Physics 11Date: ______

UNIT 1: Mathematics for Physics 11

Physics is essentially the study of the physical universe. It is the most basic and fundamental science. Mathematics is often developed to deal with Physics problems e.g. calculus. Physicists study the movement of objects, energy, the forces in nature and a wide variety of natural phenomena.

Physicists use a variety of techniques to study the natural world. Typically, physicists try to create explanations that allow us to predict how nature behaves e.g. an equation or formula.

Part A: SI Units.

Physics involves lots of measurements and calculations. The most common measurement system that you will see in physics are the centimeter-gram-second (CGS) and the meter-kilogram-second (MKS) systems. Together these two systems are called the SI system (Systeme International d’Unites).

Units of Measurement in the CGS System
Measurement / Unit / Abbreviation
Length / Centimeter / cm
Mass / Gram / g
Time / Second / s
Force / Dyne / dyne
Units of Measurement in the MKS System
Measurement / Unit / Abbreviation
Length / meter / m
Mass / kilogram / kg
Time / second / s
Force / Newton / N
Energy / Joule / J
Pressure / Pascal / Pa
Electric current / ampere / A
Magnetism / Tesla / T
Electric Charge / Coulomb / C

Part B: Conversions.

Forthis class,youshouldtohaveknowledgeofthemetric (decimal)systemconversionfactors.

Multiplication Factor / SIPrefix / SISymbol
1,000,000=106 / mega / M
1,000=103 / kilo / k
100=102 / hecto / h
10=101 / deka / da
.1=10-1 / deci / d
.01=10-2 / centi / c
.001=10-3 / milli / m
.000001=10-6 / micro / µ

Table1. SImultiplicationfactorsandprefixes

Abrieflist ofcommonly usedconversionfactorsis providedbelow. Forfurtherinformation,refertoCarter,D.R. (1989).SI: Theinternational systemofunits.InNordinFrankel,BasicBiomechanicsoftheMusculoskeletal System,Philadelphia: Lea & Fibinger, pp. xvii-xxiii.

360degree=1revolution=6.283radians

1inch / = / 2.54cm
1foot / = / 0.3048m
1yard / = / 0.9144m
1mile / = / 1609m
1lb. / = / 4.448N

Unit Analysis:

Example 1: Convert 520 m to km.

Example 2: Convert 3.4 days into minutes.

Example 3: Convert 4.6 km/h to m/s.

  1. Convert the given measurement to the appropriate unit.

a)17 000 m =______km

b) 2.54 cm =______m

c) 4.6 g =______kg

d) 1 day =______s

e) 9000 s=______h

  1. Calculate the following:

a) 1.05 m + 5 cm =______m

b) 600 g + 1.5 kg - 400 g =______g

c) 2.5 cm x 3.6 cm x 9.1 cm=______cm3

d) 100 m3 6.25 m=______

  1. Convert the following:

a) 5 m/s to km/hb) 62 km/h to m/s

Part C: Precision & Accuracy

Precision-Precisionmeasuresthe agreementbetweenresults of

repeatedexperiments.It refersto the uncertaintyin a measurement. Thelesstheuncertainty(moresigfigs),thehighertheprecision.

e.g.measurementsof3.142,3.139,and3.140indicategood

precision.Butifthestandardvalueforthemeasuredquantity is2.9345,thenthemeasurementsaresaidtobehavepoor

accuracy.

Accuracy-Accuracymeasurestheagreementbetweena measurementandtheacceptedstandardvalue.

e.g.measurementsof7.1,7.2,and7.3indicategoodaccuracy(the averageis7.2)iftheacceptedvalueis7.21.Inthiscasethe

precisionispoor.

e.g.measurementsof2.139,2.138,and2.137indicategood

accuracyandgoodprecisioniftheacceptedvalueis2.1379.

Part D: Significant Figures

Whenwemakeameasurementthereisalwaysanerroror

uncertaintyassociatedwiththemeasurement. Forexamplewemay measurethelengthofaboxusingameterstickruledincentimeters. Thelengthisfoundtobeabout57cm.Wewrite57±0.5cm.The

uncertaintyisforourpurposes(our rule of thumb),one-halfofthe smallestunitonthemeasuringdevice(Peoplewithgoodeyesightmight giveanuncertaintyof0.25cm).Thismeansthattheboxhasalength of between56.5and57.5cm.Themeasurementissaidtohavetwo

sig-figsor significant figures.Ifwemeasurethelengthusinga meterstickruledinmmwegetamoreprecisemeasurementwitha smalleruncertainty.Wemayfindalengthof568±0.5mm.This measurementhasthreesigfigs.

RULES FOR ‘SIG FIGS’

1.Any non-zero number counts: a) 4563 sig figsb) 0.97234 sig figs

2.Zeros to the left of a decimal count.

690.3 sig figs

6902 sig figs no decimal

3.Zeros to the right of a decimal are tricky. If there are numbers to the left of a zero, they

count, otherwise ignore them…

67.004 sig figs67.00016 sig figs

0.000352 sig figs0.003053 sig figs

0.0089004 sig figs

Additional Questions:

1. How many significant figures are in the following numbers?

a) 425b) 1.2

c) 25.2d) 6.3706

e) 8.11002f) 2500

g) 450,000h) 5080.

i) 0.00897j) 0.1000

k) 7.01 x 103l) 7.00 x 10-4

m) 0.0089700

2)Roundthefollowingtotwosigfigs.

a) 18.3 b) 2.851 c) 0.276 d) 3.45 e) 1.549

3)Roundthefollowingtothreesigfigs.

a) 15360 b) 6.845 c) 0.02538 d) 1.6349 e) 15.65

How do you express your answer in Physics 11?

Simply round your answer to three sig figs. To maintain accuracy we should always carry an additional sig fig through our calculations until we are at our answer. Compute the following:

a)14.5 + 3.275 – 0.21 =b) 147 – 12.4 + 0.004 =

c) 45 x 17.3 =d) 17.3 / 32.75 =

e) (43)(12.7) f) 17.9

(63.4)(.041) (.05)(2.32)

g) 23.4 + 35h) 17.3 – (13.2)(4)

(3.2)(.54) (6.2)(-3.21)

Answer the following:

1)MauriceGreeneranthe100.00meterdashinarecordtimeof

9.79s.Calculatethevelocityin km/hr.

2)IanThorpesetaworldrecordinswimmingthe400.00mfreestyle inatime3:41.33s.Calculatethespeedinkm/hr.