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Lecture 1 Measurement & Units. Physical quantities (in mechanics) Basic quantities : in mechanics the three fundamental quantities are Length (L), mass (M), time (T)

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slide1

Lecture 1

Measurement & Units

General physics I, lec 1 By: T.A.Eleyan

slide2

Physical quantities (in mechanics)

Basic quantities : in mechanics the three fundamental

quantities are

Length (L), mass (M), time (T)

Derived quantities : all other physical quantities in mechanics can be expressed in term of basic quantities

Area

Volume

Velocity

Acceleration

Force

Momentum

Work

…..

…..

General physics I, lec 1 By: T.A.Eleyan

slide3

Mass

The SI unit of mass is the Kilogram, which is defined as the mass of a specific platinum-iridium alloy cylinder.

Time

The SI unit of time is the Second, which is the time required for a cesium-133 atom to undergo 9192631770 vibrations.

Length

The SI unit of length is Meter, which is the distance traveled by light is vacuum during a time of 1/2999792458 second.

General physics I, lec 1 By: T.A.Eleyan

slide4

Systems of Units

  • SI units (International System of Units):
    • length: meter (m), mass: kilogram (kg), time: second (s)
  • *This system is also referred to as the mks system for meter-kilogram-second.
  • Gaussian units
    • length: centimeter (cm), mass: gram (g), time: second (s)
  • *This system is also referred to as the cgs system for centimeter-gram-second.
  • British engineering system:
  • Length: inches, feet, miles, mass: slugs (pounds), time: seconds

We will use mostly SI units, but you may run across some problems using British units. You should know how to convert back & forth.

General physics I, lec 1 By: T.A.Eleyan

conversions
Conversions

When units are not consistent, you may need to convert to

appropriate ones.

Units can be treated like algebraic quantities that can cancel each other out.

1 mile = 1609 m = 1.609 km

1 ft = 0.3048 m = 30.48 cm

1 in = 0.0254 m = 2.54 cm

1m = 39.37 in = 3.281 ft

1 mile = 5280 ft

  • Questions:
  • Convert 500 millimeters into meters.
  • Convert 4.2 liters into milliliters.
  • Convert 1.45 meters into inches.
  • Convert 65 miles per hour into kilometers per second.

Example: Convert miles per hour to meters per second:

General physics I, lec 1 By: T.A.Eleyan

prefixes
Prefixes

Prefixes correspond to powers of 10

Each prefix has a specific name/abbreviation

Power Prefix Abbrev.

1015 peta P

109 giga G

106 mega M

103 kilo k

10-2 centi P

10-3 milli m

10-6 micro m

10-9 nano n

10-12 pico p

10-15femto f

Distance from Earth to nearest star 40 Pm

Mean radius of Earth 6 Mm

Length of a housefly 5 mm

Size of living cells 10 mm

Size of an atom 0.1 nm

General physics I, lec 1 By: T.A.Eleyan

slide7

Dimensional Analysis

Definition: The Dimension is the qualitative nature of

a physical quantity (length, mass, time).

brackets [ ] denote the dimension or units of a physical quantity:

General physics I, lec 1 By: T.A.Eleyan

slide8

Idea:Dimensional analysis can be used to derive or check formulas by treating dimensions as algebraic quantities.

Quantities can be added or subtracted only if they have the same dimensions, and quantities on two sides of an equation must have the same dimensions.

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

left hand side

right hand side

This equation is correct because the dimension of the left and right side of the equation have the same dimensions.

General physics I, lec 1 By: T.A.Eleyan

slide9

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 rnvm

Where k is the proportionality constant of dimensionless unit.

The right hand side [a] = L/T2

The left hand side

Therefore

or

General physics I, lec 1 By: T.A.Eleyan

slide10

Hence

n+m=1             and       m=2

 Therefore

n =-1

and the acceleration a is

                        a = k r -1v2

Problem:

1. Show that the expression x = vt +1/2 at2 is dimensionally correct , where x is coordinate and has unit of length, v is velocity, a is acceleration and t is the time.

2. Show that the period T of a simple pendulum is measured in time unit given by

General physics I, lec 1 By: T.A.Eleyan

density
Density

Every substance has a density, designated  = M/V

Dimensions of density are, units (kg/m3)

  • Some examples,

Substance (103 kg/m3)

Gold 19.3

Lead 11.3

Aluminum 2.70

Water 1.00

General physics I, lec 1 By: T.A.Eleyan

atomic density
Atomic Density

In dealing with macroscopic numbers of atoms (and similar

small particles) we often use a convenient quantity called Avogadro’s Number, NA = 6.023 x 1023 atoms per mole

Commonly used mass units in regards to elements

1. Molar Mass = mass in grams of one mole of the substance (averaging over natural isotope occurrences)

2. Atomic Mass = mass in u (a.m.u.) of one atom of a substance.

It is approximately the total number of protons and neutrons in one atom of that substance.

1u = 1.660 538 7 x 10-27 kg

What is the mass of a single carbon (C12) atom ?

= 2 x 10-23 g/atom

General physics I, lec 1 By: T.A.Eleyan