Vector addition by summing scalar components

Error

There was an error loading the page.

Contributors

History

○

Chris King 5 years, 9 months ago

Created this as a copy of Vector addition by summing scalar components - easy.

Name	Status	Author	Last Modified
Vector addition by summing scalar components - easy	Ready to use	William Haynes	08/03/2025 17:27
Find magnitude and direction of three vectors	Ready to use	William Haynes	01/01/2021 00:53
Vector addition by summing scalar components	draft	Marie Nicholson	04/02/2021 15:37
Timur's copy of Vector addition by summing scalar components	draft	Timur Zaripov	03/04/2019 11:16
Timur's copy of Find magnitude and direction of three vectors	draft	Timur Zaripov	03/04/2019 11:24
Timur's copy of Vector addition by summing scalar components - easy	draft	Timur Zaripov	03/04/2019 11:27
Magnitude and direction of three vectors	draft	Maria Aneiros	25/05/2019 02:07
Maria's copy of Find magnitude and direction of three vectors	Ready to use	Maria Aneiros	25/05/2019 02:19
Vector addition by summing scalar components - easy	draft	Xiaodan Leng	10/07/2019 22:01
Find magnitude and direction of three vectors	draft	Xiaodan Leng	10/07/2019 22:02
Vector addition by summing scalar components	draft	Chris King	12/07/2019 05:09

There are 21 other versions that do you not have access to.

Question statement

Three forces, A, B, and C are drawn to scale of 1 square = {scale} {units[1]}. Find the resultant by summing the scalar components.

Note: For full marks don't forget to add a zero for decimal numbers less than one, add negative signs if required and don't forget the correct units.

{geogebra_applet('vpfnqe8q', [['fa',FA],['fb',FB],['fc',FC]])}

Give any introductory information the student needs.

			Name	Type	Generated Value

A1	vector	vector(-5,0)
FA	vector	vector(1,-4)
B1	vector	vector(0,0)
FB	vector	vector(0,1)
C1	vector	vector(5,0)
FC	vector	vector(-5,-5)
units	list	[ "m", "kN" ]
debug	boolean	false
D	vector	vector(0,-8)
scale	number	0.1

			Name	Type	Generated Value

FR	vector	vector(-4,-8)
theta	number	-116.5650511771
ref	integer	0
angle_from_ref	list	List of 4 items
resultant	quantity	quantity(0.8944271909999159, "kN")

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
vector(-5,0)

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(-5,0)

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.

First, find the scalar components of the three forces. These are divided into the X and Y components and multipled by the force.

$A_x =$ 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:

$R_x = \Sigma F_x = \var{scale FA[0]}+\var{scale FB[0]}+\var{scale FC[0]} =\var{scale FR[0]}$ {units[1]}

$R_y = \Sigma F_y = \var{scale FA[1]}+\var{scale FB[1]}+\var{scale FC[1]} =\var{scale FR[1]}$ {units[1]}

$R=\sqrt{R_x^2 + R_y^2} = \var{siground(resultant,4)}$

$\theta = \tan^{-1}\left(\left|\frac{R_y}{R_x}\right| \right) =$ {siground(degrees(arctan(FR[0]/FR[1])),4)}°

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 exam:

Motion Problems by Chris King in Engineering: Physics and Materials.

Loading...

Error

Vector addition by summing scalar components

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Chris King 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `vector`

Parts

Gap-fill

Loading...

Error

Vector addition by summing scalar components

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Chris King 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: vector

Parts

Gap-fill

Generated value: `vector`