Vectors: Resolving Forces 2

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Ruth Hand

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2 years, 8 months ago

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Ruth Hand 2 years, 8 months ago

Gave some feedback: Ready to use

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Ruth Hand 6 years, 1 month ago

Created this as a copy of Resolve forces into components.

Name	Status	Author	Last Modified
Resolve forces into components	Ready to use	Amy Chadwick	25/08/2016 18:20
John's copy of Resolve forces into components	draft	John Bridges	18/09/2016 23:35
Brendan's copy of Resolve forces into components	draft	Brendan Murray	15/12/2016 14:33
Vectors: Resolving Forces 2	Ready to use	Ruth Hand	10/10/2022 13:29
Resolve forces into components	draft	Xiaodan Leng	11/07/2019 05:38

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Question statement

$F = \var{force1} \, \mathrm{N}$ at an angle of $\theta = \var{theta1}^{\circ}$ clockwise from the left horizonatal.
$P = \var{force2} \, \mathrm{N}$ vertically upwards.
$Q = \var{force3} \, \mathrm{N}$ at an able of $\theta^{\ast} = \var{theta2}^{\circ}$ clockwise from the right horizontal.

Give your answers to the following questions in Newtons to 3 decimal places.

Give any introductory information the student needs.

			Name	Type	Generated Value

f1x	number	-1.4334717982
f1y	number	3.734321706
f3x	number	9.292402207
f3y	number	-1.9751610628

			Name	Type	Generated Value

force1	integer	4
force2	number	3
force3	number	9.5
theta1	integer	69
theta2	integer	12
yangle1	integer	21
yangle2	integer	102

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
-force1*cos(radians(theta1))

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `number`

-1.4334717982

← Depends on:

force1
theta1

This variable doesn't seem to be used anywhere.

Advice

a) - c)

Resolve each force in the HORIZONTAL:

$P$ doesn't contribute.

The force $F$ is at $\var{theta1}^{\circ}$ to the horizontal, therefore has a contribution of $F \times \cos \var{theta1}^{\circ} = \var{force1} \times \cos \var{theta1}^{\circ} = \var{precround(force1*cos(radians(theta1)),3)}$ . This force is acting to the left.

The force $Q$ is at $\var{theta2}^{\circ}$ to the horizontal, therefore has a contribution of $Q \times cos \var{theta2}^{\circ} = \var{force3} \times \cos\var{theta2}^{\circ} = \var{precround(force3*cos(radians(theta2)),3)}$ . This is acting to the right.

Therefore the sum of components in the $x$ -direction is

forces acting to the right - forces acting to the left

$\var{precround(force3*cos(radians(theta2)),3)} - \var{precround(-force1*cos(radians(180-theta1)),3)}$

$= \var{precround(force1*cos(radians(180-theta1)) + force3*cos(radians(theta2)),3)}$

(if this value is positive then it is acting to the right, if it is negative it is acting to the left)

d) - g)

Resolve each force from the VERTICAL:

For the force $P$ this is acting completely in the positive direction, at no angle. Therefore it's contribution is $\var{force2}$ .

The force $F$ is at $\var{theta1}^{\circ}$ to the horizontal, therefore has a contribution of $F \times \sin \var{theta1}^{\circ} = \var{force1} \times \sin \var{theta1}^{\circ} = \var{precround(force1*sin(radians(theta1)),3)}$ . This force is acting upwards.

Therefore the sum of components in the $y$ -direction is

forces acting up - forces acting down

$\var{precround(force3*sin(radians(theta2)),3)} - \var{precround(-force1*sin(radians(180-theta1)),3)}$

$= \var{precround(force1*sin(radians(180-theta1)) + force3*sin(radians(theta2)),3)}$

(if this value is positive then it is acting to the right, if it is negative it is acting to the left)

Give a worked solution to the whole question.

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This question is used in the following exams:

Forces by Ruth Hand in MASH Bath: Moodle quizzes and TS.
NCM4 PRACTICE Adding Subtracting Resultant Vectors by Terry Young in NC Math 4.
Vectors by Chris Templet in Chris's workspace.
Vectors by Dean Ang in Dean's workspace.
Vector Exam by Dean Ang in Dean's workspace.
EGD125_Quiz1 by Matt Falk in Matt's workspace.
MATH2411-Vectors by Blathnaid Sheridan in Blathnaid's workspace.
Numeracy and A-level skills comprehensive test - Business School UH - Updated by Krishna Kedia in Krishna's workspace.
Numeracy and A-level skills comprehensive test - University of Hertfordshire by Alessandro Palazio in Alessandro's workspace.

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Ruth Hand 2 years, 8 months ago

Ruth Hand 6 years, 1 month ago

Error in variable testing condition

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a) - c)

d) - g)

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Vectors: Resolving Forces 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ruth Hand 2 years, 8 months ago

Ruth Hand 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Number entry

Advanced settings

a) - c)

d) - g)

Generated value: `number`