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Hooke's law

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Name:
Hooke’s Law
Laboratory Exercise
Robert Hooke (1635-1703) wrote that the business and design of the Royal Soiety is ! o i#$ro%e the knowledge of naturall things& and all useful 'rts& anufatures& ehanik $ratises& ngynes and *n%entions by +$eri#ents, o e+a#ine all syste#s& theories& $rini$les& hy$otheses&ele#ents& histories& and e+$eri#ents of things naturall& #athe#atiall& and #ehaniall& in%ented& reorded& or $ratised& by any onsiderableauthor anient or #odern *n order to the o#$iling of a o#$lete syste# of solid $hiloso$hy for e+$liating all $heno#ena $rodued by natureor art& and reording a rationall aount of the auses of things
All to advance the glory of God
& the honour of the .ing& the royall founder of the Soiety& the benefit of his kingdo#& and the generall good of #ankind/
(ikel 130-1)
Background
Automobile suspensions, playground toys and even retractable ball-point pens employ springs. Most springs have aneasily predicted behavior when a force is applied. onse!uently, the force that a spring applies to a body, as the spring is extended or compressed, can be mathematically determined. his type of relationship can be described by anumber of mathematical relationships. #n this lab, you will see which one describes the springs we are using.$obert %oo&e, a contemporary of 'ewton, tried to define a set of mathematical laws to predict the behavior of forces directed towards the center of something ()central forces), e.g. planetary gravity*. %e examined central forces that were inversely proportional to the distance between two ob+ects. his linear relationship does not hold true in light of our present &nowledge of planetary gravitation, but wor&s well for springs. %oo&e)s Law, as commonly used, states that the force a spring exerts on a body is directly proportional to the displacement of the system (extension of the spring*. hat is,
F = -k x
, where
F
is the force exerted,
x
is the extension of the spring, and
k
is the proportionality (or spring* constant that varies from spring to spring. (ther forms, applicable to collapsing balls andother systems, are
= -
k +
2
,
= -
k +
/
and other powers of
+
.*
Introduction & Theory
An important property of solids is their 0stretchiness0 or 0s!uee1iness,0 which is called their elasticity. #n the case of many solids, the amount of stretch or s!uee1e is proportional to the force causing the stretch or s!uee1e. his relationship can be expressed as2
+
which is read as 0force is proportional to stretch (or s!uee1e*0. o change this expression into ane!uation, a constant of proportionality must be included. he expression ends up ta&ing the form2
s
3
k +
where & is the constant of proportionality (in this case, the spring constant*. he value for & depends on the material being stretched or s!uee1ed. his e!uation expresses what has come to be&nown as %oo&e)s Law. 4445our problem in this experiment is to see if the spring on theapparatus obeys %oo&e)s Law, and find the value of & for your spring.444 he spring potential energy,
2
s$ring
or
s
,
can be written as
s
3 6
k
+
/
Aaratus !sed
he apparatus used consists of a weight holder attached to a spring. A pointer enables the studentto mar& the distance the spring moves when weights are placed on the weight holder. 7ee 8ig 9. 8igure 92 %oo&e)s Law apparatus
rocedure
8irst, line up the pointer on the weight holder with the 1ero on the scale. hen hang a mass (in grams* on the scale and record the distance the pointer moves (in centimeters*. 7ight
hori4ontally
to read the position of the pointer along the scale (how does the mirror behind the scale help to do this:*. ;o this for 9/ different masses, hanging the masses in ever increasing amounts and recording the information on your data table. ;o not use more than /<= grams of mass when collecting your data. >hen you have completed your measurements, be sure to remove all masses from the spring so as not to leave it stretched for a prolonged period of time. 'ext, convert the masses you have recorded in grams to &ilograms. Also convert the distance measurements you made in centimeters to meters. 8inally, ma&e a graph of force vs. stretch using your results (?sing Excel is recommended2 highlight the data, ma&e a scatter @chart, label axis, give title, then @add trendline B linear, display e! C $
/
(the loser to 1 this is the s#aller the error)
* 8orce will go on the y-axis (vertical axis* and will be in newtons. 7tretch will go on the x-axis (hori1ontal axis* and will be in meters. #f your spring obeys %oo&eDs Law, the points on your graph should lie along a nearly straight line.
LAB #$ %#T $'TI%N
y$e your re$ort (not your $artners) our re$ort should ha%e eah of the following setions as subheadings ne re$ort $er $erson& ie e%eryone needs to ha%e their own data
!# %$
>hat is the purpose of the experiment: #n one or two sentences, state what law or theory you are trying to prove.
HIT%#(
Give a brief discussion on the srcin or early uses of the idea or the experiment. Explain who is first credited with discovering the law or performing the experiment and what was he or she trying to prove or disprove.
TH$%#(
>hat is the reasoning behind the experiment: Give a brief explanation as to what your data and results should show under error free conditions (i.e., under theoretical conditions*. List what formulas are needed to obtain results from your data:
#%'$)!#$
A step-by-step description of what you did to get your experimental data. #nclude a labeled diagram of your apparatus. >ere there extra steps which you found necessary or different from those described in the lab write-up:
)ATA
#nclude your srcinal data table with the
instructor’s signature
as well as
your signature in ink
. 5ou may include acleaned up version of your data table in your report, but the srcinal data table still needs to be attached.
#$!LT
>hat does the data show: rovide a brief discussion of its meaning. his is where any graphs, such as the one re!uired by the %oo&e)s Law experiment, should be presented and analy1ed. >hat is the li&ely degree of error in your results: 5ou don)t need to give an actual error percentage, but do tell whether you thin& the degree of error is insignificant (i.e., you can ignore it*, minor (i.e., it is something to &eep in mind*, or significant (i.e., you lab partner really messed things up*. 7how all e!uations (i.e., the formulas you mentioned in your heory section* and wor& outexamples as to how you used them. 8inally, number and answer all !uestions in complete sentences in paragraph form.
'%N'L!I%N
;id you show what you set out to show (as mentioned in your urpose section*: #f not, then why not: >here did possible errors creep into your data: #f your line of best fit has a y-intercept of something other than 1ero, that demonstrates error. Explain a solution to this discrepancy. Answer the !uestions presented in the lab. %ow could any errors in your data be further minimi1ed if you were to perform the experiment over again.
*uestions
y$e the answers to the following uestions in o#$lete sentenes in the Results or 8onlusions setion of your lab re$ort
(it isn9t reuired to
type
euations:showing work) 2lease note that you are answering a uestion by $utting
*+
in bold at the beginning of that sentene to #ake it easier to grade hanks (g
Q1
he slo$e of #y line of best fit is ,* found this by,)
F92 n your graph, draw in the 0best fit0 straight line and compute the slope of your line from
(re#e#ber units)
slope 3
∆
y
∆
x3 (8
/
- 8
9
*(x
/
- x
9
*F/2 Explain why this slope is your best experimental value for &, the spring constant for your spring: (%int2 hin& of how %oo&eDs Law compares to a linear e!uation.*F2 ?se your %oo&eDs law e!uation to find the force of the spring for some value you didnDt measure. hec& to see if this fits in with the datagraph.F2 (A* ?se your graph to predict what the extension of your spring would be if a == g mass were supported from the spring. (H* >hy would your graph (if it could be extrapolated far enough* ' give the correct distance your spring would extend under a load of I.= &g: >ould your spring support such an extension: F<2 %ow did the mirror-bac&ed scale of the %oo&e)s Law apparatus help to ma&e your measurements more accurate: (%int2 hin& about one of the first concepts in we learned about in physics*FI2 Explain why there is a negative sign in %oo&eDs Law.FJ2 alculate how much stored potential energy is in your spring under each weight load and fill in the last column of your data sheet with the values (in Koules, K3'
m* that you find.
Show work in results and disuss in onlusions
F2 8inally, list two practical or everyday applications of %oo&e)s Law. (an you thin& of where springs are used in your world:*
Force V. Position
y =
19.666
x + 0.067
slope = k, spring constantk = 19.67 N/m
R
2
=0.9984
0.0000.5001.0001.5002.0002.5003.0000.00000.05000.10000.1500
Distance from equilirium !meters
# p r i n g $ s f o r c e ! n e % t o n s
%oo&eDs Law ;ata able rialMass(in grams*Mass(in &ilograms*8orce(in newtons*7tretch(in centimeters*7tretch(in meters*ElasticotentialEnergy(in +oules*9/<IJ9=999/ example Excelgraph withline of best fitexample data
$,uation or ./orce0 1weight:
stretch x (m* force ('*
0.0093 0.2450.0225 0.4900.0415 0.9800.0588 1.2250.0710 1.470
$,uation or $3astic4ring $
2

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