Vector addition by summing scalar components

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William Haynes

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4 years, 9 months ago

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William Haynes 1 year, 2 months ago

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Revised diagram to consistently call the forces A, B and C.

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William Haynes 2 years, 7 months ago

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Redrew ggb, found bug in advice, set angle tolerance to 0.1 degree.

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William Haynes 2 years, 7 months ago

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Bugs reported in this problem

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William Haynes 4 years, 9 months ago

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William Haynes 4 years, 11 months ago

Gave some feedback: Has some problems

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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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William Haynes 6 years, 8 months ago

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Name	Status	Author	Last Modified
Vector addition by summing scalar components	Ready to use	William Haynes	20/01/2024 02:18
Timur's copy of Vector addition by summing scalar components	draft	Timur Zaripov	03/04/2019 11:27
Maria's copy of Vector addition by summing scalar components	Ready to use	Maria Aneiros	25/05/2019 02:51
Michael's copy of Vector addition by summing scalar components	draft	Michael Proudman	07/12/2021 12:01
Exam12 - Vector Addition	draft	Michael Proudman	07/12/2021 09:54
nuExam12 - Vector Addition	draft	Michael Proudman	07/12/2021 09:54
Vector addition by summing scalar components	draft	Xiaodan Leng	10/07/2019 22:04

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Question statement

Three forces act on the bracket at point $A$ as shown: $\color{darkgreen}{ \mathbf{A} = \var{FA}\ \var{units[1]}}$ , $\color{blue}{\mathbf{B} = \var{FB}\ \var{units[1]}}$ and, $\color{red}{\mathbf{C} = \var{FC}\ \var{units[1]}}$ .

Find the magnitude and direction of the resultant force $\mathbf{R}$ by summing scalar components.

{geogebra_applet('btgqdpqx', [['A',A],['B',B],['C',C],['α', radians(mod(alpha,360))]])}

Force A: {fa} at {alpha} = {forceA}

Force B: {fb} at {beta} = {forceB}

Force C: {fc} at {gamma} = {forceC}

Resultant: {R} at {rho} = {forceR}

Give any introductory information the student needs.

			Name	Type	Generated Value

A	vector	vector(0,0)
B	vector	vector(11,-7)
C	vector	vector(8,7)
alpha	integer	80
FA	integer	90
FB	integer	80
FC	integer	65
units	list	[ "cm", "N" ]
debug	boolean	false

			Name	Type	Generated Value

ForceA	vector	vector(15.6283,88.6327)
beta	number	-32.4711922908
gamma	number	41.1859251657
ForceB	vector	vector(67.4929,-42.9500)
ForceC	vector	vector(48.9175,42.8028)
ForceR	vector	vector(132.0387,88.4855)
rho	number	33.8279461434
R	number	158.9462236354
angle_from_ref	list	List of 4 items

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
vector(0,0)

JME function reference

Description

Position of 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(0,0)

→ Used by:

beta
gamma

Statement

Parts

Components of Components Gap-fill
Components of Resultant Gap-fill
1. Gap Rx Engineering Accuracy with units
  Add
2. Gap Ry Engineering Accuracy with units
  Add
Magnitude Gap-fill
1. Gap R Engineering Accuracy with units
  Add
Direction Gap-fill

Gap-fill

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

Find the scalar components of the component forces A, B, and C.

$A_x =$ Ax $B_x =$ Bx $C_x =$ Cx

$A_y =$ Ay $B_y =$ By $C_y =$ Cy

Advice

Vector Addition:

$R_x = \Sigma F_x = (\var{siground(ForceA[0],4)}) + (\var{siground(ForceB[0],4)}) +( \var{siground(ForceC[0],4)}) = \var{siground(ForceR[0],4)}$ {units[1]}

$R_y = \Sigma F_y = (\var{siground(ForceA[1],4)}) + (\var{siground(ForceB[1],4)}) +( \var{siground(ForceC[1],4)}) = \var{siground(ForceR[1],4)}$ {units[1]}

$ R=\sqrt{R_x^2 + R_y^2} = \sqrt{(\var{siground(ForceR[0],4)})^2 +(\var{siground(ForceR[0],4)})^2} = \var{siground(abs(ForceR),4)}$ {units[1]}

$\theta = \tan^{-1}\left(\left|\frac{R_y}{R_x}\right| \right) = \tan^{-1}\left(\frac{\var{abs(siground(ForceR[1],4))}}{\var{abs(siground(ForceR[0],4))}} \right) = \var{siground(degrees(arctan(abs(forceR[1]/forceR[0]))),4)}° \text{ from the } x \text{-axis in quadrant } \var{quadrant(forceR)} \text{ i.e. } \var{siground(rho,4)}° $ from the positive x-axis.

Give a worked solution to the whole question.

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Vector addition by summing scalar components

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Taxonomy: Context

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William Haynes 1 year, 2 months ago

William Haynes 2 years, 7 months ago

William Haynes 2 years, 7 months ago

William Haynes 4 years, 9 months ago

William Haynes 4 years, 11 months ago

William Haynes 6 years, 7 months ago

William Haynes 6 years, 8 months ago

William Haynes 6 years, 8 months ago

Error in variable testing condition

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Generated value: `vector`

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Vector addition by summing scalar components

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 1 year, 2 months ago

William Haynes 2 years, 7 months ago

William Haynes 2 years, 7 months ago

William Haynes 4 years, 9 months ago

William Haynes 4 years, 11 months ago

William Haynes 6 years, 7 months ago

William Haynes 6 years, 8 months ago

William Haynes 6 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: vector

Parts

Gap-fill

Generated value: `vector`