

William Haynes 4 years, 8 months ago

William Haynes 4 years, 8 months ago

William Haynes 6 years, 9 months ago

William Haynes 6 years, 9 months ago

William Haynes 6 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`