Bending moments

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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 as a copy of Particle displacement.

Name	Status	Author	Last Modified
Ball height	Ready to use	Don Shearman	16/04/2024 03:06
Particle displacement	Ready to use	Don Shearman	08/05/2024 05:57
Bending moments	Ready to use	Don Shearman	16/04/2024 03:06

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

a	number	1.2
b	number	4.7
c	number	3.7
ans	number	0.6719523503
ans2	number	-4.588619017

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(0.5..1.9 #0.1 except 1)

JME function reference

Description

Coefficient of x^2 in equation

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`

1.2

→ Used by:

ans
ans2

Advice
"Unnamed part" - prompt

Parts

Gap-fill
1. Gap Number entry
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Gap-fill

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

The bending moment, $M$ , of a beam is given by

$\simplify{M={a}x^2+{b}x-{c}}\quad x\ge 0$ where

$x$ is the distance in metres along the beam.

Find the value of $x$ for which $M$ is $0$ . Write your final answer in the box below and show full working on your handwritten notes.

$x=$ Unnamed gapm (round answer to 2 decimal places)

Advice

We require $M=0$ , hence we need to solve the equation

$\simplify{{a}x^2+{b}x-{c}}=0$

Using the quadratic formula we have

$\begin{align} x&=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\&=\frac{-\var{b}\pm\sqrt{\simplify[!collectNumbers]{{b}^2-4*{a}*{-c}}}}{\var{2*a}}\\&=\frac{-\var{b}+\sqrt{\simplify{{b}^2-4*{a}*{-c}}}}{\var{2*a}}\text{ or }\frac{-\var{b}-\sqrt{\simplify{{b}^2-4*{a}*{-c}}}}{\var{2*a}}\\&=\var{ans}\text{ or }\var{ans2}\end{align}$

Since we are told that $x\ge 0$ we can ignore the negative answer and conclude that the bending moment will be $0$ at a distance approximately $\var{precround({ans},2)}$ m from the end of the beam.

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Part	Test	Passed?
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Gap-fill		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.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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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

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Generated value: `number`

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Bending moments

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`