Phy 1010 lec (1).pptx

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Physical Quantities, Units and Measurement Physical Quantities, Units and Measurement

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Introduction

what is physics

The dictionary definition of physics is “the study of matter, energy, and the interaction between them”, but what that really means is that physics is about asking fundamental questions and trying to answer them by observing and experimenting. Physicists ask really big questions like:

How did the universe begin? How will the universe change in the future? How does the Sun keep on shining? What are the basic building blocks of matter?

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PHYSICAL QUANTITIES

•

A quantity that can be measured.

•

A physical quantities have numerical value

and unit of measurement.

•

For example temperature 30 degrees

celcius, 30 is numerical value & ‘degree

celcius’ is the unit. Written as 30

o

C

.

Temperature = 30 degree Celcius = 30o c

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*The physical quantities can be classified into base

quantities

and derived quantities.

1-Base Quantities

are physical quantities that cannot

be derived from other physical quantities.

There are

seven base quantities

:

length mass time current

temperature,

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BASE QUANTITIES

•Scientific measurement using SI units (International System

Units).

Base Quantities Symbol SI Unit Symbol of SI unit

Length L meter m

Mass m kilogram kg

Time t second s

Temperature T Kelvin K

Electric current I ampere A

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• 2-Derived Quantities :are physical quantities derived from

combination of base quantities through multiplication or division or both.

Derived Quantities Symbol Relationship with base quantities Derived units

Area A Length x Length m2

Volume V Length x Length x Length m3

Density ρ Mass

Length x Length x Length kg/m

3

Velocity v Displacement

Time m/s

Acceleration a Velocity

Time m/s

2

Force F Mass x Acceleration N

Work W Force x Displacement J

Energy Ep

Ek

Mass x gravity x high =

½ x mass x velocity x velocity J

Power P Force x Displacement

Time W

Pressure p Force

Area N/m

2

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• Vector quantities are quantities that have both

magnitude and direction

Magnitude = 100 N

Direction = Left A Force

The physical quantities can be classified into

Scalars and Vectors

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• Scalar quantities:

are quantities that have magnitude only.

Two examples are shown below:

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Mass

:

The amount of matter in a body.

• SI Units: kilogram (kg)

• Common Units:

pounds (lbs) and ounces (oz) 1 kg is approx. 2.2 lbs

1 kg = 1000 g 1 oz = 28.35 g

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Length: A measure of distance.

• SI Unit: meter (m)

• Common Units: inches (in); miles (mi) 1 in = 2.54 cm = 0.0254 m

1 mi = 1.609 km = 1609 m

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Volume: Amount of space occupied by a body.

• SI Unit: cubic meter (m3₎

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Density: Amount of mass per unit volume of a substance.

•_{SI Units:}_kg/m3

•_{Common Units:}_g/cm3_{or g/mL}

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International system SI Unit (m K s)

International system (c g s) Unit

International system (f b s) Unit

Measuring Systems

Length

Mass

time

Meter m

Kilogram Kg

Second S

centimeter cm

Gram g

Second S

Foot ft

Bound b

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1.2 SI Units

• _{Example of derived quantity: area}

Defining equation: area = length × width

In terms of units: Units of area = m × m = m2

Defining equation: volume = length × width × height

In terms of units: Units of volume = m × m × m = m3

Defining equation: density = mass ÷ volume

In terms of units: Units of density = kg / m3_{= kg m}−3

L

W

H

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1.2 SI Units

• _{Work out the derived quantities for:}

Defining equation: velocity =

In terms of units: Units of speed = m/s

Defining equation: acceleration =

In terms of units: Units of acceleration = m/s2

Defining equation: force = mass × acceleration

In terms of units: Units of force = Kg m/s2

time

nt

displaceme

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Defining equation: Work = Force x Displacement

In terms of units: Units of Work = J = Kg m2_/s2

1.2 SI Units

Defining equation: Energy = Mass x gravity x high

In terms of units: Units of Energy = J = Kg m2_/s2

Defining equation: Power = Force x displacement / time

Defining equation: Pressure = Force / area

In terms of units: Units of Power = W = Kg m2_/s3

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Temperature

:

is the measure of how hot or cold an object is.

• _{SI Unit: Kelvin (K)}

• Common Units: Celsius (ºC) or Fahrenheit (ºF)

Converting between K , ºC and ºF:

T

_K

= T

_C

+273.15

T

_C

= T

_K

– 273.15

T

_F

= 9/5 T

_C

+ 32

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“When the thermometer is held in the mouth or under the armpit of a living man in good health” it indicates 98 F

Black board example 19.1

a) What is the temperature in Celsius (centigrade)?

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PREFIXES

• Prefixes :

• are used to simplify the

description of physical

quantities that are either very big or very small.

Prefix Symbol Value

Peta P 1015

tera T 1012

giga G 109

mega M 106

kilo k 103

hekto h 102

deka da 10

deci d 10-1

centi c 10-2

milli m 10-3

micro _m 10-6

nano n 10-9

pico P 10-12

Femto F 10-15

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STANDARD FORM

Standard form or scientific notation is used to express magnitude in

a simpler way. In scientific notation, a numerical magnitude can be written as : A x 10n_, _{where 1 ≤ A < 10 and}_n_{is an integer}

For each of the following, express the magnitude using a scientific notation.

1-20000000 2-345000 3-0.0000023 4-0.00000006 5-123402123100 Solution:

1- 2x 107 2- 345x 103

3- 23x 10-6

4- 6x 10-8

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Dimensional Analysis

The word dimension in physics indicates the physical

nature of the quantity. For example the distance

has a dimension of

length

, and the speed has a

dimension of

length

/

time

.

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Example

Using the dimensional analysis check that this equation x = ½

at2_{is correct, where} _x_{is the distance,}_a_{is the acceleration} and t is the time.

Solution

x

= ½

at

2

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Example

Show that the expression

v =

v

_o

+ at is dimensionally

correct, where v and v

_o

are the velocities and a is the

acceleration, and t is the time

Solution

The right hand side

[

v

] = L/T

The left hand side

L/T + L/T

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Example

Suppose that the acceleration of a particle moving in circle of radius r with uniform velocity v is proportional to the rn and vm. Use the dimensional analysis

to determine

the power n and m.

Solution

Let us assume a is represented in this expression

a

=

k r

n

v

m

Where k is the proportionality constant of dimensionless unit. The right hand side

n+m=1 and m=2 Therefore. n =-1 and the acceleration a is

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Exercise

Part A:

See if you can determine the dimensions of the following quantities:

volume

acceleration (velocity/time) density (mass/volume)

force (mass × acceleration) charge (current × time)

Check your answers

You are correct if you wrote down:

1.Volume L3

2.acceleration (velocity/time) L/T2

3.density (mass/volume) M/L3

4.force (mass × acceleration) M·L/T2

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answers

1. pressure (force/area) M·L-1·T-2

2. (volume)2 _L6

3. work (in 1-D, force × distance) M·L2_/T2

4.

energy (e.g., gravitational potential energy = mgh = mass × gravitational acceleration × height)

M·L2_/T2

Now find the dimensions of these:

1.pressure (force/area) 2.(volume)2

3.work (in 1-D, force × distance)

4.energy (e.g., gravitational potential energy = mgh

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Which one of the following quantities are dimensionless?

1

-68

2

-sin

(68 )

3

-e

4

-force

5

-6

6

-frequency

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What are the dimensions of the following?

1.[sin (

w

t)]

2.[3]

3.[force]

4.[height]

5.[frequency]

Check your answers