Reaction forces

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Don Shearman

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From users who are members of MfEP Progress Quizzes :

Hanh Vo

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Ready to use

3 years, 4 months ago

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Don Shearman 11 months, 2 weeks ago

Published this.

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Hanh Vo 3 years, 4 months ago

Gave some feedback: Ready to use

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Don Shearman 3 years, 8 months ago

Created this.

Name	Status	Author	Last Modified
Reaction forces	Ready to use	Don Shearman	08/05/2024 06:12
Electronic circuit	Ready to use	Don Shearman	17/04/2024 02:20
Blending Liquids	draft	Don Shearman	16/04/2024 03:07
Electronic circuit 2	draft	Don Shearman	17/04/2024 02:24

There are 3 other versions that do you not have access to.

Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

W	integer	5000
a	integer	3
b	integer	9

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1500..6000 #500)

JME function reference

Description

Weight of vehicle in kg, random between 1500 and 6000 in steps of 500.

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`

5000

→ Used by:

Advice
"Unnamed part" - prompt
"Unnamed part" → "$R_1$" - Minimum accepted value
"Unnamed part" → "$R_1$" - Maximum accepted value
"Unnamed part" → "$R_2$" - Minimum accepted value
"Unnamed part" → "$R_2$" - Maximum accepted value

Parts

Gap-fill
1. Gap $R_1$ Number entry
  Add
2. Gap $R_2$ Number entry
  Add

Gap-fill

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

The weight of a vehicle is supported by reaction forces $R_1$ and $R_2$ at its front and rear wheels. If the weight of the vehicle is $W=\var{W}$ N, the reaction forces satisfy the following system of equations:

$\begin{align} R_1+R_2 - \var{W} &=0\\\var{a}R_1 -\var{b}R_2 &=0 \end{align}$ Find the values of

$R_1$ and

$R_2$ . Write your final answer in the box below and show full working on your handwritten notes. (Note: Leave answers in fraction form wher appropriate. For example to enter the fraction

$\frac32$ type 3/2.)

$R_1=$ $R_1$ N

$R_2=$ $R_2$ N

Advice

We need to solve

$\begin{align} R_1+R_2 - \var{W} &=0\\\var{a}R_1 -\var{b}R_2 &=0\end{align}$ which can be written as

$\begin{align} R_1+R_2 &= \var{W}\quad (1)\\ \var{a}R_1 -\var{b}R_2 &=0\quad (2)\end{align}$

Using the method of elimination to eliminate $R_2$ we multiply equation $(1)$ by $\var{b}$ to get

$\begin{align}\var{b}R_1+\var{b}R_2 &= \var{b*W}\quad (3)\\ \var{a}R_1 -\var{b}R_2 &=0\quad (4)\end{align}$

Taking $(3)+(4)$ we obtain

$\var{a+b}R_1=\var{B*W}$

and hence

$R_1=\simplify{{b*W/(a+b)}}$

Substituting this into $(1)$ gives us

$\simplify[unitFactor]{{b*W/(a+b)}}+R_2 = \var{W}$ and hence

$R_2=\simplify{{W-b*W/(a+b)}}$

Thus the reaction forces are $R_1=\simplify{{b*W/(a+b)}}$ N and $R_2=\simplify{{W-b*W/(a+b)}}$ N.

(Note that this problem could also be solved by eliminating $R_1$ instead of $R_2$ or by the method of substitution, however the final answers will be the same.)

Give a worked solution to the whole question.

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

SCC Class Test 1 by Hanh Vo in SCC PrelimMaths.
Don's copy of Class Test 1 for testing by Don Shearman in Don's workspace.
Class Test 1 by Don Shearman in MfEP Progress Quizzes.
third year diagnostic test by Alison Loddick in third year diagnostic test.
third year algebra diagnostic test by Alison Loddick in third year diagnostic test.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

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Checkpoint description

Don Shearman 11 months, 2 weeks ago

Hanh Vo 3 years, 4 months ago

Don Shearman 3 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Reaction forces

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Don Shearman 11 months, 2 weeks ago

Hanh Vo 3 years, 4 months ago

Don Shearman 3 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`