Hooke's Law and Simple Harmonic Motion

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Physics 1X – IT in the Physics Context
IT in the physics context
Aims
 To realise the potential of Microsoft Word and Excel as tools for the understanding
of Physics.
 To gain experience in using various scientifically-useful functions of Word and
Excel.
 To use Word and Excel to create components of a laboratory report.
 To introduce the mastering physics tutorial system
 To provide material to allow exemption from the Certificate of Basic IT
competence.
Introduction
In the P1X/Y lab you are required to submit reports on a subset of the experimental
work which you carry out in each module. You are also required to make use of
spreadsheets to analyse data during some of the experiments. The primary aim of the
exercises presented here is to help you learn (or revise) the skills needed for these
requirements. Note that the laboratory experiments rely on the fact that you are
already skilled at entering equations and producing graphs in Excel, so you need to
learn these skills before the 1st week of experiments.
The university also requires that each student attain a 'Certificate of Basic IT
competence' before entry into 2nd year. By adequately completing the tasks in this
exercise you will have shown IT competence and will have your name added to a list
which will be forwarded to the IT Education Unit in the university and you will
automatically gain exemption from their course.
Since the amount of previous experience students have is quite varied, this exercise is
self-paced. You are under no pressure to complete everything in the timetabled
session, all you are required to do is to submit your assignment at the end of term (see
timetable). Please note, though, that demonstrator help will only be available during
the timetabled sessions.
Note, you are free to use any of the Departmental Open Access Computer Cluster PCs
at any time and are encouraged to check your email and the moodle site regularly.
You will also need to login regularly to complete your Mastering Physics
assignments.
Getting started
Before beginning any of the exercises, you will need to login into a PC on the
University network, and start the appropriate applications. You will be told how to do
this at the introductory lab session. Please ask a demonstrator if you experience
problems1.
1You will need to be processed by the registry before you can login in to the university network.
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Physics 1X – IT in the Physics Context
All the information you require to carry out these exercises is provided within this
document. However, additional help with using IT packages is offered by the IT
Education Unit in the University. The following web address contains links to short
help sections:
http://apps.iteu.gla.ac.uk/ITEU/html/topups/index.jsp
You may find it helpful to have this displayed in a web browser as you go through the
exercises. This web link is only for help perform the exercises in this book not those
on that web page.
As a first step, please use a browser to navigate to the P1X/1Y Moodle site at
http://moodle.gla.ac.uk/physics/moodle/ and enrol yourself in the class. The enrolment
key (that you will be asked for when you first access the P1 area of Moodle) is
Physics1X/1Y. Moodle is the medium through which all material and announcements
relating to the class will be communicated, so it is important that you get into the
way of accessing it regularly.
1. Mastering Physics
You will be set regular tutorial problems using the Mastering Physics tutorial system.
The system is accessible at the web site http://www.masteringphysics.com and is
linked from our Moodle site.
We are using the version marked
“Mastering Physics for Young/Freedman University Physics 11th edition”
1.1 Registering
 If you have bought a new copy of the textbook you will have obtained an access
key with the textbook, which you will need to enter. If you have bought a second
hand copy of the textbook you will need to buy online access to Mastering
Physics, which you can also do from this web site.
 One of the registration questions asks for the postcode of the university:
G12 8QQ.
 Please enter your university email address. Remember to check your email
regularly as we will use this to communicate with you.
 You will then be able to set up your username and password. Keep a record of this
– you will need it to access the website.
 After registering you should log in to the Mastering Physics for University Physics
11th Edition site (not the standalone one).
When you log-in for the first time it will ask you for
i.
the course ID – (Please be careful, you will not be able to change the
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Physics 1X – IT in the Physics Context
course ID once it is entered.) The course ID for October 2006 is:

P1XY2006
and
ii.
your student ID number – this is your matriculation number.
1.2 Complete the introductory exercises
 Click on "assignment list" in the left-hand blue menu column. You can then select
and complete the "Introduction to Mastering Physics" assignment.
 Once you have completed the assignment open a new file in Word. Copy the
details from the Mastering Physics “current assignment” and paste them into the
Word document. Save this as masteringphysics.doc on your floppy disk/memory
stick and close the file. You can add this later to the it_assignment.doc you create
in the following exercises.
2. Using Microsoft Word
Microsoft's Word package is the most commonly used word processor. In this
exercise you will be introduced to some of the useful functions the package possesses
for scientific writing. These will be vital for writing your laboratory reports.
A good, thorough laboratory report contains diagrams of experimental set-ups,
equations, tables of results and so on. Here you will learn how to create these
elements electronically.
Sections 2.1 and 2.2 instruct you in the use of a series of these tools, teaching you
what they can do and how to use them. Once you have gained this experience, section
2.3 asks you to employ those skills in four exercises. Your attempts at these exercises
must be saved in a word document and presented for marking.
Important note – remember to save your work frequently on to the floppy disk you've
been provided with!
2.1 Drawing diagrams.
Here you will use the Microsoft Draw package.
2.1.1 Creating objects
 The first step is to bring up the drawing toolbar. To do this, click on View →
Toolbars → Drawing. This toolbar contains several buttons. Run your mouse
along the icons to learn what each does.
 Click on the Line button. When you move the mouse back over the page, a + will
appear. A line is drawn when you depress the left mouse button and drag + across
the screen. The line terminates by releasing the mouse button. Holding down the
shift key together with the left mouse button will produce a horizontal, vertical or
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Physics 1X – IT in the Physics Context
45 o line.
 Now draw a rectangle, an ellipse and an arc. You can vary the sizes of all these
shapes by clicking on one edge or corner and dragging.
 Microsoft Draw does not restrict you to fixed shapes. Find the freeform and
scribble buttons and draw a couple of random shapes.
 Having now created your Microsoft Draw masterpiece, you can give it a title by
inserting a text box. Click on the Textbox button and then click the mouse
somewhere on your page. By clicking inside this box you can write your title.
2.1.2 Editing objects
 Click on one of the lines you've already drawn. Now go to Edit → Copy and then
Edit → Paste to create a duplicate of that line. Now click on the Line Style button
and change the thickness of your line. Create another copy and use the Dash Style
button to create a dashed line.
The Line Style and Dash Style functions can be used to alter any of the shapes you
created.
 Copy a couple of your shapes and experiment with the options.
Draw objects can also be edited by right clicking on the object. This brings up an
options window that allows you to specify the size, colour, etc of the object.
 Draw a circle and then use the editing options to change the colour of the circle's
interior to blue and its boundary line to red.
2.2 Using Microsoft Equation editor
In this section you will be shown how to create three separate equations using the
Microsoft Equation package.
To insert an equation using the equation editor, click:
Insert → Object → Microsoft Equation 3.0 → O.K.
A box in which you insert the equation and the Equation Editor Toolbar will appear.
The toolbar is shown below.
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Physics 1X – IT in the Physics Context
Type in the following equations:
(i) A  B  C   A  B  A  C
 Type A into the Equation Editor box. Select
with the mouse and, keeping
the left mouse button depressed, move the mouse pointer to the appropriate
symbol. When you release the mouse, the symbol will be inserted.2,3
 Select
and as above enter ( ) into the equation.
 Type B+C inside the round brackets.
 Complete the equation inside the Equation Editor box.
 Return to your word file by clicking outside the Equation Editor box twice.
It is possible to edit the text of an equation by pointing at the equation with the mouse
and double-clicking.
(ii) f 
 The
df
df
df
i
j
k
dx
dy
dz
symbol is obtained by selecting
from the Equation Editor toolbar.
 The expressions with a numerator and denominator (the partial derivatives) are
obtained by selecting
selecting
symbol.
(iii) U1  U 2 
, and the underscore defining the unit vectors by
. Highlight the text to be underscored, then select the appropriate
U2
 Eds
U1
 Here, use
and
.
You can copy and paste equations just as you did objects in Microsoft Draw. Just
click on the equation you're interested in and select Edit → Copy. Then click on the
page where you wish the copy to appear, then select Edit → Paste.
2
You can also insert the symbol by clicking on the first box, releasing the mouse button, then clicking
a second time on the symbol you want.
3
By the way, if you want to add a footnote of your own, click on the appropriate spot in the text then
go to Insert → Footnote. (If you are using Office 2003, it's Insert → Reference → Footnote.)
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Physics 1X – IT in the Physics Context
Example – put the equations into a table.
 Click on a line below equation 3, then click on Table → Insert → Table. This will
bring up the "Insert Table" box. Set the number of columns to be 3 and the
number of rows to be 2, then click on OK.
 In the cells in row 1 type "Equation 1", "Equation 2" and "Equation 3". Now copy
equation 1 and paste it into the first cell in row 2. Repeat this procedure for
equations 2 and 3.
Have you been remembering to save your file as you've gone? If not, best do so now!
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Physics 1X – IT in the Physics Context
2.3 Exercises
A)
 Using Microsoft Draw, create the following picture.
N
T
T
M2
M1
M1gsin

M2g
M1g
M1gcos
Figure 1: Forces acting on a block on a slope.
B)
 Below is a sketch a student made in their lab book when they were carrying out an
experiment to measure the period of a mass bouncing on a spring. They now have
to write it up as a report. Create an electronic version of this diagram.
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Physics 1X – IT in the Physics Context
C)
 Another student is writing a report on an experiment where a glider was slid down
an air track and its speed noted at two points. They wish to include a table
containing the results from their experiment. The table from their lab book is
below. Turn this into a Word table.
D)
 Reproduce the following equations:
at 2
s  ut 
2
F 12 
kQ1Q2
2
N
1 
8
r2
rˆ
1
xi  x 2

N 1 i
Physics 1X – IT in the Physics Context
3. Using Excel to analyse and present data
Microsoft's Excel package allows you to tabulate and manipulate data which you have
collected whilst performing an experiment. You can manipulate the data by entering
equations and graph the results.
Here, as in section 2, the initial sections (3.1 – 3.3) instruct you in the use of a series
of Excel's tools, teaching you what they can do and how to use them. Once you have
gained this experience, section 3.4 asks you to employ those skills in three exercises.
Your attempts at these exercises must be saved in an excel document and presented
for marking.
Again – remember to save your work frequently on to the floppy disk you've been
provided with!
3.1 Handling tables of data
 Open up a web browser and go to the following web site:
http://www.physics.gla.ac.uk/~psneddon/P1X_labs.html
(This page is also linked from the Moodle site in the Laboratory information section.)
 Open the file P1X_excel_exercise_A.xls
You should see a spreadsheet with the following information:
William
Sophie
Elizabeth
Peter
Thomas
Christopher
Carol-Anne
Bonnie
Sylvester
Patrick
Jon
Sarah
Katy
Paul
Nicola
Louise
Baker
Manning
Sutton
McGann
McCoy
Pertwee
Aldred
Jamieson
Eccleston
Davison
Troughton
Bryant
Sladen
Hartnell
Langford
Hill
Exam Mark
68
70
62
67
70
70
77
66
59
61
69
79
55
48
65
79
Laboratory Mark
75
72
64
72
81
75
80
68
66
71
71
80
59
56
78
86
Total Mark
The spreadsheet details the results of a section of a Physics class giving the lab and
exam mark of students (marked out of 100). We want to calculate the total result for
each student for the course.
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Physics 1X – IT in the Physics Context
3.1.1 Sorting your data
One of Excel's strengths is its ability to allow you to Sort a set of data in several ways.
For instance, we could reorder the above data into exam mark order. However,
typically a results list is listed in alphabetical order.
 Select all the data (i.e. cells A2 to D17) and then go to Data → Sort and select
column B and Ascending order. The table should now be ordered in Surname
alphabetical order.
Now, technically the Data Protection Act makes it illegal for the University to share a
student's results with the general public, so before we go any further you need to
make the data anonymous – i.e. delete the names from this spreadsheet.
 Select columns A and B of the spreadsheet. (Click on the A, then whilst holding
down the shift button, click on the B.) Then go to Edit → Delete.
However, we want some way to identify the students, so each row of data needs a
number.
 Highlight the new column A, then go to Insert → Columns. The existing data
should be shunted one column to the right, leaving a new, empty column A. Label
the contents of the column in cell A1 by typing in ‘identifier’. Then fill in the
numbers 1 – 16 down the list.
3.1.2 Calculating the "Total Mark"
The total mark a student gains in Physics is a combination of their mark for their
exams and their laboratory mark. It is not a straight addition of the two, though. The
exam mark makes up 80% of the total, the labs 20%. We need, therefore, to scale the
results on the spreadsheet.
 Insert two new columns between the "Laboratory Mark" and "Total Mark"
columns. Label these "Scaled Exam Mark" and "Scaled Lab Mark" respectively.
If you cannot see the full heading once it's typed, adjust the column width
appropriately. This is done by positioning the mouse over the very top of the
divider line at the right hand edge of the column you want to widen. Then simply
click and drag right until you can see the full text.
 To scale the exam mark, enter the following into cell D2:
=0.8*B2
and press Enter. This multiplies the contents of cell B2 (student 1's exam mark)
by 0.8, i.e. calculates 80% of that mark. The cell in the spreadsheet should now
contain the scaled result.
 You now want to do the same for students 2 – 16. The most efficient way to do
this is to click your mouse on the bottom right hand corner of cell D2. Now drag
the mouse down until all the cells up to and including D17 are highlighted. When
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Physics 1X – IT in the Physics Context
you release the mouse button, these cells will fill in. Click on any one of these and
you will see an equation of the same form as above, but with a different cell
number. (e.g. B5, B8, etc.)
 Using the same technique, complete the "Scaled Lab Mark" column, remembering
that you want to scale the laboratory marks to 20% here.
You can now calculate the total mark for each student, by adding the contents of
columns D and E together in column F.
 Enter =D2+E2 into F2, hit Enter, and then repeat the click, drag, release
procedure. The column should now contain the final mark of each student
 Sort the data so that the students with the highest total marks are listed at the top.
3.2 Manipulating experimental data
Return to the webpage mentioned in Part 2.1 (or the P1 Moodle site) and open up the
file P1X_excel_exercise_B.xls
A student carries out an experiment to calculate the acceleration of a moving object.
They do this by measuring the object's speed, v , at various times, t . The spreadsheet
you have just opened shows the measured results.
The relevant equation of motion for this object is:
v  v0  at
where v 0 is the object's initial velocity and a is its acceleration. If a graph of v  v0 
versus t is plotted, the gradient of the graph will be the acceleration.
3.2.1 Performing calculations
 On the spreadsheet write "v0" in cell D14, and then "4" in D2. i.e. D2 has the
value of the initial velocity.
We are going to put the data for the y-axis of the graph – the values of v  v0  – into
column C.
 Give the column a suitable heading in C1, then click in cell C2. Enter the
following equation:
=(B2-$D$2)
4
If you want to make the 0 a subscript, click in the cell and select the number. Then click Format →
Cells and tick the "Subscript" box. Click OK, and then hit Enter again to leave the cell.
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Physics 1X – IT in the Physics Context
and then hit Enter. (You're taking the data in the velocity column and subtracting
the initial velocity.) Now, as you did in part A, click on the right hand bottom
corner of C2 and drag down to C9 to fill in the rest of the column.
The use of the "$" signs is vital. Without them, when you drag down, the cell
subtracted would move from D2 to D3, D4, etc. Using the "$" locks the reference to
the correct place. Try it and see!
3.2.2 Plotting data graphically
You now want to plot the graph of v  v0  vs t .
 Select the time data (A1 – A9), then whilst holding the Ctrl button select C1 – C9.
 Now click on the Chart Wizard icon. Select XY Scatter → Scatter, then click
Next.
 A preview of your graph should now appear (step 2 of the Chart Wizard). Check
the data range is what it should be (i.e. =Sheet1!$A$1:$A$9,Sheet1!$C$1:$C$9),
then click Next.
 Step 3 of the Chart Wizard allows you to label your graph. Input suitable x and yaxes labels, as well as a title for your graph. Click Next.
 The final step of the Wizard determines where the graph will go.
example, select Sheet 1 and click on Finish.
For this
3.2.3 Finding the gradient of a graph
To find the gradient of a line drawn in Excel we use a programme called Trendline.
 Right click on any of the data points. In the menu this brings up, click on Add
Trendline.
 In the Type tab, select "Linear".
 In the Options tab, select "Automatic" and "Display equation on chart".
OK.
Click
There should now be a best fit line through the data points and an equation of the
form y = mx + c (the equation for a straight line of gradient m and intercept c). Here
the intercept = 0 and the gradient (= acceleration) = 0.8 ms -2 .
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Physics 1X – IT in the Physics Context
3.3: Evaluating (and plotting) a complex equation
In this section you are going to plot the following function:
f x  
  x   2 
exp 

2 2 
2 2

1
[*]
This is a Gaussian distribution with mean value  , and standard deviation  .
 The first step is to open a new spreadsheet and call it Gaussian.xls
3.3.1 Evaluating
Now we need to evaluate the equation f x  for a range of x values. i.e. we need to
convert the above equation into a form that Excel can recognise and interpret. The
following steps will do this by breaking the expression into smaller terms,  ,  , and
 , where:

1
2 2
,   x    ,   2 2
2
 
f x    exp  
 
i.e. [*] becomes:
 In your spread sheet create suitable column headings along Row 1. e.g.:
1
2
A
mu
B

C
x

D
alpha

E
beta
F
gamma
G
f(x)
For this example we shall define the mean,  (mu), to be 5 and the standard
deviation,  (sigma), to be 2.
 Enters these numbers into cells A2 and B2 respectively.
 Column C will contain your x-values. The first point is 0.0, so enter this in cell
C2.
Now we start putting in the equations. We want to put the equation for  in cell D2.
1
Recall  
. In Excel, this is expressed as =1/(2*sqrt(2*Pi())).
2 2
The function sqrt() calculates the square root of whatever is within the brackets. Here
this is 2 , or 2*Pi().
 Put the Excel version of the equation  into cell D2 and click Enter. Make sure
you have all the correct brackets in place. This is vital in Excel. If there is not the
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Physics 1X – IT in the Physics Context
same number of opening brackets as closing brackets, Excel will query your
equation. However, if the numbers match it will just calculate whatever you have
typed, whether those brackets are in the right place or not.
Now we put the equation for  in cell E2. Recall    x    . In Excel this is
expressed as =(C2-$A$2)^2. Here the $A$2 is picking up the contents of cell A2,
which is the value of  .
2
 Enter the Excel version of the equation for  into E2 and hit Enter. In Excel the
"^" symbol means "to the power", and is applied after the calculation within the
brackets.
 Now input the equation for  in F2. In Excel language,   2 2 is expressed as
=2*$B$2^2.
We are now ready to calculate f x  by combining the equations that have been
entered into cells D2, E2 and F2.
 Type the following into G2:
=D2*exp(-E2/F2)
In Excel, the equation exp() calculates the exponential of whatever is in the
brackets.
Now that we have calculated f x  at x = 0.0, we need to calculate it over a range of
x values.
 Create a list of x values from 0.0 to 10.0, increasing in steps of 0.2. To do this,
type =C2+0.2 into cell C3. Then click on the bottom right hand corner of C3 and
drag the mouse down to cell C52. When you release the mouse, you should have
the required list.
 Fill in the corresponding values of  ,  ,  and f x  by repeating the same
click, drag and release procedure on cells D2, E2, F2 and G2. Note – the contents
of Columns D and F should be the same in every cell. If not, go back and check
that you have correctly typed in the equation in D2 and/or F2.
3.3.2 Plotting
 To plot this function f x  , follow the instructions detailed in Part 2.2.2, selecting
column C for your x -values and G for your y -values.
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Physics 1X – IT in the Physics Context
3.3.3 Using Excel functions
In addition to being able to enter your own equations into Excel, the software comes
with a range of useful equations, or functions, which you can use. We've already
encountered the square root function. Here we will introduce some of the others.
 Open a new spreadsheet and enter the number 1 – 10 into column A.
 In cell B1, type the following:
=sum(A1:A10)
As the name of the function implies, this function adds up the contents of the cells A1
through A10. If this number is then divided by 10, the average of the series of
numbers is obtained. It's not a very efficient way to find the average though.
 In cell B2, type the following:
=average(A1:A10)
This calculates the average directly.
These are just two examples of the functions available. A full list can be found by
going to Insert → Function.
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Physics 1X – IT in the Physics Context
3.4 Exercises
A)
 Go back to the table of data you created in Exercise 2.3C and copy it into a new
Excel spreadsheet.
 Insert a new column between the time and acceleration columns and give it the
heading a – calculated. (Make sure you can see the full heading.) From your
knowledge of dynamics, create an Excel equation to generate an acceleration
value for each set of data. Format the resulting values so that they have the same
number of decimal places as the rest of the data. Does this match with the
numbers in the original acceleration column?
 Calculate the average value for each of u , v , t and a .
 Now calculate the error on this average by using the stdev function.
 Format the averages and errors to the same number of decimal places as the
original data. Then format the error cells to show an extra decimal place – what
do you notice?5
B)
A student has carried out a simple experiment to test Ohm's Law. They built a series
circuit containing a single resistor and a variable power supply. They varied the
voltage across the resistor, and monitored the current for each voltage. Their data is
given below.
V(V)
0
1
2
3
4
5
I(mA)
0
1.4
3
4.6
6.1
7.3
 Plot a graph of current against voltage, clearly labelling the axes.
 From the graph, determine the value of the resistor.
A second resistor is now added to the circuit in parallel to the first. The total
resistance of this combination is given by the following equation:
1
Rtotal

1
1

R1 R2
 Using Excel, calculate the total resistance of this new combination, taking the first
resistor’s value you determined and the letting the second resistor vary from
5
See the danger of rounding!
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Physics 1X – IT in the Physics Context
100  to 1 k in 100  steps.
C)
 Evaluate the following function between t  0.0 and t  50.0 in steps of 0.5.
t


Q   C 1  e RC 


(   5 V , C  1  10 6 F and R  10 MΩ .)
 Plot this function, clearly labelling the axes.
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Physics 1X – IT in the Physics Context
4. On-line library resources
The ITEU material for this part can be found at:
http://apps.iteu.gla.ac.uk/ITEU/html/topups/intro1.jsp
 Access the university library's website – the link to this can be found from
http://www.gla.ac.uk
 Click on the Merlin-Catalogue link and carry out a Title search on 'University
Physics'.
 Now perform an Author/Title search on University Physics by Young and
Freedman.
 Now use the Keyword option to obtain a list of references relevant to a topic
within one of your subjects of study. Mark some of the references, then email
them to yourself.
 Open up your mail application and copy the text you have received.
 Open up your word document from part 2 and paste the e-mailed library
information into it. Preface it with the heading 'Possible References'. Save the file
again.
5. Searching the WWW
 Find the University's collection of Subject Indexes and select the BUBL Link
Subject Tree.
 Follow the index links through to the "Physics: general resources section". You
are now presented with a short list of external links, accompanied by short
descriptions of each website. Select one site and see how well that site matches its
description. Copy the web address of the site into your word document.
 Return to the Subject Gateways page and select the link to HERO – the Higher
Education and Research Opportunities in the United Kingdom website. Now see
if you can find a useful link on this web site. If you find something quickly, you
can try to find some other sites here or explore some other Subject Indexes.
Again, put the address into your word document.
 Go to the list of search engines on the Merlin pages (under "Information
resources"). Access Google and search for web pages on the subject of Optics.
Now repeat the search, but add the term Quantum. Put the top three links from
each search into your word document.
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Physics 1X – IT in the Physics Context
6. Finishing off
When you have completed the material from each of the above sections, save the
file(s), and print out:
 Your word document: we recommend that this document contains all your work
from the Word section. Certainly, it must contain your attempts at exercises 2.3
A-D. In addition, don’t forget to include the Mastering Physics section.
 Your excel spreadsheets: again we recommend printing out all the work you have
carried out and must contain your attempts at exercises 3.4 A-C. Make sure that
you print both tables and, where appropriate, graphs clearly. Check what you'll be
printing using the Print Preview option.
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