Physics And Measurement

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Learning outcomesBy the end of the chapter, students should be able to:

LO1:

Use appropriate prefixes in calculations.

LO2:

Manipulate the dimensional analysis to determine the S.I unit of physical quantity, homogeneity of an equation and to construct an equation

LO3:

Perform unit conversions.2

Subtopics for chapter 1

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Introduction: Importance of Physics1. Physics is the fundamental of Sciences and

Engineering.2. Physics provides important information to

support Engineering Applications.

6 Major Areas of Physics1. Classical Mechanics 2. Relativity3. Thermodynamics4. Electromagnetism5. Optics6. Quantum Mechanics

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Introduction: Overlapping FieldsIn many research areas there is a

great deal of overlap among physics, chemistry, and biology.

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Evidence for this overlap is seen in the names of some subspecialties in science• biophysics, • biochemistry,• chemical physics,• biotechnology, and so on.

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No measurement is exact; there is always some uncertainty due to limited instrument accuracy and difficulty reading results.

Introduction: Measurement and Uncertainty

1.1 Standard and Units

Any number that is used to describe a physical phenomenon quantitatively is called physical quantity

The most common unit used by scientists and engineers around the world is International System, SI.

It is commonly called the “metric system”, but since 1960, it is known as International System, or SI (abbreviation for its French name, Système International).

1.1 Standard and Units: Fundamental Quantities and Their Units

Quantity SI Unit

Length meter

Mass kilogram

Time second

Temperature Kelvin

Electric Current Ampere

Luminous Intensity Candela

Amount of Substance mole

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1.1 Standard and Units:Quantities Used in MechanicsIn mechanics, three fundamental (Basic) quantities are used

LengthMassTime

Will also use derived quantitiesThese are other quantities that can be expressed in terms of the basic

quantitiesExample: area, speed, volume, densityArea is the product of two lengths

Area is a derived quantityLength is the fundamental quantity

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1.1 Standard and Units :LengthLength is the distance between two points in space.

UnitsSI – meter, m

Defined in terms of a meter – the distance traveled by light in a vacuum during a given time

One meter is defined as the distance that light travels in a vacuum in 1/299,792,458 second.

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1.1 Standard and Units: MassUnits

SI – kilogram, kg

Defined in terms of a kilogram, based on a specific platinum–iridium alloy cylinder kept at the International Bureau of Weights and Measure , France.

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1.1 Standard and Units :TimeUnits

seconds, s

Defined in terms of the oscillation of radiation from a cesium atomic clock.

One second is defined as the time required for 9,192,631,770 cycles of the microwave radiation to change the energy state of the cesium atom.

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1.1 Standard and Units : Reasonableness of ResultsWhen solving a problem, you need to check your answer

to see if it seems reasonableReviewing the tables of approximate values for length,

mass, and time will help you test for reasonablenessE.g., is the result 3 min = 180 sec reasonable? Yes, since the second is a smaller unit than the

minute, so there’re more seconds than minutes in same time interval.

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1.1 Standard and Units : The British systemThese units are used only in the US and a few other

countries.British units are now officially defined in terms of SI

units:

1 inch = 2.54 cm (exactly)

1 pound = 4.448221615260 newtons (exactly)British units are only used in mechanics and

thermodynamics; there is no British system of electrical units.

1.1 Standard and Units : US Customary System

Still used in the US, but text will use SI

Quantity Unit

Length foot

Mass slug

Time second

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1.1 Standard and Units : PrefixesPrefixes correspond to powers of 10We usually express multiples of 10 or 1/10 in exponential

notation: 1000 =103

1/1000 = 10-3

Each prefix has a specific name

Each prefix has a specific abbreviation

The prefixes can be used with any basic units

They are multipliers of the basic unit16

Unit prefixes Length

1 nanometer = 1 nm = 10-9 m 1 micrometer = 1 m = 10-6 m1 millimeter = 1 mm = 10-3 m1 centimeter = 1 cm = 10-2 m1 kilometer = 1 km = 103 m

Mass

1 microgram = 1 g = 10-6 g = 10-9 kg1 milligram = 1 mg = 10-3 g = 10-6 kg

1 gram = 1 g = 10-3 kgTime

1 nanosecond = 1 ns = 10-9 s1 microsecond = 1 s = 10-6 s1 millisecond = 1 ms = 10-3 s

.

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1.2 Dimensional Analysis: Basic Quantities and Their DimensionDimension has a specific meaning – it denotes the

physical nature of a quantity

Dimensions are denoted with square bracketsLength [L]

Mass [M]

Time [T]

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1.2 Dimensional Analysis: Dimensions and Units

Each dimension can have many actual unitsTable 1.5 for the dimensions and units of some derived

quantities

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1.2 Dimensional Analysis: Functions of Dimensional Analysisa. To determine the SI unit of any physical

quantity.

b. To check the homogeneity / consistency of an equation & to prove the validity of an equation.

c. To construct an equation.

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1.2 Dimensional Analysis: To prove the validity of an equation

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Show that the equation of v = u + at is homogen.

v = u + at

[LEFT HAND SIDE] [RIGHT HAND SIDE]=v = displacement / time

v = s / t

[v] = [s] / [t]

= L / T

= LT-1

u = displacement / time

u = s / t

[u] = [s] / [t]

= LT-1

= = at = acceleration x time

= =

[at] = [a] x [t]

DIMENSION comparison: LEFT HAND SIDE = RIGHT HAND SIDE

CONCLUSION: The equation is homogen / consistent

= ( [v] / [t] ) x [t]

= (LT-1 / T) x T

= = LT-1

1.2 Dimensional Analysis: To construct an equation.

Form the equation of period (T) for a simple pendulum in terms of mass of pendulum (m), length (l) and gravity (g).

1st STEP: Write the general relation of period, T α mx ly gz

2nd STEP: Write the general equation, T = k mx ly gz

3rd STEP: Write the dimensional form [T] = [k] [mx] [ly] [gz]

T = Mx Ly (LT-2)z 4th STEP: Write the dimensions

1.2 Dimensional Analysis: To construct an equation.

5th STEP: Compare Left Hand Side with the Right Hand Side of the equation

T = Mx Ly (LT-2)z OR T = Mx Ly Lz T-2z

6th STEP: We can write as:

T1 = T-2z (1)

M0 = Mx (2)

L0 = Ly Lz (3)

1 = -2z

0 = x

0 = y + z

7th STEP: From (1): z = -1/2

8th STEP: Insert z value into (3): 0 = y + (-1/2)

Therefore, y = 1/2

1.2 Dimensional Analysis: To construct an equation.9th STEP: From (2): we have x = 0

10th STEP: WE already have: x = 0 , y = ½, z = -1/2. Substitute the value into the equation of T.

T = k mx ly gz T = k m0 l1/2 g-1/2

T = k l1/2 g-1/2

T = k

Conversion of UnitsIn certain cases, you may need to convert units to

appropriate onesFor example :

1 mile =1609 m =1.609 km

1 ft =0.304 m = 30.48 cm

1 m =39.37 in. =3.281 ft

1 in. =0.0254 m = 2.45 cm (exactly )Units can be treated like algebraic quantities that can

cancel each other out

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1.3 Unit ConversionsAlways include units for every quantity, you can carry the

units through the entire calculationMultiply original value by a ratio equal to oneExample

Note the value inside the parentheses is equal to 1 since 1 in. is defined as 2.54 cm

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15.0 ?

2.5415.0 38.1

1

in cm

cmin cm

in

Exercise 1 A) Find the number of kilometer in 1.00 mile using the

conversion factors given.

Solution :Convert units from mi to kmGiven :

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B) Find the number of feet in 1.00 km Solution:Convert from km to ft

Exercise: Question 2According to the label on a bottle of a salad dressing, the volume of the contents is 0.473 liter (L). Using only the conversions 1 L = 1000 cm3 and 1 inch = 2.54 cm, express this volume in cubic inches.

Exercise: Question 3The density of lead is 11.3 g/cm . What is this value in kilograms per cubic meter?

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Exercise: Question 4How many years older will you be in 1.00 billion seconds from now? (Assume a 365-day year).

Exercise: Question 5The most powerful engine available for the Chevrolet Camaro developed 360 horsepower and had a displacement of 327 cubic inches. Express this displacement in liters (L) by using only conversions 1L = 1000 cm3 and 1 inch = 2.54 cm.

Exercise: Question 6A Honda fuel-efficient hybrid car gets gasoline mileage of 55.0 mpg (miles per gallon). (a)Express this mileage in km/L (L=liter). Use 1 mile = 1.609 km, 1 gallon = 3.788 L. (b)If this car’s gas tank holds 45 L, how many tanks of gas will you use to drive 1500 km?