lower 6 chapter 1 dimensions and units

8/9/2019 Lower 6 CHAPTER 1 Dimensions and Units

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1.0 PHYSICAL QUANTITIES1.0 PHYSICAL QUANTITIES

AA base quantitybase quantity

is :is :

a physical quantitya physical quantity

which cannot bewhich cannot be

defined in terms ofdefined in terms of

other physicalother physical

quantities.quantities.

A derived quantityA derived quantity

is :is :

a physical quantitya physical quantity

that combines basethat combines base

quantity either byquantity either by

multiplication ormultiplication or

divisiondivision


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1.1 LIST OF 5 BASIC QUANTITIES, UNITS AND

DIMENSIONS

Base quantityBase quantity

SymbolSymbol

forfor

quantityquantity

S.I. UnitS.I. UnitSymbol forSymbol for

S.I. UnitS.I. UnitDimensionsDimensions

LengthLength

MassMass

TimeTime

Electric currentElectric current

TemperatureTemperature


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volume

massensityd !

time

ntdisplacemeelocityv !

time

velocityinchangeonaccelerati !

area

forcepressure!

1.3 DETERMINE THE DERIVED UNIT FOR THE FOLLOWING

DERIVED QUANTITIES.

Derived quantityDerived quantityFormulaFormula

DerivedDerivedunitunit

Name ofName ofderivedderived

unitunit

DimensionDimension

areaarea area = length x widtharea = length x width m x m = mm x m = m22

volumevolumevolume = length x widthvolume = length x width

x heightx height

m x m x mm x m x m

= m= m

33

densitydensity

velocityvelocity

momentummomentummomentum = mass xmomentum = mass x

velocityvelocitykg m skg m s--11

AccelerationAcceleration

ForceForceforce = mass xforce = mass x

accelerationaccelerationkg m skg m s--22

NewtonNewton

(N)(N)

pressurepressure


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1.4 Examples1.4 Examples

i) Experiment indicates that the speed c depends oni) Experiment indicates that the speed c depends on

acceleration g , wavelengthacceleration g , wavelength PP and densityand density ..

C = k gC = k g x PP y z

Given k is a dimensionless constant ,

But x, y and z are numerical values.

Find the values of x, y and z


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SolutionsSolutions

[LT[LT--1] = k[LT1] = k[LT--22]] xx . [L]. [L] yy . [ML. [ML--33]] zz

[L] : 1 = x + y[L] : 1 = x + y 3z3z

[T] :[T] : --1 =1 = -- 2x2x[M] : 0 = z[M] : 0 = z


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TutorialTutorial

ii)ii) The period of a loadThe period of a load

of mass m suspendedof mass m suspended

by a spring oscillatesby a spring oscillates

with a period given bywith a period given by

T = 2T = 2TT ( m/k ) ( m/k )

Find the dimension ofFind the dimension ofk ?.k ?.

iii)iii) Specific heat capacitySpecific heat capacity

c is defined as heatc is defined as heat

supplied to raise unitsupplied to raise unit

mass of a substancemass of a substanceper unit degree rise inper unit degree rise in

temperature.temperature.

What is the dimensionWhat is the dimension

of c?.of c?.


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Tutorial (continued.)Tutorial (continued.)

iv) The period T of a simple pendulumiv) The period T of a simple pendulum

depends on the lengthdepends on the length ^^ , mass m and, mass m and

acceleration due to gravity g.acceleration due to gravity g.

Use dimension analysis to obtain an equationUse dimension analysis to obtain an equation

for the period T of a simple pendulumfor the period T of a simple pendulum


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1.5 SCALAR AND VECTOR1.5 SCALAR AND VECTOR

QUANTITIESQUANTITIES SCALAR QUANTITYSCALAR QUANTITY

is a physical quantity thatis a physical quantity thatrequires only magnituderequires only magnitude

Examples:Examples:

VECTOR QUANTITYVECTOR QUANTITY

is a physical quantity thatis a physical quantity thatis represented by bothis represented by both

magnitude and direction.magnitude and direction.

Examples:Examples:


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1.6 Applications1.6 Applications

RESOLUTION OF FORCESRESOLUTION OF FORCES

There are 3 types:There are 3 types:

1.1. Two forces in the same direction:Two forces in the same direction:

F = FF = F11 + F+ F22 2.2. Two forces in the opposite direction:Two forces in the opposite direction:

F = FF = F11 FF22

3.3. Two forces perpendicular to one another:Two forces perpendicular to one another:

FF 22 == FF1122 ++ FF22

22

TanTan UU == FF11 / F/ F22


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Applications ( continued .)Applications ( continued .)

4.4. Two forces parallel to one another:Two forces parallel to one another:

(Apply Law of parallelogram in polygon)(Apply Law of parallelogram in polygon)


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1.7 Tutorial1.7 Tutorial


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1.8 FORCES IN EQUILIBRIUM1.8 FORCES IN EQUILIBRIUM

i. (Example of 3 forces)i. (Example of 3 forces)


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1.8 ii. Two perpendicular forces1.8 ii. Two perpendicular forces

Fx = F cosFx = F cosUU

Fy = F sinFy = F sinUU

UU is an angle betweenis an angle between

the force F to thethe force F to the

horizontal linehorizontal line

the sign of the forcethe sign of the force

depend on the quadrantdepend on the quadrantwhere the force , F iswhere the force , F is

placedplaced

y


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1.8 iii. Example(continued)1.8 iii. Example(continued)

Find theFind the

values of Pxvalues of Pxand Py forand Py for

thethe

followingfollowing

figures.figures.


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1.8 iv. Example (continued)1.8 iv. Example (continued)

a)a) Draw a triangle ofDraw a triangle of

forces.forces.

(b)(b) Calculate the valueCalculate the valueofof

(i)(i) MM

(ii)(ii) NN


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1.8 v. Example(continued)1.8 v. Example(continued)

What is the

magnitude andthe direction of

the resultant

force acting on

the trolley.


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1.8 vi. Example(continued)1.8 vi. Example(continued)

Calculate theCalculate the

magnitude ofmagnitude of

the resultantthe resultantforce acting onforce acting on

the trolley.the trolley.


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1.8 vii. Example (continued)1.8 vii. Example (continued)

A = W sinA = W sin UU

B = W kosB = W kos UU


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1.8 viii Applications1.8 viii Applications

(Find the resultant force )(Find the resultant force )


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ERRORSERRORS

PrecisionPrecision is the degreeis the degree

of a measuringof a measuring

instrument to recordinstrument to record

consistent reading forconsistent reading for

each measurement by theeach measurement by the

same way.same way.

AccuracyAccuracy is the degreeis the degree

of closeness of theof closeness of the

measurements to themeasurements to the

actual or accepted valueactual or accepted value

Sensitivity is the degree of a measuring instrument to record small

change in its reading.


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ERRORSERRORS


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Sources of systematic errors are:Sources of systematic errors are:

(i)(i) Zero errors or end errorsZero errors or end errors

Zero errors occurs when the instrument givesZero errors occurs when the instrument givesa nona non-- zero reading when in fact the actualzero reading when in fact the actualreading is zero.reading is zero.

(ii)(ii)Personal error of the observer.Personal error of the observer.

Physical constraints or limitations of thePhysical constraints or limitations of theobserver can cause systematic errors.observer can cause systematic errors.

An example is the reaction time.An example is the reaction time.

(iii)(iii) Errors due to instrumentsErrors due to instrumentsExample:Example:

A stopwatch which is faster than normalA stopwatch which is faster than normalwould give readings which are always largerwould give readings which are always larger

than the actual time.than the actual time.


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ERRORSERRORS

The main source of random error isthe observer or has non -constantsize of error and is unpredictable.


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ERRORS & ACCURACYERRORS & ACCURACY

Example for time:Example for time:

t =t = 2.12.1 ss 0.1 s0.1 s

Percentage errors =Percentage errors =

size of errorsize of error x 100 %x 100 %size ofsize of

measurementmeasurement

Uncertainty/

absolute error

Measured

value

lower 6 chapter 1 dimensions and units

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