Simultaneous equations to solve forces in a system

Error

There was an error loading the page.

Contributors

Vicky Hall

History

○

Vicky Hall 8 years, 8 months ago

Created this as a copy of Q7 (simultaneous equations to solve forces in a system, and solve for x).

Name	Status	Author	Last Modified
Q3 (simultaneous equations, solve for x and y)	draft	TEAME CIT	06/10/2016 16:14
Q7 (simultaneous equations to solve forces in a system, and solve for x)	Ready to use	TEAME CIT	06/10/2016 16:15
Simultaneous equations to solve forces in a system	draft	Vicky Hall	06/02/2018 13:11

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

Question statement

The forces $F_1$ and $F_2$ in a system are described by the simultaneous equations given below.

Solve for $F_1$ and $F_2$ , giving your answers to $1$ decimal place where necessary.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	7
b	integer	9
c	number	44
a1	integer	2
b1	integer	-5
c1	number	-10.9
ans1	number	2.3
ans2	number	3.1
num1	integer	2
num2	integer	4
num3	integer	9
ans	decimal	dec("-6.75")

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(6..9)

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: `integer`

→ Used by:

Advice
"Unnamed part" - prompt

Parts

Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

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

$\simplify{{a}F_1 + {b}F_2 = {c}}$

$\simplify{{a1}F_1 + {b1}F_2 = {c1}}$

$F_1$ = Gap 0.

$F_2$ = Gap 1.

Advice

Have a look at this youtube video to understand simultaneous equations better: Simultaneous Equations

Multiply the first equation by $\var{b1}$ and the second equation by $\var{b}$ so they both have the same $F_2$ coefficient:

$\begin{align} \simplify{{a*b1}F_1+{b*b1}F_2} &= \var{c*b1} \\ \simplify{{a1*b}F_1+{b1*b}F_2} &= \var{c1*b} \end{align}$

(It is also fine to multiply the first equation by $~\var{a1}$ and the second equation by $~\var{a}$ in order to make the $F_1$ coefficients the same.)

Then, subtract the second equation from the first to get

$\simplify[std]{{a*b1-a1*b}F_1} = \var{c*b1-c1*b}$

So $F_1 = \simplify[std]{{(c*b1-c1*b)/(a*b1-a1*b)}}$ .

Substitute this value of $F_1$ into the first (or second, but here we use the first) equation and rearrange to obtain $F_2$ :

$\begin{align} \simplify[std]{{a}*{(c*b1-c1*b)/(a*b1-a1*b)} + {b}F_2} &= \var{c} \\ \simplify[std]{{b}F_2} &= \simplify[std]{{c}-{a*(c*b1-c1*b)/(a*b1-a1*b)}} \\ F_2 &= \simplify[std]{{(c-a*(c*b1-c1*b)/(a*b1-a1*b))/b}} \end{align}$

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
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Loading...

Error

Simultaneous equations to solve forces in a system

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Vicky Hall 8 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Simultaneous equations to solve forces in a system

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Vicky Hall 8 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`