Uncerttaint
Grastaiona Acceeraton values found Hom v vs t graph
9.792
t0.149
9.987
.744
+0.144
9.834
9.45)
9-319
9.381
9.78
9.387
+0.lol
t0.191
-0.112
-
524
o.262
+0 144
- 0.256
t0.133
9.75
9.819
to-l08
2.807
+0.1H
+0.lb4
9.7
t0.068
9.451
-0. 192
9.721
9.233
9.18
9.682
to. o78&
0.406)
t0.14
0.039
AValves are less than true valve bemuse of the
foce ofo
Averaqe Valae:
ress fance.
9.34me
o.198
Trve Value
Actual, , correct
Valwe
- Notaludoys Known
Ex: 9 .3Im/s
Measored Value
Va.lve actually measured
-Meosured valve sheuld be as close to troe vale as posible
Ex:
: 9.312 m/s
Erof
DiFfererce between true valve § mea sured value
-
Usval
ofected b ad8tona orces
object
on
meas ured a 1.192m
Ex epected 9.81 m/s
S here is an eof o
0.15m/s
ThinK abovt list Sources of errof in Conclusion
E:Meagured valve i
trve valve
This
0.1S /s
is
Value also nclvde
We
to
ertor
becawse
pudard
Less han t e
the measored
frce fon Ar D
design the experiments to have as tle
as
poSsible.
Ex: We drop a mall lacrosse ball
alLorqe
We con
bosketball so
never Completely
these s
instead o f
less Ar Drag
eliminale error.
Uncertoin
-Range of valvesafound the measured value
the esoipmt
to Show the limitochions
- Uncertainty range should include ttve valve
**ALL meosurecd value must have uncertalnty!\
Ex
4
9.63
0.s
ms
9.139y49Slo.3
Means trve valve is
Estmatinq Uncer tintg
Precisien o Eqiprent
Ptin mom uncer tainy rom precsion o egviphet
h
Solest ineriment of measure
Ex Rule
every Imm
mors
miniimu
vncerta
£o. Smm
Reai st.c vncertnty rom precsion o euipment
1s the Smalest inerement of meo5Ure
Ex
Ruler
mars every Im
vncer tony
Loctuotions
in
USe Siae
E
I mm
is
maas vred value
fluetoahon as
Scale fluctuaes
use Vncertatn
rom
oncer tain
1651 to
i.1g
186.4g
Physical Limitocions
Ex:
Stop
tme f2.73ss
of o. ols
precison gies vncertain ty
reads
wadch
a
Use
Computer
0.2sS
is
homon reoction time
vncertainy oft0.ls
Measvremens
Cannot
Must
use
-
of
presion
use
egupment
Measwrenems
Repeated
auerage vave
USe
- Find deviahton
and
0S
betueen
meosured
value
moasvred vaues
querage valve
Xi- Xaug
- Average Deviatia is
do
*For
a
use
Smal
Average Devatten
of
g
Uncerin
a large
on
e Stondord Devioi
:12X; -Xo
N
9.6t0.2 m
lood)
n
ofmeasvremets
3
as
meoufemends (
MAx devioto
9.6t o4 m
Use
ror
ero
looo)
All measvred
values have
vncertarnty
We want to o5se these measured valves
to get calcdated valbes
Ex
m:
99.4 o.4 m/
Weight mg 2.P4 56 N
For Calcooded value
We
in
each
Vowes
Propaaades Uncertinhy
ytuy
F%%)
uF
o.0o2 kg
Aeeneed to Ancd
that weqhls the
pro poaled uncertanty
Importanee of the oncerta.hy
meaured
0.286 t
calcvlated value
Partol Derwatoes
-
treat everythng else
os
Constant
Consder shet he deriva-hve $
g only
with
respect to
FlMy) 3y
3
:3
3y
Con s.
Constants (Notx)
32 x
Cons
12y*a
18*y"2
dy
Uncer tain
must be
certain unifs
in
meters
distance
X14.2 0.l cm
time
142t 0.0ol m
Seconds
Ongles
-
radians
63t 2
tE |.1ot o.o3 rad
kilbgramS
mass
0.28% t0.002
m 286 2 g
Ex:
0.
X
m: 0.18. t 0. boze
9.t o. »p*
Weight
uW
ma
2.3456N
J m Um
a)
M
dm
Cons
m
Const
N
gam)+(mu9
0.116 o . N
W- 2.1to.lN
k
m
Ex Cylinder
r 12.
h
olcm
0.124 t0.00 m
0.418
1.8to:lam
t 0.00Zm
V Trh
V T6.124 (01)=
,
Cons
th
Const
Const
u
rhur +(Tr uh
21Trh