ISLE%labs%for%Physics%9%
The$inspiration$for$these$labs$comes$from$the$PAER$group$at$Rutgers$$
!
General!Information:!!
$
There$are$3$types$of$Investigative$Science$Learning$Environment$(ISLE)$labs:$observation$experiments,$
testing$experiments,$and$application$experiments.$$$
$$
Observation$experiments$are$intended$for$students$to$learn$skills$such$as$changing$one$variable$at$a$time,$
clearly$recording$and$representing$observations,$and$making$accurate$observations$without$mixing$them$
with$explanations.$$This$is$the$first$step$of$the$experimental$cycle,$and$allows$you$to$observe$phenomena,$
look$for$patterns$in$data,$and$start$to$devise$explanations$(once$observations$are$carefully$completed).$
$
The$next$step,$once$explanations$have$been$devised,$is$to$do$testing$experiments,$which$is$an$independent$
test$students$design$that$will$test$a$hypothesis$based&on$a$specific$explanation$or$rule.$$This$helps$you$
practice$the$skill$of$making$predictions$about$the$outcome$of$an$experiment$based$on$an$
explanation/rule/relationship.$$For$a$testing$experiment,$you$can’t$just$do$the$experiment$and$record$what$
happens$–$they$must$have$a$predicted$outcome$based$on$some$explanation$–$and$if$the$outcome$of$the$
experiment$agrees$with$the$prediction$it$gives$confidence$that$the$explanation$may$be$correct,$but$if$it$
disagrees,$then$you$know$the$explanation$is$incorrect.$$In$order$to$make$this$judgment,$you$also$need$to$
apply$basic$uncertainty$calculations.$$$(A$guide$for$understanding$uncertainty$is$included$in$this$packet.)$
$
The$third$type$of$experiment$is$the$application$experiment,$where$you$apply$some$
explanation/rule/relationship$that$you$have$tested$enough$that$you$think$it$is$‘good’,$and$you$apply$it$to$
understand$a$new$situation.$$Some$application$experiments$require$that$you$determine$some$unknown$
quantity$multiple$ways$–$in$order$to$determine$if$the$methods$are$consistent,$it$is$necessary$to$apply$basic$
uncertainty$analysis.$
$
By$performing$this$sequence$of$experiments,$it$is$possible$to$explore$and$devise$a$physics$relationship,$test$
it,$and$when$you$are$convinced$it$is$good,$apply$it$to$understand$a$new$situation$–$providing$you$with$a$
complete$understanding$of$the$basic$physics$relationships$(equations).$$By$designing$your$own$
experiments,$it$gives$you$creative$control,$and$assures$that$you$understand$the$steps$that$you$perform,$as$
they$are$done$by$your$conscious$choice,$and$not$by$following$instructions$or$‘playing$around.’$
$
Lab!write2ups:!!
$
$There$is$one$lab$writePup$per$group,$each$group$member$must$put$their$name$at$the$top$of$the$writePup$in$
order$to$obtain$credit.$$Since$the$ISLE$labs$are$labs$you$design$yourself,$and$are$intended$to$help$you$learn$
specific$skills$such$as$justifying$your$conclusions,$comparing$results,$and$understanding$how$uncertainty$
comes$into$play,$it$is$important$that$you$explain$your$work$carefully$in$the$form$of$a$lab$writePup.$$The$lab$
writePup$is$done$in&the&lab,$there$is$nothing$for$you$to$do$after$the$lab$period.$$The$writePup$is$not$formal,$
but$does$need$to$be$clear.$$Your$lab$may$have$specific$questions$for$you$to$answer,$or$specific$statements$of$
tasks$to$complete,$in$which$case$you$need$to$answer$and$document$those$things$in$your$writePup.$$The$lab$
will$include$a$general$set$of$bullet$points$that$always$need$to$be$addressed$within$your$writePup.$$Those$
general$bullet$points$are$specific$to$the$type$of$experiment:$observation,$testing,$or$application.$Abide$by$
the$bullet$guidelines$as$closely$as$possible,$and$by$all$means$read$ahead$and/or$make$preliminary$tests$of$
the$equipment$if$it$helps$to$abide$by$them.$However,$if$something$you$do$or$observe$seems$more$
appropriately$addressed$in$a$different$bullet,$it$is$okay.$Just$don't$skip$anything.$
$
Do$not$make$the$mistake$of$writing$too$much$in$your$lab$reports.$$Your$information$does$not$need$to$be$
presented$in$paragraph$form,$or$often,$even$in$complete$sentences.$$You$can$use$equations$instead$of$trying$
to$write$the$math$out$in$words.$$Your$reports$should$have$a$few$sentences$or$bullet$points,$equations$
and/or$diagrams$where$appropriate.$$You$should$address$the$required$points$succinctly$and$clearly.$$Your$
reports$should$not$be$lengthy$or$wordy.$$This$is$good$practice$in$science$writing$and$will$also$save$both$you$
and$the$grader$valuable$time.$$
!
Grading:!!
$
If$you$do$not$pass$the$lab,$you$do$not$pass$the$course.$$Your$TA$will$grade$your$lab$writePup$based$on$some$
subset$of$the$items$you$are$asked$to$include.$$Each$item$will$be$graded$out$of$a$possible$of$3$points.$$0$points$
means$the$item$is$not$included$in$the$report.$$1$point$means$the$item$is$included,$but$incompletely,$or$
incorrectly.$$2$points$means$the$item$is$included,$but$with$some$small$mistake,$or$it$isn’t$completely$
explained.$$3$points$means$it$is$correct$and$complete.$$Roughly$5P9$items$will$be$chosen$for$grading$each$
week.$There$is$a$set$of$“rubrics”$for$you$and$for$the$TA$to$use$to$evaluate$your$work.$$You$are$strongly$
encouraged$to$check$your$writePup$with$the$rubrics$while$you$are$doing$the$lab.$$They$are$not$just$used$for$
grading,$but$are$also$intended$to$help$you$fully$understand$the$skills$you$are$to$develop$and$demonstrate,$
and$to$help$you$assess$and$improve$the$quality$of$your$work.$You$TA$will$further$discuss$grading$policies.$
!
Conclusion:!!
$
Lab$is$not$for$testing$your$knowledge,$but$is$a$place$for$developing$it.$$Take$advantage$of$the$time$to$explore$
the$physics$relationships$to$your$own$satisfaction,$make$sure$your$work$makes$sense$to$you,$and$use$your$
TA$as$a$resource$to$make$sure$you$leave$the$lab$with$a$good$understanding$of$the$material.$
$
EXPERIMENTAL UNCERTAINTIES
!"# $%&'()*+# ,-*./(/&# )*.# 01# 21*'-314# 15*)/+&6# 7.1# )*.# ".+&# 8."9# (/'# :*+-1# 9(/%# *# )13/*(.# 3*.;1# "<#
-.)13/*(./&6# =%('# <*)/# )*.# 01# 15$31''14# (.# /%1# '/*.4*34# <"32# X ± !X6# =%('# 15$31''1'# /%1# 15$13(21./13>'#
?-4;21./#/%*/#/%1#@/3-1@#:*+-1#"<#X#+(1'#01/911.#X - !X#*.4#X + !X6##
Uncertainties of measurements
1. Instrumental uncertainties
A:13&#21*'-3(.;#(.'/3-21./#%*'#*.#(.%131./#-.)13/*(./&#/%*/#('#41/132(.14#0&#/%1#precision of the instrument.
B'-*++&#/%('#:*+-1#('#/*81.#*'#*#%*+<#"<#/%1#'2*++1'/#(.)3121./#"<#/%1#(.'/3-21./#')*+16#=%*/#('#C6D#2(++(21/13#('#
$31)('(".#"<#*#3-+13E#C6D#'1)#('#$31)('(".#"<#*#9*/)%1'#1/)6#
F.'/3-21./*+# -.)13/*(./(1'# *31# /%1# 1*'(1'/# ".1# /"# 1'/(2*/1E# 0-/#
-.<"3/-.*/1+&#/%1&#*31#."/#/%1#".+&#'"-3)1#"<#/%1#-.)13/*(./&#(.#&"-3#
21*'-314#:*+-16#
G"-#2-'/#01#*#:13&#'8(++<-+#*.4#+-)8&#15$13(21./*+('/#/"#;1/#3(4#"<<#*++#
"/%13# '"-3)1'# *.4# /"# %*:1# /%1# 21*'-3121./# -.)13/*(./&# 1,-*+# /"# /%1#
(.'/3-21./*+#".16#
#
2. Random uncertainties#
H"21/(21'#9%1.#&"-#21*'-31#/%1#'*21#,-*./(/&#&"-#)*.#;1/#4(<<131./#31'-+/'#1*)%#/(21#&"-#21*'-31#(/6#=%*/#
%*$$1.'# 01)*-'1# 4(<<131./# (.)"./3"++*0+1# <*)/"3'# *<<1)/# &"-3# 31'-+/'# 3*.4"2+&6# =%('# /&$1# "<# -.)13/*(./&E#
random uncertainty,#)*.#01#1'/(2*/14#".+&#0&#31$1*/(.;#/%1#'*21#21*'-3121./#'1:13*+#/(21'6#I"3#15*2$+1#(<#
&"-#21*'-31#/%1#4('/*.)1#*/#9%()%#)*..".0*++#%(/'#/%1#;3"-.4E#&"-#)"-+4#;1/#4(<<131./#4('/*.)1'# 1:13&# /(21#
&"-#31$1*/#/%1#'*21#15$13(21./6#I"3#15*2$+1E#'*&#&"-#/""8#/%311#21*'-3121./'#*.4#"0/*(.14#DC#2E#DJ#2E#*.4#
KL# 21/13'6# ="# 1'/(2*/1# /%1# absolute value of the random uncertainty &"-# <(3'/# <(.4# /%1# *:13*;1# "<# &"-3#
21*'-3121./'M#
X "#$DC2#N#!"DJ2#N#!"KL2O#P#Q#"#DC#26#
G"-#/%1.#estimate approximately %"9#2-)%#/%1#:*+-1'#*31#'$31*4#9(/%#31'$1)/#/"#/%('#*:13*;1#R#(.#/%('#)*'1#
91#%*:1#*#'$31*4#"<#*0"-/#!X#S#J#26#=%*/#('E#"-3#21*'-3121./#"<#/%1#4('/*.)1#9*'##
X S#DC#2#%#J#26#
T#U
V"'/#)*..".0*++'#9(++#;1/#(./"#/%1#
3*.;1#<3"2#X-!X#/"#X+!X.#
C#
U
#
=%-'#2-+/($+1#/3(*+'#*++"9#&"-#/"#<(.4#/%1#*:13*;1#:*+-1#*.4#/"#1'/(2*/1#/%1#-.)13/*(./&#3*.;16#
#
J
3. Effect of assumptions
!""#$%&'()"* ')+,-,)&* ')* .(#-* $(/,0* $1.* 10"(* 2()&-'3#&,* &(* &+,* #)2,-&1')&.* (4* &+,* /,"'-,/* 5#1)&'&.6* 7(-*
,81$%0,9*.(#*:'"+*&(*4')/*&+,*"%,,/*(4*&+,*3100*$(;')<*()*&+,*40((-6*=(#*1-,*1""#$')<*&+1&*1*3100*$(;,"*10()<*
1* "&-1'<+&* 0'),* :+'0,* ')* 412&* &+,* "#-412,* (4* &+,* 40((-*')* 3#$%.* 1)/* &+,* 3#$%"* 2()&-'3#&,* "'<)'4'21)&0.* &(* &+,*
/'"&1)2,*&+1&*&+,*3100*2(;,-"*1)/*&+#"*/,2-,1",*&+,*"%,,/*&+1&*&+1&*.(#*2102#01&,6*>,%,1&')<*&+,*$,1"#-,$,)&*
:'00*)(&*0,&*.(#*<,&*-'/*(44*&+,*3#$%'),""*(4*&+,*40((-*1)/*:'00*2()&-'3#&,*&(*&+,*#)2,-&1')&.*:'&+*:+'2+*.(#*
:'00*/,&,-$'),*&+,*;10#,*(4*&+,*"%,,/6*?+'"*&.%,*(4*#)2,-&1')&',"*'"*)(&*"(*,1".*&(*-,2(<)'@,*1)/*&(*,;10#1&,6**
7'-"&*(4*1009*.(#*+1;,*&(*/,&,-$'),*&+,*"'<)*(4*&+,*,44,2&9*'6,6*:+,&+,-*&+,*1""#$%&'()*')2-,1","*&+,*;10#,*(4*&+,*
5#1)&'&.9*/,2-,1","*'&*(-*144,2&"*'&*-1)/($0.6*?+,)*&-.*&(*,"&'$1&,*&+,*"'@,*(4*&+,*,44,2&6**
7(-* ,81$%0,9* .(#* $,1"#-,* &+,* /'1$,&,-* (4* &+,* 31",3100*
1""#$')<*'&*'"*%,-4,2&*"%+,-,6*A(:,;,-9*&+,*-,10*"'@,*(4*&+,*
3100* $1.* /'44,-* 3.* BCD$$* '4* .(#* $,1"#-,* ')* /'44,-,)&*
/'$,)"'()"6* ?+'"* /'44,-,)2,* :'00* /,&,-$'),* &+,* #)2,-&1')&.*
(4*.(#-*$,1"#-,$,)&6*
*
E&* '"* /'44'2#0&* &(* <';,* "&-'2&* -#0,"* 1)/* ')"&-#2&'()"* ()* +(:* &(* ,"&'$1&,* #)2,-&1')&',"* ')* <,),-106* F12+* 21",* '"*
#)'5#,*1)/*-,5#'-,"*&+(#<+&4#0*1%%-(12+6*G,*')<,)'(#"*1)/*-,1"()130,6**
Comparison uncertainties
E4* .(#* 1-,* 2($%1-')<* &+,* #)2,-&1')&',"* ')* &+,* ;10#,"* (4* &:(* 5#1)&'&',"* &+,)* 3.* 1)10.@')<* &+,* 13"(0#&,*
#)2,-&1')&.* -1)<,"* .(#* 21))(&* &,00* :+'2+* (4* &+,* $,1"#-,$,)&"* '"* $(-,* 122#-1&,* 3,21#",* &+,* #)'&"* (4* &+,*
$,1"#-,/*5#1)&'&',"*1-,*/'44,-,)&6*A(:*21)*:,*/,2'/,*&+,)*:+'2+*5#1)&'&.*+1"*1*01-<,-*#)2,-&1')&.H*A,-,*:,*
),,/*&(*2($%1-,*relative uncertainties9*&+,*-1&'(*(4*&+,*absolute*#)2,-&1')&.*1)/*&+,*5#1)&'&.*'&",04*!X / X6*
?+'"*$1.*3,*,8%-,"",/*1"*1*4-12&'()*(-*1"*1*%,-2,)&1<,*3.*$#0&'%0.')<*&+,*-1&'(*3.*BIIJ6***
?+,*"'@,"*(4*&+,*2'-20,"*1&*&+,*%'2&#-,*1-,*/,&,-$'),/*
:'&+*/'44,-,)&*122#-12.6**
?+,* 13"(0#&,* "'@,* (4* &+,* "(4&* ,/<,* KL* #)'&"M* '"* &+,*
"1$,* 4(-* 3(&+* 30#,* 2'-20,"6* A(:,;,-* &+,* 01-<,* 30#,*
2'-20,* KLI* #)'&"M* 0((N"* "+1-%,-* &+1)* &+,* "$100* (),*
KOI#)'&"M6* ?+1&* +1%%,)"* 3,21#",* :,* 2($%1-,*
relative #)2,-&1')&',"9* :+'2+* 1-,* BIJ* 4(-* &+,* 01-<,*
2'-20,*1)/*OIJ*4(-*&+,*"$100*(),6*
Note: Common sense and good judgment must be used in representing the uncertainties*when stating a result. Consider
a temperature measurement with a thermometer known to be reliable to ± 0.5 degree Celsius. Would it make sense to
say that this causes a 0.5% uncertainty in measuring the boiling point of water (100 degrees) but a whopping 10% in
the measurement of cold water at a temperature of 5 degrees? Of course not! (And what if the temperatures were
expressed in degrees Kelvin? That would seem to reduce the relative uncertainty to insignificance!). However in most
calorimetry tasks value of interest is not temperature itself but only the change of the temperature or the temperature
difference.
*
D
Reducing uncertainties
!"#$#%&'()#$*+,"$,"#$-+.-)#/$/"0*/$&$*&1$,0$.#23-#$,"#$.#)&,+4#$35-#.,&+5,1$+5$103.$'#&/3.#'#5,6$!"#$/&'#$
&7/0)3,#$35-#.,&+5,1$1+#)2/$,"#$/'&))#.$.#)&,+4#$35-#.,&+5,1$+8$,"#$'#&/3.#2$4&)3#$+/$)&.9#.6$
:3((0/#$103$"&4#$&$707$&,,&-"#2$,0$&$/(.+59$&52$*&5,$,0$'#&/3.#$,+'#$80.$+,$,0$0/-+))&,#$3($&52$20*5;$7&-<$,0$
+,/$/,&.,+59$(0/+,+056$=8$103$&.#$3/+59$&$*&,-"$,0$'#&/3.#$ /0'#$,+'#$+5,#.4&);$,"#$&7/0)3,#$35-#.,&+5,1$08$,"#$
'#&/3.#'#5,$*+))$7#$>6?$/6$=8$103$50*$'#&/3.#$,"#$,+'#$5##2#2$80.$,"#$707$,0$90$3($&52$20*5$05#;$103$9#,$?$
/6$!"+/$'#&5/$,"&,$103$"&4#$&$.#)&,+4#$35-#.,&+5,1$08$@>A$+5$,"#$,+'#$'#&/3.#'#5,6$B"&,$+8$103$'#&/3.#2$,"#$
,+'#$ 80.$ ?$ 0/-+))&,+05/$ +5/,#&2C$ :&1$ 103$ '#&/3.#$ ,"#$ ,+'#$ 80.$ ?$ 0/-+))&,+05/$ &52$ 9#,$ D?$ /6$ !"#$ +5/,.3'#5,&)$
35-#.,&+5,1$ +/$ still >6?$ /E$ !"#$ relative uncertainty +5$ 103.$ '#&/3.#'#5,$ 08$ ,"#$ ,+'#$ +5,#.4&)$ +/$ 50*F$ ,+'#$
.#)&,+4#$35-#.,&+5,1$G$H>6?$/ID?$/J$K@>>A$!"DA$
By measuring the time for a longer time period, you have managed to reduce the uncertainty in your time
measurement by a factor of 5!
$
L8$ -03./#$ 103$ /"03)2$ 50,$ 80.9#,$ &703,$ ,"#$ 074+03/$ *&1$ 08$ .#23-+59$ .#)&,+4#$ 35-#.,&+5,+#/$ 71$ '+5+'+M+59$
&7/0)3,#$ 35-#.,&+5,1$ *+,"$ 7#,,#.$ 2#/+95;$ 2#-.#&/+59$ #88#-,$ 08$ &//3'(,+05/$ 0.$ +5-.#&/+59$ ,"#$ &--3.&-1$ 08$
+5/,.3'#5,$+8$+,$+/$(0//+7)#6$
Uncertainty in calculated value
=,$ +/$ +'(0.,&5,$ ,0$ #/,+'&,#$ 2&,&$ 35-#.,&+5,+#/$ 7#-&3/#$ 35-#.,&+5,+#/$ (.0(&9&,#$ ,".039"$ ,"#$ -&)-3)&,+05/$ ,0$
(.023-#$35-#.,&+5,1$+5$.#/3),/6$
N05/+2#.$ 50*$ ,"#$ 80))0*+59$ #%&'()#6$ :3((0/#$ 103$ <50*$ ,"#$ &4#.&9#$ '&//$ 08$ 05#$ &(()#$ m *+," ,"#$
35-#.,&+5,1 #m. =8$103$*&5,$50*$,0$-&)-3)&,#$,"#$'&//$08$,"#$7&/<#,$08$,"#$@>>$&(()#/$103$*+))$9#,$,"#$4&)3#$M
± #M =$ @>>m ± @>>#m. =,$ '#&5/$ ,"&,$ relative$ 35-#.,&+5,1$ 08$ -&)-3)&,#2$ 4&)3#$ M$ .#'&+5/$ ,"#$ /&'#$ &/$ ,"#$
.#)&,+4#$35-#.,&+5,1$08$,"#$/+59)#$'#&/3.#2$(&.&'#,#.$m
#M / M$G$#m / m6
=8$103$"&4#$'0.#$,"&5$05#$'#&/3.#2$(&.&'#,#.;$#/,+'&,+59$35-#.,&+5,1$08$,"#$.#/3),$'&1$7#$'0.#$-0'()+-&,#26$
O0*#4#.;$ +8$ 05#$ 08$ 103.$ /03.-#/$ 08$ 35-#.,&+5,1$ +/$ much larger$ ,"&5$ ,"#$ 0,"#./$ H-0'(&.+59$ relative$
35-#.,&+5,+#/EJ$,"#5$103$-&5$5#9)#-,$0,"#.$/03.-#/$&52$3/#$,"#$weakest link rule.
$
Weakest link rule
!"#$(#.-#5,$35-#.,&+5,1$+5$,"#$-&)-3)&,#2$4&)3#$08$/0'#$P3&5,+,1$+/$&,$)#&/,$&/$9.#&,$&/$,"#$9.#&,#/,$(#.-#5,&9#$
35-#.,&+5,1$08$,"#$4&)3#/$3/#2$,0$'&<#$-&)-3)&,+056$
!"3/$,0$#/,+'&,#$35-#.,&+5,1$+5$103$-&)-3)&,#2$4&)3#$103$"&4#$,0F$$
@6 Q/,+'&,#$,"#$absolute uncertainty +5$#&-"$'#&/3.#2$P3&5,+,1$3/#2$,0$8+52$-&)-3)&,#2$P3&5,+,16$
D6 N&)-3)&,#$,"#$relative percentage uncertainty +5$#&-"$'#&/3.#2$P3&5,+,16$$
R6 S+-<$03,$,"#$)&.9#/,$(#.-#5,&9#$35-#.,&+5,16$!"+/$*+))$7#$,"#$(#.-#5,$35-#.,&+5,1$+5$103.$-&)-3)&,#2$
P3&5,+,16$
Comparable uncertainties
=5$-&/#$103$"&4#$'#&/3.#2$4&)3#/$*+,"$-0'(&.&7)#$35-#.,&+5,+#/$,"#$.3)#/$&.#$'0.#$-0'()+-&,#2F$,"#1$2#(#52$
05$,"#$,1(#$08$,"#$'&,"#'&,+-&)$.#)&,+05/"+($103$3/#$80.$-&)-3)&,+056$=5$,"#$'0/,$8.#P3#5,$-&/#$08$'3),+()1+59$
,*0$ 4&)3#/$ ,"#+.$ .#)&,+4#$ 35-#.,&+5,+#/$ &226$ L5#$ 08$ ,"#$ -05/#P3#5-#/$ 08$ ,"+/$ .3)#$ +/$ ,"&,$ ,"#$ .&+/+59$ ,0$ ,"#$
/#-052$ (0*#.$ 2037)#/$ ,"#$ .#)&,+4#$ 35-#.,&+5,1$ &52$ ,"#$ .&+/+59$ ,0$ ,"#$ ,"+.2$ (0*#.$ ,.+()#/$ +,.$ !"3/;$ +5$ ,"#$
$
R
!"#$%&!'#()*!+',-!'.!&#,/*!'012!.,#/1,3'/1',-!'2#&20&#,!4'*)&0$!')5',-!'(#6!(#&&'7/&&'(!',-.!!',/$!6'&#.8!.',-!1'
,-!'.!&#,/*!'012!.,#/1,3'/1',-!'$!#60.!4'.#4/069'
Why do you need to know uncertainty?
:6',-!'$!#60.!4'*#&0!'/1'#8.!!$!1,'7/,-',-!'%.!4/2,/)1;'<)',-!'4#,#'5/,',-!'%-36/2#&'$)4!&;'=.!',7)'$!#60.!4'
*#&0!6' ,-!' 6#$!;' >)0' 2#11),' #167!.' ,-!6!' ?0!6,/)16' 7/,-)0,' 2)16/4!./18' ,-!' 012!.,#/1,/!6' )5' 3)0.'
$!#60.!$!1,69':14!!4+'-)7'2#1'3)0'2)$%#.!',7)'*#&0!6'/5',-!'4/55!.!12!'(!,7!!1',-!$'/6'6$#&&!.',-#1',-!'
012!.,#/1,3'/1',-!/.'$!#60.!$!1,;'''
C-/2-' (012-' )5' 8.#66' /6' -/8-!.;' >)0' 2#11),' ,!&&'
,-/6' (!2#06!' ,-!/.' -!/8-,6' #.!' 4!,!.$/1!4' 7/,-' ,-!'
012!.,#/1,3'&#.8!.',-#1',-!'-!/8-,'4/55!.!12!9':5'3)0'
2#11),',!&&'7-/2-')5',7)'*#&0!6'#.!'&#.8!.'3)0'2#1'
2&#/$',-!$',-!'6#$!9''
'
@-06',)'$#A!'B048$!1,'#()0,',7)'*#&0!6'X'#14'Y'3)0'-#*!',)'5/14',-!'.#18!6'7-!.!',-!6!'*#&0!6'&/!9':5',-!'
.#18!6' X ± !X #14 Y ± !Y' )*!.&#%' 3)0' 2#1' 2&#/$' ,-!' *#&0!6' X' #14' Y' ,-!' 6#$!' 7/,-/1' 3)0.' !"%!./$!1,#&'
012!.,#/1,39'
Summary
C-!1'3)0'#.!'4)/18'#'&#('#14'$!#60./18'6)$!'?0#1,/,/!6',)'4!,!.$/1!'#1'01A1)71'?0#1,/,3D'
" <!2/4!'7-/2-'5#2,).6'#55!2,'3)0.'.!60&,'$)6,9'
" C-!.!*!.'%)66/(&!',.3',)'.!402!'!55!2,6')5',-!6!'5#2,).69''
" C-!.!*!.'%)66/(&!+',.3',)'.!402!'012!.,#/1,/!6'(3'$!#60./18'&)18!.'4/6,#12!6').',/$!6'!,29'
" <!2/4!'7-#,',-!'#(6)&0,!'012!.,#/1,/!6')5'!#2-'$!#60.!$!1,'#.!9'
" @-!1'5/14',-!'.!&#,/*!'012!.,#/1,/!6')5'!#2-'$!#60.!$!1,9'
" :5' )1!' 012!.,#/1,3' /6' $02-' &#.8!.' ,-#1' ,-!' ),-!.6' 3)0' 2#1' /81).!' #&&' ),-!.' 6)0.2!6' #14' 06!' ,-/6'
012!.,#/1,3',)'7./,!',-!'*#&0!')5',-!'012!.,#/1,3')5',-!'?0#1,/,3',-#,'3)0'#.!'2#&20&#,/189'
" E/14',-!'.#18!'7-!.!'3)0.'.!60&,'&/!69'F#A!'#'B048$!1,'#()0,'3)0.'.!60&,6',#A/18'/1,)',-!'#22)01,',-!'
012!.,#/1,39'
'
'
G
Ability to design and conduct an observational experiment
Scientific Ability
Missing
Inadequate
Needs some improvement
The phenomenon to be investigated is described but there are
minor omissions or vague details.
The experiment investigates the
phenomenon and it is likely the
data will contain interesting
patterns, but due to the nature of
the design some features of the
patterns will not be observable.
The chosen measurements will
produce data that can be used to
achieve the goals of the experiment. However, independent and
dependent variables are not
clearly distinguished.
All chosen measurements can be
made, but the details of how it is
done are vague or incomplete.
A description exists, but it is
mixed up with explanations or
other elements of the experiment.
A labeled picture is present. Or
some observations are mentioned
in the context of prior knowledge.
Some shortcomings are identified
and some improvements are
suggested, but not all aspects of
the design are considered.
Is able to identify the
1 phenomenon to be
investigated
Is able to design a reliable
experiment that
investigates the
2
phenomenon
No mention is made of the
phenomenon to be
investigated.
The experiment does not
investigate the phenomenon.
An attempt is made to identify the
phenomenon to be investigated but
is described in a confusing manner.
The experiment involves the
phenomenon but due to the nature
of the design it is likely the data
will not contain any interesting
patterns.
Is able to decide what is to
be measured and identify
independent and
3
dependent variables
The chosen measurements will
not produce data that can be
used to achieve the goals of
the experiment.
The chosen measurements will
produce data that can be used at
best to partially achieve the goals
of the experiment.
Is able to use available
4 equipment to make
measurements
Is able to describe what is
observed without trying to
explain, both in words and
5
by means of a picture of
the experimental set-up.
At least one of the chosen
measurements cannot be made
with the available equipment.
No description is mentioned.
All chosen measurements can be
made, but no details are given
about how it is done.
A description is mentioned but it is
incomplete. No picture is present.
Or, most of the observations are
mentioned in the context of prior
knowledge.
Is able to identify the
shortcomings in an
6 experimental design and
suggest improvements
No attempt is made to identify
any shortcomings of the
experimental design.
An attempt is made to identify
shortcomings, but they are described vaguely and no suggestions for
improvements are made.
Adequate
The phenomenon to be
investigated is clearly stated.
The experiment investigates the
phenomenon and there is a high
likelihood the data will contain
interesting patterns. All features
of the patterns have a high
likelihood of being observable.
The chosen measurements will
produce data that can be used to
achieve the goals of the
experiment. Independent and
dependent variables are clearly
distinguished.
All chosen measurements can be
made and all details of how it is
done are clearly provided.
Clearly describes what happens
in the experiments both verbally
and by means of a labeled
picture.
All major shortcomings of the
experiment are identified and
specific suggestions for
improvement are made.
Ability to construct, modify, and apply relationships or explanations
Is able to construct a
mathematical (if
7 applicable) relationship
that represents a trend in
data
Is able to devise an
8 explanation for an
observed relationship
Is able to identify the
9 assumptions made in
devising the explanation
No attempt is made to
construct a relationship that
represents a trend in the data.
An attempt is made, but the
relationship does not represent the
trend.
No attempt is made to explain
the observed relationship.
An explanation is made but it is
vague, not testable, or contradicts
the observations.
An attempt is made to identify
assumptions, but most are missing,
described vaguely, or incorrect.
No attempt is made to identify
any assumptions.
The relationship represents the
trend but no analysis of how well
it agrees with the data is included
(if applicable), or some features of
the relationship are missing.
An explanation is made and is
based on simplifying the phenomenon but uses flawed reasoning.
Most assumptions are correctly
identified.
The relationship represents the
trend accurately and completely
and an analysis of how well it
agrees with the data is included
(if applicable).
A reasonable explanation is
made and is based on
simplifying the phenomenon.
All assumptions are correctly
identified.
Rubric B
Ability to design and conduct a testing experiment (testing an idea/hypothesis/explanation or mathematical relation)
Scientific Ability
Missing
Inadequate
Needs some improvement
Adequate
1
Is able to identify the
hypothesis to be tested
No mention is made of a
hypothesis.
The experiment does not test
the hypothesis.
2
Is able to design a reliable
experiment that tests the
hypothesis
Is able to distinguish
between a hypothesis and
a prediction
No prediction is made. The
experiment is not treated as a
testing experiment.
A prediction is made but it is identical
to the hypothesis.
Is able to make a
reasonable prediction
based on a hypothesis
Is able to identify the
assumptions made in
making the prediction
No attempt to make a prediction
is made.
Is able to determine
specifically the way in
which assumptions might
affect the prediction
Is able to decide whether
the prediction and the
outcome agree/disagree
No attempt is made to
determine the effects of
assumptions.
A prediction is made that is distinct
from the hypothesis but is not based on
it.
An attempt is made to identify
assumptions, but the assumptions are
irrelevant or are confused with the
hypothesis.
The effects of assumptions are
mentioned but are described vaguely.
Is able to make a
reasonable judgment
about the hypothesis
No judgment is made about the
hypothesis.
Is able to revise the
hypothesis when
necessary
A revision is necessary but
none is made.
3
4
5
6
7
8
9
No attempt is made to identify
any assumptions.
No mention of whether the
prediction and outcome
agree/disagree.
An attempt is made to identify the
hypothesis to be tested but is described
in a confusing manner.
The experiment tests the hypothesis,
but due to the nature of the design it is
likely the data will lead to an incorrect
judgment.
The hypothesis to be tested is
described but there are minor
omissions or vague details.
The experiment tests the hypothesis,
but due to the nature of the design
there is a moderate chance the data
will lead to an inconclusive
judgment.
A prediction is made and is distinct
from the hypothesis but does not
describe the outcome of the
designed experiment.
A prediction is made that follows
from the hypothesis but does not
incorporate assumptions
Relevant assumptions are identified
but are not significant for making
the prediction.
The hypothesis is clearly stated.
The experiment tests the
hypothesis and has a high
likelihood of producing data that
will lead to a conclusive
judgment.
A prediction is made, is distinct
from the hypothesis, and
describes the outcome of the
designed experiment
A prediction is made that follows
from the hypothesis and
incorporates assumptions.
All assumptions are correctly
identified.
The effects of assumptions are
determined, but no attempt is made
to validate them.
The effects of the assumptions are
determined and the assumptions
are validated.
A decision about the
agreement/disagreement is made but is
not consistent with the outcome of the
experiment.
A judgment is made but is not
consistent with the outcome of the
experiment.
A reasonable decision about the
agreement/disagreement is made
but experimental uncertainty is not
taken into account.
A judgment is made and is
consistent with the outcome of the
experiment but assumptions are not
taken into account.
A reasonable decision about the
agreement/disagreement is made
and experimental uncertainty is
taken into account.
A reasonable judgment is made
and assumptions are taken into
account.
A revision is made but the new
hypothesis is not consistent with the
results of the experiment.
A revision is made and is
consistent with the results of the
experiment but other relevant
evidence is not taken into account.
A revision is made and is
consistent with all relevant
evidence.
Rubric C
Scientific Ability
Ability to design and conduct an application experiment
Missing
Inadequate
Needs some improvement
1
Is able to identify the
problem to be solved
No mention is made of the
problem to be solved.
The experiment does not
solve the problem.
2
Is able to design a reliable
experiment that solves the
problem
Is able to use available
equipment to make
measurements
At least one of the chosen
measurements cannot be
made with the available
equipment.
No discussion is presented
about the results of the
experiment
All of the chosen measurements
can be made, but no details are
given about how it is done.
Is able to evaluate the results
by means of an independent
method
No attempt is made to
evaluate the consistency of
the result using an
independent method.
A second independent method is
used to evaluate the results.
However there is little or no
discussion about the differences in
the results due to the two methods.
Is able to identify the
shortcomings in an
experimental design and
suggest specific
improvements
No attempt is made to
identify any shortcomings
of the experimental design.
An attempt is made to identify
shortcomings, but they are described vaguely and no specific
suggestions for improvements are
made.
Is able to choose a
productive mathematical
procedure for solving the
experimental problem
Is able to identify the
assumptions made in using
the mathematical procedure
Is able to determine
specifically the way in which
assumptions might affect the
results
Mathematical procedure is
either missing, or the
equations written down are
irrelevant to the design.
No attempt is made to
identify any assumptions.
3
4
Is able to make a judgment
about the results of the
experiment
5
6
An attempt is made to identify the
problem to be solved but it is
described in a confusing manner.
The experiment attempts to solve
the problem but due to the nature of
the design the data will not lead to
a reliable solution.
A judgment is made about the
results, but it is not reasonable or
coherent.
The problem to be solved is
described but there are minor
omissions or vague details.
The experiment attempts to
solve the problem but due to the
nature of the design there is a
moderate chance the data will
not lead to a reliable solution.
All of the chosen measurements
can be made, but the details
about how they are done are
vague or incomplete.
An acceptable judgment is
made about the result, but the
reasoning is flawed or
incomplete.
A second independent method
is used to evaluate the results.
Some discussion about the
differences in the results is
present, but there is little or no
discussion of the possible
reasons for the differences.
Some shortcomings are
identified and some improvements are suggested, but not all
aspects of the design are
considered.
Adequate
The problem to be solved is clearly
stated.
The experiment solves the problem
and has a high likelihood of
producing data that will lead to a
reliable solution.
All of the chosen measurements
can be made and all details about
how they are done are provided
and clear.
An acceptable judgment is made
about the result, with clear
reasoning. The effects of
assumptions and experimental
uncertainties are considered.
A second independent method is
used to evaluate the results. The
discrepancy between the results of
the two methods, and possible
reasons are discussed. A
percentage difference is calculated
in quantitative problems.
All major shortcomings of the
experiment are identified and
specific suggestions for
improvement are made.
Ability to construct, modify, and apply relationships or explanations
7
8
9
No attempt is made to
determine the effects of
assumptions.
A mathematical procedure is
described, but it is incomplete, due
to which the final answer cannot be
calculated.
An attempt is made to identify
assumptions, but most are missing,
described vaguely, or incorrect.
An attempt is made to determine
the effects of some assumptions,
but most are missing, described
vaguely, or incorrect.
Correct and complete
mathematical procedure is
described but an error is made
in the calculations.
Most assumptions are correctly
identified.
Mathematical procedure is fully
consistent with the design. All
quantities are calculated correctly.
Final answer is meaningful.
All assumptions are correctly
identified.
The effects of most assumptions
are determined correctly,
though a few contain errors,
inconsistencies, or omissions.
The effects of all assumptions are
correctly determined.
Rubric D
Physics 9A Lab Schedule
Mon
Tue
Wed
Thu
Fri
Apr 3 - Apr 7
Lab 1
Lab 1
Lab 1
Lab 1
Lab 1
Apr 10 - Apr 14
Lab 2
Lab 2
Lab 2
Lab 2
Lab 2
Apr 17 - Apr 21
Lab 3
Lab 3
Lab 3
Lab 3
Lab 3
Apr 24 - Apr 28
Lab 4
Lab 4
Lab 4
Lab 4
Lab 4
May 1 - May 5
Lab 5
Lab 5
Lab 5
Lab 5
Lab 5
May 8 - May 12
Lab 6
Lab 6
Lab 6
Lab 6
Lab 6
May 15 - May 19
Lab 7
Lab 7
Lab 7
Lab 7
Lab 7
May 22 - May 26
Lab 8
Lab 8
Lab 8
Lab 8
Lab 8
May 29 - Jun 2
Memorial Day
Lab 9
Lab 9
Lab 9
Lab 9
Jun 5 - Jun 8
Lab 9
no lab
no lab
no lab
Physics'9A'Lab'1:'Motion'
!
I.'Background'Information:'DRAWING'MOTION'DIAGRAMS'
!
!
Read!this,!then!your!TA!will!go!over!an!example!with!you,!and!show!you!how!to!translate!
between!motion!diagrams!and!graphs.!
!
Motion'diagrams!
•! Dots!represent!an!object’s!positions!at!equal!time!intervals!(for!example,!at!times!
separated!by!1.0!s).!

•! v !arrows!at!each!dot!indicate!the!direction!of!motion!and!how!fast!the!object!is!moving!
(like!a!speedometer!reading).!


•! A! Δv !arrow!is!placed!between!each!pair!of!dots!and!represents!the!change!in!the! v !

arrows.!If!the!changes!are!uniform!during!each!time!interval,!a!single! Δv !arrow!
represents!the!changing!motion!during!the!entire!motion!diagram!(as!in!the!diagram!
above).!
!
II.'Observation'Experiment:'Investigating'and'representing'motion'
!
Some!bullets!have!a!parenthetical!indicator,!for!example!(O2),!which!refers!to!Observation!
experiment!ability!2!in!the!guidelines!you!have!for!Observational,!Testing,!and!Application!
experiments.!All!bullets,!whether!so!designated!or!not,!must!be!addressed!in!your!lab!
writeLup,!and!a!random!subset!will!be!graded.!Don’t&forget&this;&it&applies&to&all&labs&this&
quarter.!
!
Purpose!of!this!activity:!
•! Design!an!experiment!to!observe!motion!
•! Represent!motion!in!multiple!ways!and!understand!the!relationships!between!those!
representations!
•! Practice!taking!data!in!a!scientific!fashion!
•! Make!clear!observations!and!distinguish!them!from!explanations!
!
You!have!a!cart!and!a!metal!ramp,!meter!sticks,!a!stopwatch!and!tape!for!marking!locations!
on!the!ramp.!The!task!for!your!group!is!to!describe!the!motion!of!the!cart!under!at!least!two!
different!conditions,!and!to!represent!each!condition!two!different!ways.!
!
!
First!do!a!few!trial!runs!so!that!you!get!used!to!calling!out!the!time!at!equal!intervals!and!
marking!the!location!–!it!may!take!all!of!your!group!members!working!together!to!mark!the!
cart!accurately!and!frequently.!Note:!Please&don’t&write&on&the&tracks,&and&if&you&choose&to&
mark&the&track&with&pieces&of&tape,&please&remove&them&when&you’re&done.!Use!the!following!
as!an!experimental!guide!and!for!knowing!what!to!include!in!your!report:!
!
a.! (O2,O3)!Design!two!experiments!to!investigate!the!phenomenon;!determine!what!is!to!
be!measured,!and!identify!independent!and!dependent!variables.!
b.! Draw!a!clearly!labeled!diagram!of!each!of!your!two!experimental!setLups.!Make!sure!
you!represent!the!important!aspects!of!your!experiments.!
!
Perform!the!experiments.!(You!should!have!at!least!four!time!points!for!each.)!
!
c.! (O5)!Describe!what!you!observe!without!trying!to!explain!it.!In!particular:!
1.! Describe!the!motion!of!the!cart!in!words,!justifying!use!of!physical!terms!such!as!
‘constant’!
2.! Draw!a!motion!diagram!for!the!cart!using!the!visual!information!obtained!during!
the!experiment!
3.! Make!a!position!vs.!time!graph,!velocity!vs.!time!graph,!and!acceleration!vs.!time!
graph!for!the!cart.!(There!is!printable!graph!paper!on!the!computers.)!
d.! Discuss!how!your!data,!motion!diagrams!and!graphs!satisfy!the!purpose!of!the!
experiment.!
e.! (O6)!Assess!the!shortcomings!of!your!experiment,!suggest!improvements,!and!identify!
sources!of!experimental!uncertainty.!
!
III.'Observation'Experiment:'Determining'a'relationship'between'ramp'
angle'and'acceleration'
!
Purpose!of!this!activity:!
•! Get!familiar!with!the!motion!sensors!and!Capstone!software!
•! Design!an!experiment!to!determine!a!mathematical!relationship!
•! Construct!a!mathematical!relationship!from!data!
•! Interpret!data!and!graphs!
!
You'll!be!using!motion!detectors!to!determine!the!locations!of!objects!at!various!times.!In!
order!to!use!them!effectively,!be!aware!of!the!following.!
•! The!ultrasonic!waves!are!emitted!in!a!cone!about!30!degrees.!Anything!within!that!
cone!can!reflect!them!and!possibly!cause!an!accidental!measurement.!Watch!for!
chairs,!desks,!projecting!apparatus,!other!people,!etc.!Also,!some!targets!may!not!
supply!a!strong!reflection.!Avoid!loose!clothing.!
•! Objects!closer!than!0.4!m!will!not!be!detected!properly.!
•! Don't!save!any!data.!
•! Connect!the!Motion!Detector!to!ports!1!(yellow)!and!2!(black)!of!the!Pasco!Box.!
!
You!have!a!cart!and!a!metal!ramp,!a!meterstick,!and!a!motion!detector,!which!you!should!
affix!to!the!top!end!of!the!ramp,!near!where!the!mounting!rod!passes!through.!The!task!for!
your!group!is!to!determine!a!mathematical!relationship!between!the!angle!of!the!ramp!and!
the!acceleration!of!the!cart,!based!on!your!experimental!data.!The!computer!file!(which!is!
in!PhysicsProgramsL>Phy9A)!“Motion!x!and!v!vs!t”!will!graph!the!velocity!of!the!cart!when!
you!click!the!"Record"!button.!Do!a!linear!fit!for!velocity!to!determine!the!acceleration,!by!
first!generating!a!dataLhighlighting!area!with!the!
!button!in!the!toolbar,!then!moving!it!
where!it’s!needed,!then!invoking!the!“Linear!:!mx+b”!feature!under!the!
!button.!
Note:!You’ll!definitely!be!using!a!spreadsheet!later!in!lab,!and!should!you!wish!to!use!one!
today,!it!is!the!file!“Simple!Plot!&!Trendline”.!
!
a.! (O2)!Design!an!experiment!to!investigate!the!phenomenon.!
b.!! Draw!a!clearly!labeled!diagram!of!your!experimental!setLup.!Make!sure!you!represent!
the!important!aspects!of!your!experiment.!
c.! (O3)!Determine!what!is!to!be!measured,!and!identify!independent!and!dependent!
variables.!
!
Perform!the!experiments.!
!
d.! (O5)!Describe!what!you!observe!without!trying!to!explain!it,!both!in!words!and!any!
additional!sketch(es)!that!might!be!needed.!
e.! Explain!specifically!how!you!are!finding!the!acceleration!from!your!data!and!why!you!
are!being!asked!to!do!a!fit!from!the!velocity!graph.!
f.! (O7,8,9)!Construct!a!mathematical!relationship!representing!the!trend!in!your!data,!
explain!the!relationship,!and!identify!assumptions!on!which!it’s!based.!
g.! How!could!you!test!the!relationship!you!found?!Give!a!brief!description!(you!are!not!
required!to!conduct!the!test).!
h.! (O6)!Assess!the!shortcomings!of!your!experiment,!suggest!improvements,!and!identify!
sources!of!experimental!uncertainty.!
!
Physics'9A'Lab'2:'Kinematics'
Most!relevant!text!references:!Secs.!2.4L3L3!
!
I.'Background'Information:'Weakest'Link'Rule'and'Uncertainties'
!
Suppose!that!after!a!hike!in!the!mountains,!a!friend!asks!how!fast!you!walked.!You!recall!
that!the!trail!was!about!6!miles!long!and!that!it!took!between!two!and!three!hours.!You!use!
the!average!time!of!2.5!h!and!tell!him!that!your!average!speed!was:!
!
Average!speed!=!6!miles/2.5!h!=!2.4!miles/h.!
!
This!answer!implies!that!you!knew!your!speed!within!±!0.05!miles/h!(using!significant!
figures).!
!
Implied!average!speed!uncertainty!=![(±!0.05!miles/h)!/!(2.4!miles/h)]!x!100!=!±2!%!
!
However,!the!time!interval!for!the!trip!(2.5!±!0.5)!hours!had!an!uncertainty!of!±!0.5Lhour!
and!a!percent!uncertainty!of:!
!
Time!interval!uncertainty!=![(±!0.5!h)!/!(2.5!h)]!x!100!=!±!20!%!
!
How!could!your!answer!convey!a!±2%!uncertainty!when!one!of!the!numbers!used!in!the!
calculation!was!uncertain!by!±!20%?!Your!answer!should!have!no!greater!precision!than!
the!least!certain!quantity!used!to!calculate!it.!Your!answer!should!have!at!least!±20%!
uncertainty.!
!
±!0.2!x!2.4!miles/h!=!±!0.5!miles/h.!
!
Thus,!you!should!have!said!that!you!walked!at!about!2.4!miles/h!±!0.5!miles/h.!
!
Weakest'Link'Rule!
The!percent!uncertainty!in!the!calculated!value!of!some!quantity!is!at!least!as!great!as!the!
greatest!percentage!uncertain!value!used!to!make!the!calculation.!First!estimate!the!
percent!uncertainty!in!each!quantity!used!to!make!the!calculation.!The!final!answer!is!
assigned!the!same!percent!uncertainty!as!the!greatest!percentage!uncertain!quantity!used!
in!the!calculation!(as!a!rough!estimate!of!the!total!uncertainty).!
!
!
II.'Testing'Experiment:'STATION'B:'Predicting'where'two'carts'will'meet'
!
All!bullets!must!be!addressed!in!your!lab!writeLup,!and!a!random!subset!will!be!graded.!
!
Purpose:!
•! Combining!experimental!data!with!problem!solving!to!make!predictions!for!the!
outcome!of!a!new!situation!
•! Considering!factors!that!will!impact!the!outcome!of!the!situation!
•! Smashing!things!together!(because!that’s!fun!)!
!
Your!task!is!to!place!two!carts!in!the!appropriate!initial!position!in!order!for!them!to!meet!
at!the!center!point,!when!released!from!rest!at!the!same!time!down!two!ramps!with!very!
different!ramp!angles!(you!should!check!to!make!sure!that!the!angles!are!more!than!15!
degrees!different!from!each!other).!Make'sure'the'foam'pad'is'between'the'two'ramps'
at'the'base,'so'the'carts'don’t'actually'collide'in'the'center,'but'hit'each'side'of'the'
foam'pad'simultaneously.!This!is!a!problem!solving!exercise!–!you!will!use!the!equipment!
to!take!any!necessary!data,!but!you!are!not!allowed!to!do!the!final!‘test’!of!your!calculation!
until!you!have!approval!from!your!TA,!and!they!are!there!to!see!it.!(You!are!not!allowed!to!
use!‘trial!and!error’!to!solve!this!–!the!challenge!is!to!calculate!it!out!and!predict!the!right!
locations!and!test!that!prediction!in!front!of!your!TA!)!!
!
Write!the!following!in!your!report:!
!
a.! Make!a!sketch!of!your!experiment,!including!labels!for!all!important!aspects.!
b.! What!quantities!will!you!need!to!find!in!order!to!predict!the!appropriate!starting!
locations?!
c.! Do!any!necessary!measurements!or!calculations!to!determine!the!values!of!those!
quantities.!
d.! (T4)!Make!a!reasonable!prediction!based!on!the!kinematicLmodel!hypothesis!about!
where!to!initially!place!the!carts!such!that!they!meet!in!the!center.!
e.! Use!the!weakest!link!rule!to!estimate!the!uncertainty!in!your!calculations.!
f.! (T5)!Identify!the!assumptions!made!in!making!the!prediction.!
g.! (T6)!Determine!specifically!the!way!in!which!assumptions!might!affect!the!prediction!
(for!example,!will!ignoring!a!certain!effect!mean!you!should!actually!place!the!cart!a!
little!higher!or!a!little!lower!and!why?)!
!
When'your'calculations'are'completed,'show'the'results'to'your'lab'instructor'and'
then'try'the'experiment.'
!
h.! Record!the!outcome!of!your!experiment.!
i.! (T7)!Decide!whether!or!not!the!prediction!and!the!outcome!agree/disagree.!
j.! Reconcile!any!difference!in!your!prediction!and!the!outcome!of!the!experiment.!Be!
specific.!For!example,!you!can!discuss!how!experimental!uncertainties!affected!the!
outcome,!or!how!you!can!improve!your!calculations.!
!
III.'Testing'Experiment:'STATION'A:'Falling'Rocks'
!
Use!the!testing!experiment!rubrics!to!guide!what!you!include!in!your!lab!report.!If!you!are!
unsure!how!to!apply!them!you!may!use!the!bullets!in!the!previous!!testing!experiment!for!
guidance,!but!some!testing!experiment!rubrics!not!used!there!may!be!useful!here.!A!subset!
of!the!rubrics!will!be!used!for!grading.!Be!sure!to!incorporate!error!analysis!using!the!
weakest!link!rule!detailed!above.!Note:!It!would!probably!be!good!to!try!a!few!runs!before!
deciding!exactly!where!to!position!parts!of!your!apparatus.!Also,!as!before,!please&don’t&
write&on&the&tracks,&and&if&you&choose&to&mark&the&track&with&pieces&of&tape,&please&remove&
them&when&you’re&done.!
!
A!bitter!controversy!has!recently!broken!out!between!the!residents!of!a!new!housing!
development!in!the!foothills!and!the!Town!Council!over!the!safety!of!a!number!of!large!
rocks!perched!on!the!slope!of!a!hill!that!ends!with!a!cliff,!down!to!a!lake,!on!the!opposite!
side!of!which!is!the!housing!development.!At!the!heart!of!the!dispute!is!the!relationship!
between!the!height!above!the!edge!of!the!cliff!at!which!the!rocks!are!balanced!(h)!and!the!
distance,!horizontally!from!the!base!of!the!cliff,!that!the!rocks!will!travel!(d)!should!they!roll!
down!the!hill.!One!group!of!engineers!has!done!a!study!and!concluded!that!h!is!
proportional!to!d2.!However,!a!second!group!repeated!the!study!and!concluded!that!h!is!
proportional!to!d.!If!the!first!group!is!correct,!all!rocks!would!land!in!the!lake.!If!the!second!
is!correct,!some!could!overshoot!the!lake!and!smash!into!the!houses.!Both!groups!
investigated!the!situation!using!apparatus!consisting!of!a!sloped!ramp!and!a!steel!ball.!In!
both!cases,!the!steel!ball!was!rolled!down!the!slope!from!different!heights,!and!h!and!d!
were!measured.!The!UCD!Physics!Department!has!been!approached!to!resolve!the!
controversy!and!now!asks!you!to!investigate!the!situation!urgently!with!the!same!
apparatus.!A!full!report!is!sought,!detailing!all!aspects!of!the!experiments,!measurements,!
calculations,!and!graphs!as!well!as!your!findings!on!who!is!right!or!wrong.!In!particular,!pay!
careful!attention!to!your!graphs!of!d!and!h!compared!to!your!graphs!of!d2!and!h,!and!how!
these!graphs!were!used!to!determine!the!proportionality,!as!we!will!be!showing!them!to!
reporters!at!a!press!conference!later!this!week.!
!
!
''
Physics'9A'Lab'3:'Motion'and'Force''
Most!relevant!text!references:!Chapter!4!
!
I.'Background'Information:'Drawing'FreeSBody'Diagrams'
!
!
!
!
•!
•!
•!
•!
•!
•!
•!
!
!
Strategy'–'Constructing'a'FreeSBody'Diagram'(FBD)!
Make!a!sketch!of!the!process!described!in!the!problem.!
Circle!an!object!(or!objects)!of!interest!in!the!sketch!L!we!call!it!the!system.!!!
If!you!can!model!the!system!as!a!particle,!place!a!“particle”!dot!to!the!side!to!represent!
the!system.!!
Look!for!objects!outside!the!system!–!external!objects!–!that!interact!with!the!system.!
Decide!what!objects!are!important!and!what!objects!are!not.!(You!might!think!that!the!
surfaces!are!smooth!and!you!can!neglect!friction,!for!example.)!
Draw!a!force!arrow!that!represents!each!of!these!external!interactions!that!you!are!
going!to!consider.!Place!the!tails!of!these!force!arrows!on!the!particle!dot.!Try!to!draw!
the!lengths!of!the!arrows!to!represent!the!relative!magnitudes!of!the!forces!–!longer!
arrows!for!bigger!forces.!!!
Label!the!forces!in!the!diagram.!VERY!IMPORTANT:!The!forces!in!the!diagram!should!
only!be!those!that!some!object!outside!the!system!exerts!on!the!object!inside!the!
system.!For!now,!identify!the!external!object!that!causes!each!force!and!also!the!object!

on!which!the!force!is!exerted!(for!example,! Fropeon system ).!Surfaces!can!exert!two!forces,!
one!perpendicular!to!the!surface!and!the!other!parallel!(friction).!
Earth!as!a!planet!pulls!down!on!objects!without!touching!them.!We!label!this!force!

FEarth on system .!!!
II.'Observation'Experiment:'How'is'an'object’s'motion'related'to'the'net'
force'on'it?'
!
This!short!experiment!is!not!a!traditional!observation!experiment.!Use!the!bullets!below!to!
guide!your!writeLup.!To!be!a!good!experimenter,!you!should!especially!try!to!carefully!
describe,!both!in!words!and!diagrams,!what!you!observe,!before!mixing!it!up!with!any!
attempted!or!preconceived!explanation!of!why!it!happens!or!should!happen.!
!
a.! A!freely!rolling!cart!is!in!motion!along!a!level!track!and!free!of!your!hand.!The!cart!is!the!
system!of!interest.!Draw!a!motion!diagram!and!a!free!body!diagram!for!the!moving!cart.!
Indicate!the!net!force!exerted!on!the!system.!
b.! Push!a!moving!cart!gently!with!a!uniform!force!for!a!short!time.!Again!draw!a!motion!
diagram!and!construct!a!free!body!diagram!for!the!time!while!your!hand!is!pushing!the!
cart.!Indicate!the!net!force!exerted!on!the!system.!
c.! Draw!a!motion!diagram!and!a!free!body!diagram!for!the!cart!after!the!push,!when!the!
cart!is!moving!but!your!hand!is!not!touching!it.!
d.! Propose!a!relationship!(if!any)!between!the!net!force!exerted!on!an!object,!its!motion!
and!change!in!its!motion.!How!is!the!relationship!(or!lack!thereof)!reflected!in!your!
representations!of!the!motion?!
!
III.'Testing'Experiment:'Testing'a'Claim'
!
Design!an!experiment!to!test!the!following!rule:!an!object!always!moves!in!the!direction!of!
the!net!force!exerted!on!it.!You!have!a!cart,!track,!masking!tape,!a!basketball,!string,!a!
pulley,!and!masses!to!use.!How!will!you!“test”!the!rule?!If!you!have!shown!for!one!case!that!
this!is!true,!have!you!shown!that!the!rule!is!correct?!If!you!can!show!in!one!case!that!this!is!
not!true,!then!have!you!shown!that!the!rule!is!not!correct?!Think!about!this!before!
conducting!your!testing!experiment.!
!
Write!the!following!in!your!report:!
a.! (T1)!State!the!hyphothesis.!
b.! (T2)!Design!a!reliable!experiment!to!tests!your!hypothesis,!including!a!brief!description!
of!your!procedure.!
c.! Draw!a!labeled!sketch!of!the!experimental!setLup.!
d.! Draw!a!free!body!diagram!of!the!object!while!it!is!in!the!“region!of!interest”!and!
determine!the!direction!of!the!net!force!on!the!object.!
e.! (T4)!Make!a!prediction!about!the!outcome!of!the!experiment!based!on!the!hypothesis.!
!
Perform!the!experiment.!
!
f.! Record!the!outcome!of!your!experiment.!
g.! (T7)!Discuss!whether!your!prediction!and!the!experimental!outcome!agree/disagree.!
h.! (T8)!Make!a!judgment!about!the!hypothesis!based!on!your!experimental!outcome,!your!
assumptions,!and!sources!of!uncertainty.!
i.! Summarize!your!findings.!
IV.'Testing'Experiment:'Another'Claim'
How!do!you!respond!to!this?!You!have!a!cotton!ball!or!a!coffee!filter,!meterstick!and!
stopwatch,!motion!sensor!(port!1!yellow,!2!black)!and!file!“Motion!x!and!v!vs!t”.!
!
!On the Descent of Cotton Balls: a Theoretical Perspective
J.!K.!FINKLEBOTTOM!&!P.!R.!PRIEST!
!
ABSTRACT!
Cotton!balls!fall!more!slowly!than!rocks!in!most!situations.!We!present!an!extension!
!!!!!!!!!!!!!!to!the!traditional!Newtonian!view!of!objects!to!include!freeLfalling!cotton!balls.!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
Cotton!balls!(sometimes!made!of!Rayon)!are!puffs!of!fluff,!roughly!spherical,!with!a!
diameter!of!about!3!cm!and!a!mass!between!0.5g!and!1.0g.!If!you!drop!them,!they!fall.!
!
It!has!been!observed,!however!(Galileo!and!Snerd,!1998)!that!if!you!drop!a!rock!and!a!
cotton!ball!simultaneously!from!the!top!of!a!tower,!the!rock!hits!first.!
!
Evidently!air!resistance!slows!the!cotton!ball!more!than!the!rock.!We!suggest!that!its!effect!
is!greater!because!the!cotton!ball!is!lighter.!
!
Our!reasoning!is!this:!Each!air!molecule,!on!impact,!imparts!a!small!force!to!a!falling!object.!
Using!the!traditional!force!formula!F!=!ma!(Newton,!1687),!we!see!that!each!collision!
effectively!reduces!the!gravitational!acceleration!of!any!object!falling!through!air!by!an!
amount!that!is!inversely!proportional!to!that!object’s!mass!(i.e.,!a!=!F!⁄!m!).!Thus!the!light!
cotton!ball!is!slowed!more!than!a!comparablyLsized!(and!heavier)!rock.!
!
Therefore!we!should!modify!the!formula!for!the!distance!s!fallen!in!time!t.!Instead!of!the!
traditional!
!
!
!
!
!
s=
!
1 2
gt !
2
!
!
!
!
(EQ!1)!
where!g!is!the!acceleration!of!gravity,!we!suggest!that!the!correct!model!for!falling!cotton!
balls!is!
!
!
!
!
!
!
s=
1 2
kt !
2
!
!
!
!
(EQ!2)!
where!k!is!an!acceleration!smaller!than!g.!
!
Though!the!truth!of!our!theory!seems!selfLevident,!we!await!confirmation!from!experiment.!
!
!
!
!
!
eeps!media!©!2004! !
!
!
!
!
!
Annals&of&Plausibility!
!
Physics'9A'Lab'4:'More'with'Forces'
Most!relevant!text!references:!Chapter!5!
!
I.'Application'Experiment:'Static'Friction'
!
All!bullets!must!be!addressed!in!your!lab!writeLup,!and!a!random!subset!will!be!graded.!
!
Design!at!least!two!independent!experiments!to!determine!the!coefficient!of!static!friction!
between!your!shoe!and!the!carpet!strip!provided.!(You!can!use!any!of!your!group’s!shoes,!
and!either!the!front!or!back!of!the!carpet,!whichever!gives!you!cleaner!data.!Should!you!
prefer!to!use!something!less!personal,!there!are!some!blocks!available.)!You!should!have!
carpet,!a!board,!and!a!force!measuring!device.!
!
a.! (A1)!Identify!the!problem!to!be!solved.!
b.! (A2)!Design!two!reliable!experiments!that!solve!the!problem.!
c.! Draw!sketches!of!your!experimental!designs.!
d.! Draw!a!freeLbody!diagram!for!the!shoe.!Include!an!appropriate!set!of!coordinate!axes.!
e.! (A7)!Choose!a!productive!mathematical!procedure!for!solving!the!problem.!Use!the!
freeLbody!diagram!to!devise!the!mathematical!procedure!to!solve!the!problem!for!each!
experimental!setLup.!
f.! (A3)!Discuss!how!you!will!use!the!available!experiment!to!make!the!measurements.!
g.! (A8)!Identify!the!assumptions!made!in!using!the!mathematical!procedure.!
h.! (A9)!Determine!specifically!the!way!in!which!assumptions!might!affect!the!results.!
i.! What!are!the!possible!sources!of!experimental!uncertainty?!How!could!you!minimize!
them?!
!
Perform!the!experiments.!
!
j.! Record!the!outcome!of!your!experiments.!
k.! (A4)!Make!a!judgment!about!the!results!of!your!experiments.!
l.! (A5)!Evaluate!your!results!by!comparing!the!two!independent!methods.!Use!your!
uncertainty!to!make!an!explicit!comparison!of!the!two!values!you!obtained!for!the!
coefficient!of!static!friction.!
m.! What!are!possible!reasons!for!the!difference?!
n.! Which!experiment!was!more!accurate!and!why?!
o.! (A6)!Identify!the!shortcomings!in!the!experiments!and!suggest!specific!improvements.!
!
II.'Application'Experiment:'Hanging'and'Circling'Masses'
!
All!bullets!must!be!addressed!in!your!lab!writeLup,!and!a!random!subset!will!be!graded.!
!
Design!an!experiment!to!determine!how!fast!you!need!to!spin!the!small!mass!m!when!you!
hang!a!mass!M!from!the!end!of!the!string.!The!mass!m!spins!at!the!top!of!a!plastic!tube,!and!
the!larger!mass!M!hangs!down!below!the!tube,!with!the!tube!kept!vertical.!You!have!a!string!
with!mass!m!strung!attached,!a!plastic!tube,!ruler,!stopwatch,!some!masses!and!a!mass!
hanger!to!use!for!mass!M.!Note:!If!you!attach!tape!to!the!string,!remove&it&when&you’re&done!&
Also,&please&do&not&tie&any&knots&in&the&string!!
!
Include!the!following!in!your!report:!
!
a.! (A1)!Identify!the!problem!to!be!solved.!
b.! (A2)!Design!a!reliable!experiment!that!solves!the!problem.!
c.! Draw!a!sketch!of!your!experimental!design.!
d.! Draw!freeLbody!diagrams.!Include!an!appropriate!set!of!coordinate!axes.!
e.! (A7)!Choose!a!productive!mathematical!procedure!for!solving!the!problem.!Use!the!
freeLbody!diagrams!to!devise!the!mathematical!procedure!to!solve!the!problem.!
f.! (A3)!Discuss!how!you!will!use!the!available!experiment!to!make!the!measurements.!
g.! (A8)!Identify!the!assumptions!made!in!using!the!mathematical!procedure.!
h.! (A9)!Determine!specifically!the!way!in!which!assumptions!might!affect!the!results.!
i.! What!are!the!possible!sources!of!experimental!uncertainty?!How!could!you!minimize!
them?!
!
Perform!the!experiments.!
!
j.! Record!the!outcome!of!your!experiment.!
k.! (A4)!Make!a!judgment!about!the!results!of!your!experiments.!
l.! (A6)!Identify!the!shortcomings!in!the!experiment!and!suggest!specific!improvements.!
Physics'9A'Lab'5:'Energy'Forms'
Most!relevant!text!references:!Chapters!6!&!7!
!
Testing'Experiment:'The'WorkSEnergy'Principle'
!
Design!an!experiment!to!test!whether!the!workLenergy!principle!is!applicable!to!the!
following!situation:!you!place!a!spring,!closed!at!one!end,!on!top!of!a!thin!metal!rod.!Then!
you!stretch!the!spring!down!and!then!release!it;!it!shoots!upward.!
Available!equipment:!Spring!closed!at!one!end,!meter!stick,!rod!attached!to!lab!table,!scale!
for!measuring!mass,!weights!to!attach!to!spring,!paperclips!(helpful,!when!bent!into!a!small!
W!shape,!to!attach!weights).!Note:!To&prevent&permanent&damage/distortion&of&the&spring,&
don’t&hang&more&than&350g&or&stretch&it&more&than&about&15J20cm&beyond&its&rest&length.!
!
Remember!that!to!test!a!relationship,!you!need!to!use!it!(with!some!additional!
assumptions)!to!make!a!prediction!about!an!outcome!of!a!particular!experiment.!You!then!
perform!the!experiment!and!compare!the!actual!outcome!to!the!predicted!outcome.!
!
Write!the!following!in!your!report:!
a.! First!recall!what!the!generalized!(or!‘extended’)!workLenergy!principle!is!and!express!it!
as!a!mathematical!relationship.!
b.! (T2)!Before!your!main!experiment,!design!a!preliminary!one!to!investigate!whether!
your!spring!obeys!Hooke’s!Law,!i.e.,!whether!force!is!proportional!to!displacement!all!
the!way!to!zero.!(This!data!may!be!useful!later.)!Then,!working!with!your!lab!partners,!
choose!the!best!design!for!your!main!experiment,!indicating!why!you!felt!it!best.!
c.! Draw!a!sketch!of!your!experimental!designs.!
d.! Choose!a!productive!mathematical!procedure!for!solving!the!problem.!
e.! (T5,!T6)!What!assumptions!have!you!made,!and!how!would!they!affect!your!prediction?!
Think!if!you!can!estimate!the!effects!of!assumptions!and!how!you!can!minimize!the!
effects.!
f.! What!are!possible!sources!of!experimental!uncertainty?!Use!the!weakest!link!rule!to!
estimate!the!uncertainty!in!your!prediction.!(By!all!means!refer!to!the!Experimental!
Uncertainties!supplement!at!the!beginning!of!this!lab!manual.)!
g.! (T4)!Make!a!quantitative!prediction!about!the!outcome!of!your!experiment.!Include!
experimental!uncertainty!in!your!prediction.!
!
Perform!the!experiments.!
!
h.! Record!the!outcome!of!your!experiment,!Make!tables!and/or!use!the!spreadsheet!
program!and!printout!where!appropriate.!!
i.! Did!the!outcome!match!the!prediction?!If!not,!discuss!specifically!what!might!have!gone!
wrong.!Include!the!effects!of!theoretical!assumptions!and!experimental!uncertainties.!
j.! Based!on!your!prediction!and!the!outcome!of!your!experiment,!make!a!judgment!about!
whether!the!generalized!workLenergy!principle!is!applicable!in!this!situation.!
!
Physics'9A'Lab'6:'Momentum'&'Varying'Force'
Most!relevant!text!references:!Chapter!8!
!
Testing'Experiment:'Relationship'between'force'and'change'in'motion'
!
All!bullets!must!be!addressed!in!your!lab!writeLup,!and!a!random!subset!will!be!graded.!
!
You!want!to!test!the!relationship!between!force!and!change!in!motion!for!a!collision!
between!two!carts!on!a!track.!You!are!given!a!force!sensor!and!motion!sensor!for!each!cart.!
One!cart’s!motion!sensor!should!go!to!ports!1!(yellow)!and!2!(black)!and!its!force!sensor!to!
port!A.!For!the!other,!ports!3!(yellow),!4!(black)!and!B.!The!file!is!“dp/dt”!and!it!plots!forces!
and!velocities!versus!time.!Using!this!equipment,!test!Newton’s!second!law!for!the!
following!cases:!
!
•! A!moving!cart!colliding!with!a!stationary!one!of!equal!mass.!(You!can!equalize!the!
masses!by!adding!weights!to!one.!You!might!want!to!use!tape!to!keep!them!in!place.)!!
•! A!moving!cart!colliding!with!a!stationary!unequalLmass!one.!(Remove!added!weights.)!
•! Some!other!kind!of!collision.!(Keep!the!relative!velocity!small!or!they’ll!jump!the!track!)!
!
NOTE:!The!force!during!the!collision!is!NOT!constant!–!force!changes!with!time,!so!we!have!
to!be!careful.!F!=!dp/dt,!which!for!constant!m!becomes!F!=!m(dv/dt).!We!can!now!write:!F!dt!
=!m&dv,!and!integrate!both!sides.!The!integral!of!F&dt!is!the!area!under!the!force!vs.!time!
curve,!which!you!can!find!using!the!computer!plots.!You!can!then!relate!it!to!the!integral!of!
m&dv,!which,!because!m!is!constant,!is!just:!mvf!–!mvi,!or!pf!–!pi.!
!
Besides!testing!the!relationship!between!force!and!motion!for!each!cart,!in!each!separate!
experiment,!also!compare!the!force!each!cart!exerts!on!the!other,!and!the!integral!of!F!dt!for!
each!cart.!State!what!you!find!for!those!comparisons!within!your!error,!and!draw!any!
conclusions!based!on!these!observations.!Besides!comparing!the!integral!of!F&dt!and!pf!–!pi!
for!the!“whole!collision”!you!should!also!comment!on!the!relationship!during!collisions.!
!
Write!in!your!report!the!following:!(Note:!aLg!and!k!can!be!answered!for!your!experiments!
as!a!whole,!but!hLj!should!be!answered!for!each!of!your!experiments!individually.)!
!
a.! (T1)!Identify!the!hypothesis!(rule)!to!be!tested.!
b.! (T2)!Design!a!reliable!experiment!that!tests!the!hypothesis!including!a!brief!description!
of!your!procedure.!
c.! Draw!a!labeled!sketch!of!the!experimental!setLup.!
d.! (T4)!Make!a!prediction!about!the!outcome!of!the!experiment!based!on!the!hypothesis.!
e.! (T5)!Identify!the!assumptions!made!in!making!the!prediction.!What!assumptions!about!
the!objects,!interactions,!and!processes!you!need!to!make!to!solve!the!problem?!
f.! (T6)!Determine!specifically!in!which!way!assumptions!might!affect!the!prediction.!
g.! What!are!experimental!uncertainties!in!this!experiment?!
!
Perform!the!experiments.!
Note:!Because!it!tends!to!drift,!the!force!sensor!should!be!tared!with!the!side!button!each!
time!you!take!data.!Also,!the!coordinate!
,!area!!
may!be!useful,!along!!the!dataLhighlighting!tool!
,!and/or!statistics!
!tools!
!you!used!in!an!earlier!lab.!
!
h.! Record!the!outcome!of!your!experiments.!
i.! (T7)!Decide!whether!the!prediction!and!the!outcome!agree/disagree.!
j.! Decide!whether!your!assumptions!and!experimental!uncertainties!can!account!for!any!
discrepancy!between!your!predicted!and!measured!values.!
k.! (T8)!Make!a!reasonable!judgment!about!the!hypothesis!based!on!your!experimental!
outcomes,!the!assumptions!you!made,!and!the!estimated!uncertainty.!
!
Physics'9A'Lab'7:'Putting'it'all'together'
Application'Experiment:'Pendulum'BoxSBash'
!
A!sports!company!that!manufactures!skiing!equipment!is!interested!in!determining!the!
coefficient!of!friction!between!two!surfaces.!Your!lab!group,!as!part!of!an!interview!process!
for!a!contract!with!the!sports!company,!is!asked!to!solve!the!following!problem:!A!
pendulum!bob!swings!down!from!a!horizontal!starting!position!and!hits!a!box.!
You!are!to!make!measurements!concerning!the!above!process!and!then!use!the!concepts!of!
physics!to!determine!the!coefficient!of!kinetic!friction!between!the!box!and!the!tabletop.!
You!have!the!following!equipment!for!it:!a!box,!a!pendulum!with!an!attached!object,!meter!
sticks,!tape,!a!spring!scale,!and!a!balance.!You!are!to!verify!your!measurement!with!a!
second!method.!
!
This!experiment!is!an!application!experiment!requiring!two!independent!experiments!that!
you!check!for!consistency.!Use&the&application&experiment&rubrics&to&guide&what&you&include&
in&your&lab&report.!(If!you!are!still!unsure!how!to!apply!the!rubrics!you!may!make!use!of!the!
bullets!in!the!lab!5!static!friction!application!experiment!for!guidance.)!A!subset!of!the!
rubrics!will!be!used!for!grading.!Be!sure!to!incorporate!error!analysis!using!the!weakest!
link!rule.!
!
Physics'9A'Lab'8:'Rotational'Dynamics'
Most!relevant!text!references:!Secs.!9.4L10.3.!
!
I.'Application'Experiment:'Moment'of'Inertia'
!
Design!at!least!two!independent!experiments!to!determine!the!moment!of!inertia!of!a!thick!
metal!ring.!You!are!given!a!thick!metal!ring!on!a!rotating!cradle,!which!has!a!hub!of!2.38cm!
radius!around!which!string!can!be!wound,!pulleys,!over!which!string!can!run!to!a!hanging!
weight,!some!masses,!an!electronic!scale,!a!meterstick,!and!a!stopwatch.!One!of!your!
experiments!should!be!static,!and!the!other!should!be!dynamic.!The!static!experiment!can!
be!measurements!based!on!theoretical!equations!for!moments!of!inertia.!
!
Equipment!note:!Please!check!the!relative!height!of!the!hub!on!your!cradle!and!the!pulley.!
If!the!pulley!is!too!low,!the!string!will!wind!below!the!hub,!and!disentangling!it!is!a!mess!!
!
All!bullets!must!be!addressed!in!your!lab!writeLup,!and!a!random!subset!will!be!graded.!
!
a.! (A1)!Identify!the!problem!to!be!solved.!
b.! (A2)!Design!two!reliable!experiments!that!solve!the!problem.!
c.! Draw!a!sketch!of!your!experimental!designs.!
d.! (A7)!Choose!a!productive!mathematical!procedure!for!solving!the!problem.!Use!a!freeL
body!diagram!to!help!solve!the!problem!where!applicable.!
e.! (A3)!Discuss!how!you!will!use!the!available!equipment!to!make!the!measurements.!
f.! (A8)!Identify!the!assumptions!made!in!using!the!mathematical!procedure.!
g.! (A9)!Determine!specifically!the!way!in!which!assumptions!might!affect!the!results.!
h.! What!are!the!possible!sources!of!experimental!uncertainty?!How!could!you!minimize!
them?!
!
Perform!the!experiments.!
!
i.! Record!the!outcome!of!your!experiments.!
j.! (A4)!Make!a!judgment!about!the!results!of!your!experiments.!
k.! (A5)!Evaluate!your!results!by!comparing!the!two!independent!methods.!Use!your!
uncertainty!to!make!an!explicit!comparison!of!the!two!values!you!obtained!for!the!
moment!of!inertia.!
l.! What!are!possible!reasons!for!the!difference?!If!you!have!a!large!difference!between!
your!values,!reLcheck!your!work.!Did!you!account!for!all!of!the!energy?!
m.! Which!experiment!was!more!accurate!and!why?!
n.! (A6)!Identify!the!shortcomings!in!the!experiments!and!suggest!and/or!carry!out!
improvements.!
Physics'9A'Lab'9:'Extended'Bodies'
Most!relevant!text!references:!Chap.!11,!Secs.!9.1L9.3.!
!
I.'Background'Information:'TORQUE'
When!we!advance!from!“point!particles”!to!rigid!objects!that!occupy!space,!and!which!can!
therefore!experience!forces!at!different!places,!analysis!of!motion,!or!lack!thereof,!must!
consider!not!only!force,!but!torque—the!rotational!analog!of!force.!Your!text!has!a!detailed!


discussion,!but!in!a!nutshell,!the!torque! τ !that!force! F !exerts!on!an!object!is!given!by:!
!
!
  
τ =r ×F
τ = rF sin θ !
or

where! r !is!a!vector!from!the!rotation!axis,!which!you!choose,!to!the!point!where!the!force!
is!applied.!As!an!example,!consider!the!figure,!showing!a!uniform!bar!of!10N!weight,!with!a!
frictionless!pivot!at!its!left!end!and!a!string!pulling!horizontally!outward!at!its!right!end.!
!
60°
F
!
!
Your!TA!will!discuss!how!to!determine!the!force!F.!This!would!be!a!good!time!to!ask!any!
questions!you!might!have!about!the!concept!of!torque.!
!
!
II.'Application'Experiment:'Statics'
!
An!engineering!firm!regularly!uses!structural!elements!connected!endLtoLend!by!pivoting!
links!and!in!static!equilibrium.!You’re!applying!for!a!summer!position!and!they!pose!a!task!
for!you.!Two!identical!symmetric!beams!of!known!mass!can!pivot!at!their!outer!ends!and!
are!connected!to!each!other!at!their!inner!ends!by!another!pivot.!One!beam!is!horizontal,!
while!the!other!makes!an!angle!with!the!vertical!measured!to!be!somewhere!in!the!range!
20L25°.!Your!task:!Does!the!force!the!beams!exert!on!each!other!satisfy!the!wellLknown!
static!equilibrium!conditions!for&each&object;!does!it!explain!why!each!should!not!rotate?!
You!have!two!essentially!identical!beams!with!holes!at!their!ends,!where!a!bent!paperclip!
makes!a!splendid!pivot,!a!meterstick,!a!scale,!a!plumb!bob,!a!goniometer/protractor,!
weights!and!a!rubber!band!to!stretch!from!one!beam/paperclip!to!the!other.![Note:!If!you!
happen!to!run!into!a!relationship!of!the!form! sin(β − α ) = asin α cos β ,!it!can!be!rearranged!to!
tan(β ) = (a + 1)tan(α ) .]!
!
All!bullets!must!be!addressed!in!your!lab!writeLup,!and!a!random!subset!will!be!graded.!
!
a.! (A2,!A3)!Design!a!reliable!experiment!to!solve!the!problem,!and!discuss!how!you!will!
use!the!available!experiment!to!make!the!measurements.!
b.! Draw!a!clearly!labeled!diagram!of!your!experimental!setLup.!Make!sure!you!represent!
the!important!aspects!of!your!experiment.!!
c.! Draw!freeLbody!diagrams!of!the!beams.!Include!an!appropriate!set!of!coordinate!axes.!
d.! (A7)!Choose!a!productive!mathematical!procedure!for!solving!the!problem.!Use!your!
freeLbody!diagrams.!!
e.! (A8)!Identify!the!assumptions!made!in!using!the!mathematical!procedure.!
f.! What!are!the!possible!sources!of!experimental!uncertainty?!How!could!you!minimize!
them?!
!
Perform!the!experiment.!
!
g.! Record!the!outcome!of!your!experiments.!
h.! (A4)!Make!a!judgment!about!the!results!of!your!experiment.!
i.! (A6)!Identify!the!shortcomings!in!the!experiments!and!suggest!specific!improvements.!
!
!
III.'Observation'Experiment:'Angular'Acceleration'
!
You!are!given!a!rotating!wheel,!tape!to!mark!the!location!of!a!point!on!the!wheel,!a!ruler,!
and!a!stop!watch.!Design!an!experiment!to!determine!the!average!angular!acceleration!due!
to!friction!and!air!resistance!in!the!wheel.!Determine!if!this!value!is!dependent!or!
independent!of!the!initial!angular!velocity!of!the!wheel.![Note:!Please&ensure&that&any&string&
on&the&wheel’s&hub&is&taped&or&tied&so&that&it&doesn’t&come&loose—it!isn’t!used!in!this!lab.]!
!
All!bullets!must!be!addressed!in!your!lab!writeLup,!and!a!random!subset!will!be!graded.!
!
a.! (O2)!Design!a!reliable!experiment!that!will!investigate!the!phenomenon.!!
b.! (O3)!Decide!what!is!to!be!measured!and!identify!independent!and!dependent!variables.!
c.! (O4)!Briefly!describe!how!you!will!make!use!of!the!available!equipment!to!make!your!
measurements,!explaining!explicitly!how!you!plan!to!find!angular!acceleration!from!
your!data.!!
!
Perform!the!experiment(s).!
!
d.! Record!your!data!in!an!appropriate!format.!
e.! Determine!the!average!angular!acceleration!of!the!wheel.!
f.! From!your!data,!discuss!the!relationship!between!the!initial!angular!velocity!and!the!
angular!acceleration!of!the!wheel.!
g.! (O8)!Devise!an!explanation!for!the!relationship!you!observed!in!your!data.!
h.! (O6)!Identify!shortcomings!of!your!experimental!design!by!listing!the!sources!of!
experimental!uncertainty.!Describe!improvements!you!could!and/or!did!make!to!
minimize!them.!
!