Exam12 - Vector Addition - Numbas at mathcentre.ac.uk

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Michael Proudman 5 years, 10 months ago

Created this as a copy of Michael's copy of Vector addition by summing scalar components.

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

There are 9 other versions that do you not have access to.

Question statement

Three forces act on the bracket at point A: A = {FA} {units[1]}, B = {FB} {units[1]} and, C = {FC} {units[1]}.

(The diagram may take a moment or two to load - give it chance)

Find the magnitude and direction of the resultant force R by summing scalar components.

Enter your magnitude quatities in SI units, eg. 500 N and give 2 d.p.

{geogebra_applet('dtf3t2dp', [['A',A],['B',B],['C',C],['F_a',FA],['F_b',FB],['F_c',FC],['α', alpha],['unit','"'+units[0]+'"']])}

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(4,-4)
C	vector	vector(5,-2)
alpha	integer	130
FA	integer	10
FB	integer	80
FC	integer	15
units	list	[ "cm", "N" ]
debug	boolean	false

			Name	Type	Generated Value

ForceA	vector	Vector with 2 components
beta	number	-45
gamma	number	-21.8014094864
ForceB	vector	Vector with 2 components
ForceC	vector	Vector with 2 components
ForceR	vector	Vector with 2 components
rho	number	-40.3756006801
R	number	84.099001374
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

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
Part b) Gap-fill
1. Gap Gap 0. Engineering Accuracy with units
  Add
2. Gap Gap 1. Engineering Accuracy with units
  Add
Part c) Gap-fill
1. Gap Gap 0. Engineering Accuracy with units
  Add
2. Gap Information only
  Add
3. Gap Gap 1. Angle quantity
  Add

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.

$A_x =$ Gap 0. $B_x =$ Gap 2. $C_x =$ Gap 4.

$A_y =$ Gap 1. $B_y =$ Gap 3. $C_y =$ Gap 5.

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(\left|\frac{\var{siground(ForceR[1],4)}}{\var{siground(ForceR[0],4)}}\right| \right) = \var{siground(degrees(arctan(abs(forceR[1])/forceR[0])),4)}° = (\var{siground(rho,4)}° $ from the positive x-axis.)

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Information only
Angle quantity
Angle quantity		Hasn't run yet

This question is used in the following exams:

Exam Practice by Michael Proudman in Assessment Exercises.
All the good stuff by Chris Templet in Chris's workspace.

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Exam12 - Vector Addition

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Michael Proudman 5 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: `vector`

Parts

Gap-fill

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Error

Exam12 - Vector Addition

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Michael Proudman 5 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: vector

Parts

Gap-fill

Generated value: `vector`