Lifting machine

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From users who are members of MfEP Progress Quizzes :

Hanh Vo

said

Ready to use

3 years, 4 months ago

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Don Shearman 11 months, 4 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.

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

a	number	0.8
b	integer	9
W_1	integer	170
W_2	integer	240
E_1	number	145
E_2	number	201

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(0.1..0.9 #0.1)

JME function reference

Description

value of coefficient for lifting equation - random 0.1 to 0.9 in steps of 0.1. Note that this one of the solutions that the student has to find.

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`

0.8

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap a Number entry
  Add
2. Gap b Number entry
  Add

Gap-fill

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

A lifting machine obeys the law

$E=aW+b$ where

$E$ is effort force,

$W$ is load and

$a$ and

$b$ are constants. An experiment produces the following results: An effort force of

$\var{E_1}$ N lifts a load of

$\var{W_1}$ N while an effort force of

$\var{E_2}$ N lifts a load of

$\var{W_2}$ N. Find the values of the constants

$a$ and

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

$\frac32$ type 3/2.)

$a=$ a

$b=$ b

Advice

Using the available data we have

$\begin{align} \var{E_1}&=\var{W_1}a+b\quad (1)\\ \var{E_2}&=\var{W_2}a+b\quad (2)\end{align}$

Using the method of elimination to eliminate $b$ subtract equation $(1)$ from equation $(2)$ to get

$\simplify{{E_2-E_1}}=\simplify{{W_2-W_1}}a$

and hence

$a=\var{a}$

Substituting this into $(1)$ gives us

$\var{E_1}=\simplify{{W_1*a}}+b$ and hence

$\begin{align}\var{E_1}&=\simplify{{W_1*a}}+b\\b&=\var{E_1}-\simplify{{W_1*a}}\\&=\var{b}\end{align}$

Thus the constants are $a=\var{a}$ and $b=\var{b}$ .

(Note that this problem could also be solved 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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Number entry
Number entry		Hasn't run yet
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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

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Comment

Checkpoint description

Don Shearman 11 months, 4 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: `number`

Parts

Gap-fill

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Error

Lifting machine

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Don Shearman 11 months, 4 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: number

Parts

Gap-fill

Generated value: `number`