ate
D
Course Name
Instructor Name
Student(s) Name
The number
(3.141…)
STUDENT OUTCOMES
Through this experiment, students will learn:
- How to obtain the number pi
- Line equation graphing skills
- Simple table making
- Understanding and use of the slope of a line
- Basic analysis calculation
- Experimental errors
MATERIALS
ablet PC Computer Laptop
T
Excel
Microsoft Paint
String
ernier Computer Interface
V
Word
Ruler
PROCEDURE
. Use the objects you instructor is giving you.
1
2. Use your ruler, and measure the diameter of each object given.
3. Use the string, and measure the circumference of each object given.
Use mm for all measurements
RESULTS
The formula for the circumference of a circle is:
(1)
hereCisthecircumference,Disthediameter,and
W
isthenumber
pi. There is an obvious linear relationship between the circumference
and the diameter and the purpose ofthisanalysisistorevealit.The
wholeexperimentassumesthatwedonotknowwhatpiis;we
will obtain its value through this experiment.
. Create a table that includes your measurements of the diameters
1
and circumferences.
( tolearnhowtocreateatable,referto:http://www2.hawaii.edu/~pseng/labs/resources.htmlunderHow
to create a Table with Excel)
Include your table here
( tolearnhowtoimportatable,referto:http://www2.hawaii.edu/~pseng/labs/resources.htmlunderHow
do I import a table or a graph into my word document?)
. Create a graphwiththebestfitandchooseDasyourindependent
2
variable and C as your dependent variable.
( to learn how to import a graph, refer to: http://www2.hawaii.edu/~pseng/labs/resources.html under
How do I import a table or a graph into my word document?)
(to learn how to include a best fit line, refer to: http://www2.hawaii.edu/~pseng/labs/resources.html
underHow to create a simple graph with Excel?)
Include your graph here
.a)Writedowntheequationofalineandequation(1)oneabovethe
3
other. b)Identify from equation (1), the variables that correspond to
yourslopeandyoury-intercept.c)Usethegraphobtainedinquestion
2. and state the numerical value of your slope; don’t forget your units.
4. What is the meaning of your slope based on equation (1)?
.Whenlookingatthefunctionalformofequation(1),whatmustbe
5
the value of your y-intercept? Go back to your graph, andforceyour
y-intercepttobeequaltothevalueyoujustdecideditshouldbefrom
equation(1).Includeyournewgraphhereandgiveyournewpivalue.
Isitclosertothetruevalueofpithanyouroriginalvalue?Isthiswhat
you expect? (Odd results might appear here).
( to
learn
how
to
force
the
y-intercept
to
a
given
value,
refer
to:
http://www2.hawaii.edu/~pseng/labs/resources.htmlunderHowdoIforcemyy-interepttoaspecific
value?)
Include your graph here
.Youalreadyknowwhatthetruevalueofpiis(truevalue).Basedon
6
this,computethepercenterrorusingtheexperimentalvalueofpiyou
obtained in part 5. If, for this experiment, the cut off value of the
percent error is 5%. Deduce, based on your percent error value, 1)
whetheryourexperimentalvalueofpiisaccurate,and2)whetherthe
amount of systematic errors present in your experiment is high.
( tolearnhowtocalculatethepercenterror,referto:http://www2.hawaii.edu/~pseng/labs/resources.html
underReview on concepts)
.Whatif,forsomeoddreason,wearebeingaskedtoplotnotCvsD
7
but CvsR,whereRistheradiusofthecircle.Includeanewtableas
in 1. with your new R values, and include your new graph as well.
What is the value of your slope?
Include your table and graph here
. From question 7., if one wants to extract the value of pi; what
8
needs to be done? In other words, what is the relationship between
the slope value of question 7 and pi?
. Given the equation,
9
where m1 an m2 are constant
values, and F and r are measured quantities, one could assign
quantities to both your dependent and independent variables so that
the slope between X and Y is exactly m1m
G.
2
Assign new values for X and Y so that the slope between X and Y is
exactly G. This process is called linearizing an equation.
10. Giventhefollowingsetofdata,basedonNewton’slawofgravity:
:
,
where F represents the
ttractive force between two massive objects, r represents the
a
distance between the two objects, m1 and m2 are the respective
masses and G is the gravitational constant.
(Newtons)
F
7.3*1013
r (meters)
1.0*1011
.9*1013
5
4.9*1013
3.9*1013
3.3*1013
2.9*1013
2.3*1013
2.0*1013
1.7*1013
1.5*1013
1.3*1013
.1*1011
1
1.2*1011
1.3*1011
1.4*1011
1.5*1011
1.6*1011
1.7*1011
1.8*1011
1.9*1011
2.0*1011
PlotFvsr(usingxyscatter).Givespecialcareonwhichisyourdependentand
independent variable, and the way you plot those data using excel. It is strongly
suggestedthatyouplotonlythevalueofeachparameterwithoutthe10x part,which
you would rather add only in your label and units onyourgraph(thiswouldmake
your life much easier…)
Include your graph here
1.Basedonthetypeofgraphobtainedin8.whatkindofrelationship
1
exists between the force and the distance? Is it linear?
2. We need to linearize Newton’s equation of Gravity in order to
1
extract the value ofgravitationalconstantG.Todothis,createanew
table involving the same F values from the table in 8. and a new
quantity
that you need to compute. Make sure to use scientific
otation (for instance, 1.3E13 or 1.3*1013 or as suggested in 10, only reportthe
n
values without the 10x and fix the units to make itright).
Include your table here
13. Include a new graph made by hand involving F and this new
uantity
q
; don’t forget your units. On the same graph, include
the best fit: try your best.
Include your graph here
4. Redo the same graph as in 11. using excel, and include the best fit
1
line; make sure to include the equation on your graph, restate the
interpretation of your slope, and give the value of the constant G;
don’t forget the units.
5.Ifyouaregiven
1
,assumethatthepurposeofthisgame
is to linearize this equation, (as obviously ifyouplot
(Y)vs (X),
therelationisnonlinear)assignanewvalueforYsothattherelation
between your new Y an X is linear. The slope obtained will then be
proportional to .
Solve for
intermsofyournewslope(analytically):inorderwords,
express theexactrelationshipbetweenyourslope(afterlinearization)
and .
Hint: Keep X assigned to the length
0
