Coefficient of restitution

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of HELM books :

Merryn Horrocks

said

Ready to use

1 year, 2 months ago

History

○

Merryn Horrocks 1 year, 2 months ago

Published this.

○

Merryn Horrocks 1 year, 2 months ago

Gave some feedback: Ready to use

○

Don Shearman 3 years, 9 months ago

Created this.

Name	Status	Author	Last Modified
Coefficient of restitution	Ready to use	Don Shearman	13/02/2024 09:14
Coefficient of restitution	Ready to use	Don Shearman	16/04/2024 06:24

There are 2 other versions that do you not have access to.

Question statement

When a ball is dropped from rest onto a horizontal surface it will bounce before eventually coming to rest after a time $T$ where

$T=\frac{2v}{g}\left(\frac{1}{1-e}\right)$ where

$v$ is the speed immediately after the first impact, and

$g$ is the acceleration due to gravity.

Give any introductory information the student needs.

			Name	Type	Generated Value

balls	list	[ "glass", "chrome steel" ]
blocks	list	List of 4 items
ball_s	integer	1
block_s	integer	2
velocity	list	[ 1.74, 1.93, 2.17, 2.43 ]
velocity_s	integer	2
time	number	5.29

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
["glass","chrome steel"]

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: `list`

[ "glass", "chrome steel" ]

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Gap-fill
1. Gap Number entry
  Add

Gap-fill

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

Transpose the formula to make $e$ , the coefficient of restitution, the subject.

$e=$ Unnamed gap

Advice

Part(a)

$\begin{align} T&=\frac{2v}{g}\left(\frac{1}{1-e}\right)\\ \frac{Tg}{2v} &= \left(\frac{1}{1-e}\right)\\ \frac{2v}{Tg} &= \left(\frac{1-e}{1}\right)\\ \frac{2v}{Tg} &=1-e\\ e&=1-\frac{2v}{Tg} \end{align}$

Part (b)

$\begin{align} e&=1-\frac{2v}{Tg}\\ &=1-\frac{2\times\var{velocity[velocity_s]}}{\var{time}\times 9.8}\\ &=1-\var{(2*velocity[velocity_s])/(time*9.8)}\\ &\approx\var{precround(1-(2*velocity[velocity_s])/(time*9.8),2)} \end{align}$

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
Mathematical expression
Mathematical expression		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Formulae and Transposition by Don Shearman in HELM books.
HELM Book 1.5 exercises by Merryn Horrocks in HELM books.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Merryn Horrocks 1 year, 2 months ago

Merryn Horrocks 1 year, 2 months ago

Don Shearman 3 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

Part(a)

Part (b)

Loading...

Error

Coefficient of restitution

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Merryn Horrocks 1 year, 2 months ago

Merryn Horrocks 1 year, 2 months ago

Don Shearman 3 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Part(a)

Part (b)

Generated value: `list`