Phy 201 Lab Manual

8/12/2019 Phy 201 Lab Manual

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Physics 201Lab Manual

PCC Rock CreekFellman


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Table of Contents

General Instructions for Lab Reports !

"ncertainty #nalysis an$ Propa%ation &

Micrometer Caliper Instructions'(

)ernier Caliper Instructions*

Lab 1 Con+ersions an$ Measurement'' ,

Lab 2 Position- )elocity an$ #cceleration' '' 10

Lab ! Pro.ectiles''''12

Lab & Tension an$ Friction'1!

Lab / Circular Motion an$ Centripetal Force'' 1&

Lab ( Conser+ation of ner%y''' 1*

Lab * Momentum an$ Collisons 1,

Lab , Center of Mass' 20

Lab #n%ular Momentum' 21

Make"p Lab Conser+ation of ner%y in Rollin% Motion'' 22

3ample Lab Report #'' 2!

3ample Lab Report 4'' 2*

2


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General Instructions for Lab Reports

For e+ery lab complete$- each person 5ill be responsible for han$in% in a labreport' These reports 5ill be $ue one 5eek from the $ay the e6ercise is complete$-

at the be%innin% of class' Reports may be type$ or han$5ritten as lon% as they areneat- easy to follo5- an$ contain the follo5in% elements7

Purpose 8hat you hope to accomplish throu%h the e6ercise- in your o5n 5or$s'

Procedure 4rief proce$ural notes in your o5n 5or$s' It is not acceptable tosimply 5rite 98e follo5e$ the instructions in the lab han$out': Instea$- your reportshoul$ outline the steps you follo5e$ in enou%h $etail so that it 5oul$ make sense toa person 5ho has ne+er seen the lab instructions'

Data #ll ori%inal $ata in a 5ell or%ani;e$ format'

Uncertainties The ran%e of possible +alues associate$ 5ith e+ery measurementyou take' uipment an$ 5ill also propa%ate throu%h calculations'


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"ncertainty #nalysis an$ Propa%ation

+ery measurement has a ran%e of uncertainty associate$ 5ith it' Thisuncertainty is usually a result of precision limitations of the instrument use$ to make

the measurement' #ny calculations $one usin% a measurement 5ill also ha+e a$e%ree of uncertainty' This is a measure of ho5 confi$ent you are in the result ofyour calculation' The propa%ation of the uncertainties throu%h +arious calculationshas to be carefully consi$ere$'

ne 5ay to procee$ 5ith the concept of uncertainty propa%ation is calle$ the98orst Case Calculation:- an$ is sho5n in the follo5in% t5o e6amples'

6ample D1

Len%th E !'10 cm '0/ cm 8i$th E !'/&0 cm '00! cm

#rea E L 8 E

8orst cases7

Lar%est M H 3mallest )7 Bensity E

3mallest M H Lar%est )7 Bensity E

Report final result as7 E 1'*2 %Hcm! '01 %Hcm!

&


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n the other han$- 5hen your $ata consists of a number of measurements to bea+era%e$ for a final result- the uncertainty can be reporte$ as the stan$ar$$e+iation'

6ample D!

?ou are measurin% the ran%e of a pro.ectile' The e6periment has been repeate$/ times- yiel$in% / $ifferent $istances7 !'&1 m- !'( m- !'!! m- !'/* m- an$ !'/0m'

First fin$ the a+era%e7 6 E 6i E

Jo5 fin$ the stan$ar$ $e+iation7

st' $e+' E


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.ernier Caliper

The )ernier Calipers 5e 5ill be usin% ha+e a smallest measurable +alue of 0'02mmor 0'002 cm'

"sin% the calipers to measure the si;e of ob.ects 5ill allo5 for a smaller uncertaintythan if 5e use$ a ruler' In a$$ition- you 5ill shortly see that the $esi%n of the

calipers is more appropriate than a ruler for makin% certain measurements'The $ia%ram belo5 sho5s ho5 to rea$ correct +alue on a )ernier caliper' #s sho5nthere is a main scale 5ith ma.or $i+isions marke$ in centimeters an$ sub$i+isions inmillimeters' Jotice that there are also marks


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Lab 1 Con2ersions 3 )easurement

The purpose of this e6ercise is to familiari;e the be%innin% physics stu$ent 5ith unitcon+ersions- measurement techni>ues- an$ measurin% $e+ices'

Part # Con+ersions

1' Measure the hei%ht of one of your lab partners in inches' Con+ert this +alue tometers- centimeters- millimeters- an$ kilometers'


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1*' 8hy must you enter the len%th of the ob.ect that passes throu%h thephoto%ateA 8hat other information $oes the photo%ate utili;e to calculate+elocityA

1,' Jo5 hook up the smart pulley' 4y spinnin% it 5ith your fin%er- obser+e ho5 itcan recor$ position an$Hor +elocity


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Lab - Position& .elocit' 3 4cceleration

Part # Position- )elocity- an$ #cceleration Graphs

8hen usin% the motion sensor- be%in by familiari;in% yourself 5ith the %raphin%

capabilities of the Bata 3tu$io soft5are' In particular- learn ho5 to $isplay only the$esire$ portion of your %raph on the optimal scale'

1' 3et up the motion sensor to %raph position' 8hen it is recor$in% position- it actsas the ori%in- 5ith all $istances in front of it bein% positi+e' 4efore you startrecor$in% any $ata- sketch four position +s' time %raphs that you 5oul$ e6pect toobtain for the follo5in% situations7

a= stan$in% stillb= 5alkin% at a constant slo5 spee$ a5ay from the $etectorc= 5alkin% at a constant fast spee$ a5ay from the $etector$= 5alkin% at a constant slo5 spee$ to5ar$ the $etector

2' Jo5 create position %raphs usin% the motion sensor for each of the four cases'Bo they match your pre$ictionsA If not- $escribe ho5 you 5oul$ mo+e to make a%raph that looks like your pre$iction'

!' Jo5 set up the motion sensor to %raph +elocity' 4efore you start recor$in% any$ata- sketch four +elocity +s' time %raphs that you 5oul$ e6pect to obtain for thepre2ioussituations-in addition to four ne" ones5

e= 5alkin% at an increasin% spee$ a5ay from the $etectorf= 5alkin% at an increasin% spee$ to5ar$ the $etector%= 5alkin% at a $ecreasin% spee$ a5ay from the $etectorh= 5alkin% at a $ecreasin% spee$ to5ar$ the $etector

&' Jo5 create +elocity %raphs usin% the motion sensor for each of the ei%ht cases'Bo they match your pre$ictionsA If not- $o you no5 un$erstan$ 5hyA

/' 3ketch constant acceleration %raphs for all ei%ht situations


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Part C #cceleration Bue To Gra+ity

In the pre+ious section- 5e use$ the accepte$ +alue for %ra+itational acceleration atthe earthKs surface' In this section- 5e 5ill preten$ that 5e $onKt kno5 its +alue- an$so 5e are %oin% to $o an e6periment to $etermine it'

' 3et up the photo%ate to measure +elocity' #s you $rop the picket fence throu%hthe photo%ate- the computer 5ill recor$ the +elocity of each soli$ panel as itpasses the sensor' To arri+e at a +alue for the acceleration- obtain a %raph of+elocity +s' time- an$ rea$ the a+era%e slope of the %raph'

10' Calculate the percenta%e error bet5een this +alue an$ the accepte$ +alue inyour te6tbook'

11' 8oul$ $roppin% a soli$ colore$ panel ha+e 5orke$A 8hat information fromthe e6periment $i$ the soft5are utili;e to create the %raphA

12' Gi+e a $etaile$ $escription of ho5 you 5oul$ calculate the acceleration byhan$ usin% this information'

11


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Lab + Pro6ectiles

The purpose of this lab is to e6plore an actual e6ample of t5o$imensional motion'C#"TIJ@@@@ These pro.ectiles can be $an%erous@ Make sure that the ran%e is clearbefore loa$in% the apparatus' #lso- please use only the plastic balls unlessspecifically aske$ to $o other5ise' There ha+e been complaints from our $o5nstairs

nei%hbors in the past'

1' "se a piece of paper an$ carbon paper to measure the a+era%e ran%e of theballistic launcher aime$ in the hori;ontal $irection' There are three $ifferentlaunch positions- make sure that you are usin% the first launch position


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Lab 0 7ension and 8riction

Part # Tension an$ 8ei%ht

1' First make sure the air track is le+el' "se the air track- smartpulley- an$computer interface to measure the acceleration of the air cart pulle$ by the

5ei%ht of three $ifferent masses7m E 20 %- !0 %- an$ &0 % '2' 3ketch a %enerali;e$ free bo$y $ia%ram of the han%in% mass' Remember7 free

bo$y $ia%rams are sketches of J bo$y an$ #LL forces actin% on T#T bo$y'!' #pply Je5tonKs 2n$ la5 to the han%in% mass' "se the resultin% e>uation to sol+e

for the tension in each of the three trials'&' Jo5 sketch a %enerali;e$ free bo$y $ia%ram of the cart' 8here is the normal

force comin% from in this caseA/' #pply Je5tonKs 2n$ la5 to the hori;ontal motion of the cart' "se the resultin%

e>uation to sol+e for the mass uations from steps ! an$ /' These 5ere results of applyin% Je5tonKs secon$la5 to the motion of both ob.ects' Combine these t5o e>uations an$ t5ounkno5ns to arri+e at a formula for the acceleration'

,' Jo5- +erify your ans5er by actually tryin% it out'

Part 4 Tilte$ #ir Track

' Tilt the air track usin% 5oo$ blocks so that the pulley en$ of the track is hi%hest'10'an% .ust enou%h mass from the strin% to hol$ the cart near the center of the

incline$ plane 5ithout motion uilibrium= 5hile the air is turne$ on' 8hat is

the sum of the forces on the cart at this pointA11'Gi+e the cart an initial +elocity by %ently pushin% it $o5n the track- an$ measureits acceleration usin% the computer interface' 4efore the brief push- 5hat 5asthe sum of the forces on the cartA #fter the brief push- 5hat is the sum of theforces on the cartA 8hat shoul$ the acceleration beA uestionre>uires no calculation'=

12'3ketch a free bo$y $ia%ram of the cart'

Part C Friction

1!'Place the friction block flat on your table- an$ slo5ly increase the tension in thestrin%


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Lab 9 Circular motion and Centripetal 8orce

8hen an ob.ect of mass m- attache$ to a strin% of len%th r- is rotate$ in a hori;ontalcircle- the centripetal force on the mass is %i+en by7

r

mv

F

2

=

To$ay 5e 5ill be +erifyin% this e>uation- an$ e6plorin% the relationships bet5een thecentripetal force- mass- +elocity an$ ra$ius of a rotatin% ob.ect'

1' First you must le+el the rotational apparatus' This e6periment re>uires theapparatus to be extremelyle+el' If the track is not le+el- the e6perimentalresults 5ill be 5il$ly $ifferent from the theoretical results' Carry out the follo5in%steps7 Purposely make the apparatus unbalance$ by attachin% the black !00% s>uare

mass onto the en$ of the aluminum track that is nearest the brass ob.ect 5ith! hooks'

#$.ust the le+elin% scre5 on one of the le%s of the base until the en$ of thetrack 5ith the s>uare mass is ali%ne$ o+er the le+elin% scre5 on the other le%of the base'


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&' Jo5 remo+e the s>uare black mass- an$ attach a clampon pulley to the en$ ofthe track nearer to the !hooke$ob.ect' #ttach a strin% to the open hook of the!hooke$ob.ect- an$ han% a kno5n mass o+er the pulley'


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1&' If the mass of the !hooke$ob.ect 5ere chan%e$ to half of its current +alue-5hat 5oul$ happen to the +alue of the spee$A Biscuss this 5ith your %roup- an$formulate a hypothesis' Jo5 carry out the e6periment by remo+in% the t5o si$emasses from the !hooke$ ob.ect- effecti+ely re$ucin% its mass by half' Make ane5 table- enter the ne5 +alues- an$ make sure that e>uation 1 is obeye$ oncea%ain'

1/'Repeat the e6periment usin% a $ifferent ra$ius'1('Repeat the e6periment usin% a $ifferent amount of centripetal force'1*'Biscuss the interrelationships bet5een centripetal force- mass- spee$ an$ ra$ius

in relation to the beha+ior of this particular system


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Lab : Conser2ation of Energ'

Part # Gra+itational Potential ner%y

1' Brop a rac>uetball from the hei%ht of one of the counters- an$ measure the

hei%ht of the bounce' Bo this at least fi+e times to %et an a+era%e of the bouncehei%ht'2' 8hat is the initial potential ener%y of the ballA 8hat is the potential ener%y at

the hei%ht of the first bounceA!' o5 much mechanical ener%y 5as lostA I$entify t5o 5ays in 5hich mechanical

ener%y coul$ ha+e been $issipate$'

Part 4 Conser+ation of ner%y in )ertical Motion

In this section- 5e 5ill be usin% the ballistic launcher a%ain' o5e+er- this time it5ill be set up to launch +ertically- an$ 5e 5ill be usin% superballs to cut $o5n on thenoise'

&' 3et up the photo%ate so that it measures the +elocity of the ball .ust as it lea+esthe launcher' "sin% the first launch position- recor$ the +ertical launch +elocityof the superball'


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Lab * )omentum and Collisions

Part # stimation an$ Calculation of Momentum

#n essential part of science is the in+esti%atorKs ability to estimate >uantities 5ithout

precise measurement' ne important aspect of this ability is use$ 5hen ane6perimenter $esi%ns an e6periment to in+esti%ate some physical phenomenon' Ine+ery$ay life this skill is also >uite +aluable- so 5e 5ill be practicin% the art ofestimation 5hile $eterminin% the momentum of +arious ob.ects that are in motion at$ifferent spee$s' There is no ri%ht or 5ron% ans5er- but the use of lo%ic an$reasonable assumptions in the estimation process is important for your result to beclose to the ans5er you 5oul$ obtain from an e6act measurement' For thefollo5in%- estimate both the mass an$ spee$- an$ report the resultin% momentum inscientific notation'a= a bu% cra5lin% across the si$e5alkb= a butterfly flyin% past youc= a bo5lin% ball rollin% $o5n the lane$= a fastball thro5n by a ma.or lea%ue pitchere= an a+era%e bicyclist at me$ium spee$f= a car at hi%h5ay spee$%= a *&* at cruisin% spee$h= a supertanker cruisin% from the Mi$$le ast full of oil

Part 4 Momentum an$ Oinetic ner%y in Collisions

The first ob.ecti+e of this section is to >ualitati+ely obser+e se+eral types ofcollisions' 8e 5ill then +erify >uantitati+ely the e>uations for +elocities resultin%from +arious types of collisions' 8e 5ill be consi$erin% both elastic an$ inelasticcollisions bet5een aircarts ha+in% +arious initial +elocities an$ masses'

1' ualitati+e bser+ation

For each of the follo5in% collisions bet5een rou%hly e>ual masses- pre$ict theoutcome by $ra5in% a $ia%ram of the carts both before an$ after the collision- usin%+ectors to illustrate their +elocities in each case' Then test your pre$ictions byobser+in% each actual collision' Make sure the air track is le+el'

lastic collisions mass 1 mass 2a= +elocities7 0b= +elocities7 c= +elocities7

Inelastic collisions$= +elocities7 0e= +elocities7 f= +elocities7

Jo5 repeat se+eral of the abo+e collisions- this time %i+in% the carts $ifferent massesby a$$in% 5ei%hts' Make sure you in$icate the mass $ifferences on your $ia%rams'BonKt for%et to $ra5 your pre$ictions first- then test your pre$ictions by obser+ation'

1,


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2' uantitati+e Measurement

?ou 5ill be settin% up each of the follo5in% collisions- a$$in% 5ei%ht to the air carts5hen necessary' For each one- use the photo%ates to measure the +elocities of each

cart both before an$ after the collision' Remember that the photo%ates $o notreco%ni;e $irection- so you must inclu$e the appropriate si%ns for +elocity' Then- foreach collision- use the appropriate e>uations from your te6t to calculate the e6pecte$final +elocities- an$ compare these to your e6perimental +alues'

a= # mo+in% aircart colli$es elastically 5ith a secon$ aircart that is initially at restan$ has t5ice as much mass'

b= # mo+in% aircart colli$es elastically 5ith a secon$ aircart that is initially at restan$ has half as much mass'

c= The same situation as part a=- but this time a completely inelastic collision'$= The same situation as part b=- but this time a completely inelastic collision'

For 5hich of these four collisions 5oul$ 5e e6pect kinetic ener%y to be conser+e$AFor 5hich of these four collisions 5oul$ 5e e6pect momentum to be conser+e$A

1


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Lab , Center of )ass

Part # Meter 3tick

1' Place the meter stick on the balancin% stan$ in or$er to locate its center of mass'Recor$ this +alue' Recall that the center of mass is that point of a ri%i$ bo$y

5here all of its mass can be consi$ere$ to act'2' 8ithout actually settin% it up- suppose that a /0 % mass 5ere suspen$e$ fromthe meter stick at the / cm mark- an$ calculate the ne5 center of mass of thesystem'

!' Jo5 test your calculation by placin% the stan$ at the center of mass position you.ust calculate$' Boes it balanceA If not- ho5 far from the true balance point 5asitA ?our results shoul$ $efinitely fall 5ithin the ran%e of e6perimentaluncertainty' If they $onKt- fin$ out 5hy an$ correct your setup'

&' #$$ an a$$itional han%in% 5ei%ht of your choice to the system at a position ofyour choice' Fin$ the ne5 center of mass by calculation an$ e6periment- an$compare them' nce a%ain- the results shoul$ a%ree'

/' "ntil this point- you ha+e most likely been calculatin% the center of mass bymeasurin% all $istances from the 0 cm en$ of the meter stick' Interestin%ly-$istances can be measure$ from any position on the meter stick' Try $oin% thecalculation from part &- but this time measurin% all $istances from some arbitraryposition on the meter stick'


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Lab ; 4ngular )omentum

1' The purpose of this first part is to e6perience the effects of a chan%in% moment ofinertia on an%ular +elocity' ol$ one 5ei%ht in each han$- an$ sit on a rotatin%stool' 3tart to spin 5ith your arms e6ten$e$- them brin% your arms in to5ar$your chest an$ notice the $ifference in your an%ular +elocity' Bescribe the effect-

an$ e6plain the reasonin% behin$ it'2' This part is fun e+eryone shoul$ try it@ 3ittin% on a rotatin% stool a%ain- takethe bicycle 5heel an$ %et it spinnin% as fast as you can- hol$in% it so that themomentum +ector is pointin% strai%ht up' The stool shoul$ stay still 5hen you liftyour feet up' Jo5- keepin% your feet up off the %roun$- turn the 5heel uickly as you can= so that the momentum +ector is pointin% strai%ht $o5n'6plain in 5or$s an$ pictures ue that is applie$ to the $isk by the force of the han%in%5ei%hts7 tor>ue E


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)ake


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Sample Lab Report A:

Lab 05 7ension and !e"ton=s -nd La"

Purpose7 The purpose of this lab is to stu$y the effect of tension in $ifferent

situations' First 5e 5ill consi$er the tension cause$ by a han%in% mass that isconnecte$ to another mass restin% on a flat surface' 3ince the t5o masses areconnecte$ usin% a strin% of ne%li%ible mass runnin% o+er a frictionless pulley- an$one of the masses is restin% on a frictionless surface- 5e 5ill be able to ne%lectfriction' Burin% the secon$ part- 5e 5ill a%ain ne%lect friction- but this time thehan%in% mass is connecte$ to a mass restin% on an inclinedplane' 8e 5ill attemptto fin$ the sum of the forces actin% on the cart 5hich is on the incline$ plane'

Procedure& Data& Calculations& Diagrams5

Part #7 Tension an$ 8ei%ht

1' "sin% the computer interface- 5e measure$ the acceleration of the air cartpulle$ by three $ifferent han%in% masses' The air cart represente$ in the$ra5in% by m1- is restin% on a frictionless surface an$ is connecte$ to thehan%in% mass m2- by means of a frictionless pulley' The pulley is alsointerface$ 5ith the computer an$ 5ill be use$ to measure the acceleration ofm1' 8e measure$ the acceleration for three $ifferent han%in% masses s-% '*/ 1'&&* 2'00(

m2

7

m-g


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!' Je5tonKs secon$ la5 tells us that the sum of the forces actin% on an ob.ect inany one $irection is e>ual to its mass multiplie$ by its acceleration in that$irection' 3ince both forces actin% on the han%in% block are alon% the +erticala6is- 5e can apply Je5tonKs secon$ la5 to it as follo5s7

$sum of forces do"n% ? $mass%$acceleration do"n%

$m-gs-% ? (1,A!

7$0Ag% ? $(A0A kg%B$;(,m>s-% @ $1(00*m>s-% ? (++0!7$:Ag% ? $(A:A kg%B$;(,m>s-% @ $-(AA:m>s-% ? (0:, !

&' Je6t 5e 5ill $ra5 a free bo$y $ia%ram for the air cart7

In this case- the cart is restin% on a cushion of air-Thus the air cushion is 5here the normal forceis comin% from' 3ince there is no motion in the+ertical $irection- it is safe for us to assume thatthe normal force- FJ- is e>ual to an$ in theopposite $irection as %ra+ity' Therefore theset5o forces cancel each other out' #t the same time-since there is no friction- any amount of force actin%in the hori;ontal $irection 5ill pro$uce an accelerationfor the cart'

/' #pplyin% Je5tonKs secon$ la5 to the cart tells us that the sum of the forcesactin% in the hori;ontal $irection 5ill be e>ual to the cartKs mass times thecartKs acceleration in the hori;ontal $irection' 3ince the only force actin% inthe hori;ontal $irection is the tension- T- of the strin%- 5e can set up arelationship bet5een T- m1an$ a7

$sum of the forces in the # direction% ? 7 ? $m1%$a%

m1? 7>a

Jo5 5e are rea$y to pre$ict a +alue for m1for each of our three trial cases7

#+era%in% these results for m1- 5e %et a +alue of -+A g'

2&

m1g

8!

m17

m- 7$m-% a$m-% m1?7>a

20 % '1,0 J '*/ mHs2 22( %

&0 % '!!& J 1'&&* mHs2 2!1 %

(0 % '&(, J 2'00( mHs2 2!! %


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(' 8e measure$ the actual mass of the cart on the $i%ital scale to be--1 g- so our a+era%e 5as only off by about &Q'

Part 47 Tilte$ #ir Track

*' Jo5 5e 5ill tilt the air track so that the pulley en$ of the track is hi%hest7

,' 3ince the cart is no lon%er on a le+el plane- %ra+ity 5ill no5 ha+e someeffect in pullin% the air cart to5ar$s the %roun$- or the lo5er en$ of theair track' Therefore- to balance the cart 5e must apply a force in theopposite $irection- 5hich can be accomplishe$ by han%in% a mass fromthe other en$' 8e ha$ to han% 1/ % on the strin% for the cart to remain ine>uilibrium' #t this point- since there is no motion in any $irection- thesum of the forces actin% on the cart is ;ero'

' Jo5 5e 5ill %i+e the cart an initial +elocity by %ently pushin% it $o5n thetrack' 3ince the sum of the forces is ;ero before the push- it must also be;ero after the push- an$ therefore the acceleration shoul$ be ;ero also'"sin% the computer interface- 5e measure$ an acceleration for the cart

of '00& mHs2

- 5hich is +ery close to ;ero' 8e 5oul$ also e6pect the cartto ha+e ;ero acceleration


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Conclusion5

Lookin% at the t5o separate parts of this lab- I fin$ a common link7 Je5tonKs secon$la5 of motion- 5hich tells us that the force actin% on an ob.ect in any $irection ise>ual to the ob.ectKs mass times the ob.ectKs acceleration in that $irection' 3ure-it soun$s pretty strai%htfor5ar$- but as this lab has sho5n- 5e run into $ifferent

kin$s of obstacles 5hen applyin% this la5' 3o 5hat I ha+e learne$ by $oin% thislab is that in applyin% Je5tonKs secon$ la5- 5e must also consi$er the an%le at5hich the ob.ect is mo+in%- as 5ell as any kin$s of frictional forces that may beresistin% the ob.ectKs motion- not to mention all the uncertainties in+ol+e$ in themotion of e+ery$ay ob.ects that 5e ha+e not e+en consi$ere$ in this lab'

2(


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Sample Lab Report B:

Introduction to Circuits

Purpose5 To e6plore the relationship bet5een +olta%e- resistance an$ current in a

circuit'

Procedures 3 Comments5

1' "sin% a multimeter- measure an$ recor$ the +olta%e of t5o $ifferent batteries'

4attery 1 4attery 2 4attery Pak


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& !!S102 / !!'2S102 0'(0/ 1/S10& 10 1/'2S10& 1'!2

All of the measured values fall within the range given by the color

bands.!' "sin% t5o resistors of the same or$er or ma%nitu$e ui+alent Resistance E R1 R2

Resistors Measure$ Resistance- Calculate$ Resistance- ! & ('2!S10! ('22S10!2 / !',!S10/ !',&S10/

& / 1'//S10/ 1'//S10/

&' "sin% t5o resistors of the same or$er or ma%nitu$e ui+alent Resistance E 1 H R1 1 H R2

Resistors Measure$ Resistance- Calculate$ Resistance- ! & 1'//S10! 1'//S10!2 / '1,S10& '1,S10&& / !'2/S10! !'2/S10!

/' Rules for a$$in% >ui+alent Resistances an$ Capacitances in 3eries an$ ParallelCircuits7

3eries Parallel

Resistance7 RER1R2R! 1HRE1HR11HR21HR!

Capacitance71HCE1HC11HC21HC! CEC1C2C!

6. A series circuit acts like a one-lane highway and therefore all ofthe traffic must pass along the same path, which resists and slowsdown flow.

2,


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A parallel circuit acts like a freeway and therefore the trafficcan always take the path of least resistance, which allows itto flow freely.

7. Construct a circuit consisting of a battery and a resistor andmeasure the current.

Resistor 3

oltage, Resistance, Current, A

!easured 3."" #.$"%&"'3 &."3%&"'-3

Calculated ( R ) * &."3%&"'-3

Measured and calculated answers agree.

+. Construct a circuit consisting of a battery and two resistors, withroughly the same order of magnitude, in series and measure thecurrent.

Resistors 3

!easuredAcross

attery Resistor 3 Resistor

Current, A .+"%&"'- .+"%&"'- .+"%&"'-

oltage, 3."" &." &.6"

2


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In series the current must be the same through all elements.The voltage measured across resistor 3 and 4 equaled 1.40 V and1.0 V res!ectively. The sum of these two voltages equals 3.00 V"which is the same as the voltage of the battery. In series the sumof the voltages through all of the elements must equal the powersource.

$. Construct a circuit consisting of a battery and the two resistorsused in procedure + in parallel and measure the current through thebattery, the first resistor and the second resistor. /hen measure the0oltage across each resistor.

Resistors 3

!easuredAcross

attery Resistor & Resistor #

Current, A &.$3%&"'-3 &."3%&"'-3 $.""%&"'-

oltage, #.$$ #.$$ #.$$

In parallel the voltage must be the same through all elements .The current measured across resistor 3 and 4 equaled 1.03#10$%3 Aand &.00#10$%4 A res!ectively. The sum of these two currents equals1.&3#10$%3 A" which is the same as the current through the battery.In parallel the sum of the currents through all of the elementsmust equal to the current through the power source.

Conclusion5The resistance of a resistor can be $etermine$ easily by $ecipherin% its

color ban$s' These $etermine$ resistances- althou%h not perfect- are >uite accurate'"sin% the multimeter to measure +olta%e- resistance an$ current is strai%ht for5ar$-but one must take special consi$eration 5hen measurin% current not to $ama%e tometer' For series circuits- the e>ui+alent resistance is e>ual to the sum of theresistances of the resistors an$ the reciprocal of the e>ui+alent capacitance is e>ualto the sums of the reciprocals of the capacitances of the capacitors' #n$ for parallelcircuits .ust the re+erse is true' The reciprocal of the e>ui+alent resistance is e>ualto the sum of the reciprocals of the resistances of the resistors an$ the e>ui+alentcapacitance is e>ual to the sum of the capacitances of the capcitors' In a series

!0


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circuit the current is the same throu%h all of the elements in the circuit an$ the sumof the +olta%es throu%h the elements in the circuit are e>ual to the +olta%e of thepo5er source'#n$ for parallel circuits- a%ain .ust the re+erse is true' The +olta%e is the samethrou%h all of the elements in a circuit an$ the sum of the currents throu%h theelements in the circuit are e>ual to the current throu%h the po5er source' 8hene+er

possible all circuit lab 5ork shoul$ be $one on the brea$boar$' It is easier to han$lean$ is a much more efficient 5ay to $o e6perimentation'

!1

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Phy 201 Lab Manual

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