BASIC PHYSICS AND MATERIALS - PHF110Science and Engineering Foundation Studies SEFS

Mike Walsh11 lectures:

1 – 3 Recording and analysing data

4 – 6 Basic Current Electricity

7 – 8 Resistors

9 – 11Capacitors

Rules of the Room

1. Be polite – don’t talk when someone else is speaking.

2. Respect others – don’t distract them from trying to learn [see rule 1]

3. Mobile phones – set them to silent [see rule 2]

4. Be prompt – don’t be late as this will cause a disturbance [see rule 2]

5. Engage in the lecture – respect your own ability to learn and enjoy the Physics, it’s really elegant when you get your head round it. [see all rules above]

1. Be polite – don’t talk when someone else is speaking.

2. Respect others – don’t distract them from trying to learn [see rule 1]

3. Mobile phones – set them to silent [see rule 2]

4. Be prompt – don’t be late as this will cause a disturbance [see rule 2]

5. Engage in the lecture – respect your own ability to learn and enjoy the Physics, it’s really elegant when you get your head round it. [see all rules above]

Objectives1. Know what the S.I. system of measurement is and explain why it is

required.

2. Recognise the term Dimensional Analysis and apply it correctly to scrutinize equations.

3. Explain how a prefix is used and how it is related to writing a measurement using standard form to an appropriate number of significant figures.

4. Demonstrate how values can be converted between non S.I. and S.I. units.

Working With PhysicsPhysics is concerned with developing models.

Like a map that allows us to find our way,

without us knowing what it really looks like.

Standard Units• Models in Physics are generally quantitative, i.e. involve calculations.• This means we need to measure things…

…and if different scientists in different countries don’t use the same system, experiments are not reproducible and could even be dangerous,

Add a pinch of explosiveFor a pretty effect!

Unfortunately “pinch” translates to “barrelful” in this scientists language!

not reproducible dangerous

What do I weigh?• In the UK we often state our weight in stones. I weigh about 12½ stone.

What does that mean to those who don’t know this system? What size stones…

This size ?

Or this size ?

Système International d’Unités• The French came to the rescue back in the Napoleonic era.• All scientists across the World now use the S.I. system.• The system consists of a set of base units:

Base SI UnitsQuantity

Name SymbolDimension

Symbol

Mass kilogram kg M

Length metre m L

Time second s T

Electric Current ampere A I

Temperature kelvin K θ

Luminous Intensity candela cd J

Amount of Substance mole mol N

• All other units are called derived units as they consist of different combinations of base units, e.g. a newton is a kilogram metre per second squared, [N] [kg m s–2]

1. Mass is responsible for inertia (the larger the mass the smaller the acceleration) of an

object.

2. Mass is responsible for the gravitational attraction of two bodies.

4. Mass can be measured by using scales to compare or balance

Mass

3. We can “feel” the mass of an object due to its weight (force due to

gravity).

Système International d’Unités

Base SI UnitsQuantity

Name SymbolDimension

Symbol

Mass kilogram kg M

Length metre m L

Time second s T

Electric Current ampere A I

Temperature kelvin K θ

Luminous Intensity candela cd J

Amount of Substance mole mol N

• The French came to the rescue back in the Napoleonic era.• All scientists across the World now use the S.I. system.• The system consists of a set of base units:

• All other units are called derived units as they consist of different combinations of base units, e.g. a newton is a kilogram metre per second squared, [N] [kg m s–2]

Length

Originally the length of a platinum-iridium bar supported in melting ice to give it a constant temperature and prevent deformation.This bar is still housed in Sevre near Paris.

Shown along side is the standard kilogram – still the international standard for mass!?!

The meter is now defined as the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

299 792 458 m/s is the defined value of the speed of light, c.

Système International d’Unités

Base SI UnitsQuantity

Name SymbolDimension

Symbol

Mass kilogram kg M

Length metre m L

Time second s T

Electric Current ampere A I

Temperature kelvin K θ

Luminous Intensity candela cd J

Amount of Substance mole mol N

• The French came to the rescue back in the Napoleonic era.• All scientists across the World now use the S.I. system.• The system consists of a set of base units:

• All other units are called derived units as they consist of different combinations of base units, e.g. a newton is a kilogram metre per second squared, [N] [kg m s–2]

The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom…

Time

Say no more! Move on…

Système International d’Unités

Base SI UnitsQuantity

Name SymbolDimension

Symbol

Mass kilogram kg M

Length metre m L

Time second s T

Electric Current ampere A I

Temperature kelvin K θ

Luminous Intensity candela cd J

Amount of Substance mole mol N

• The French came to the rescue back in the Napoleonic era.• All scientists across the World now use the S.I. system.• The system consists of a set of base units:

• All other units are called derived units as they consist of different combinations of base units, e.g. a newton is a kilogram metre per second squared, [N] [kg m s–2]

Electrical current measures how much charge (e.g. how

many electrons) pass a cross-sectional point in a wire

during 1 second.

Current passing through your body is dangerous for your health.

Electric Current

Direction of current

Direction of electrons

current electrons

Système International d’Unités

Base SI UnitsQuantity

Name SymbolDimension

Symbol

Mass kilogram kg M

Length metre m L

Time second s T

Electric Current ampere A I

Temperature kelvin K θ

Luminous Intensity candela cd J

Amount of Substance mole mol N

• The French came to the rescue back in the Napoleonic era.• All scientists across the World now use the S.I. system.• The system consists of a set of base units:

• All other units are called derived units as they consist of different combinations of base units, e.g. a newton is a kilogram metre per second squared, [N] [kg m s–2]

Temperature measures an intensity of the internal motion in a body (e.g. intensity of the motion

of molecules in a gas).

Temperature

We feel temperature as either hot or cold

Système International d’Unités

Base SI UnitsQuantity

Name SymbolDimension

Symbol

Mass kilogram kg M

Length metre m L

Time second s T

Electric Current ampere A I

Temperature kelvin K θ

Luminous Intensity candela cd J

Amount of Substance mole mol N

• The French came to the rescue back in the Napoleonic era.• All scientists across the World now use the S.I. system.• The system consists of a set of base units:

• All other units are called derived units as they consist of different combinations of base units, e.g. a newton is a kilogram metre per second squared, [N] [kg m s–2]

Luminous Intensity

Luminous intensity is a measure of the power emitted

by a light source.

Luminous intensity is measured by a lux meter or

light meter

We perceive luminous intensity as the brightness of

light.

Système International d’Unités

Base SI UnitsQuantity

Name SymbolDimension

Symbol

Mass kilogram kg M

Length metre m L

Time second s T

Electric Current ampere A I

Temperature kelvin K θ

Luminous Intensity candela cd J

Amount of Substance mole mol N

• The French came to the rescue back in the Napoleonic era.• All scientists across the World now use the S.I. system.• The system consists of a set of base units:

• All other units are called derived units as they consist of different combinations of base units, e.g. a newton is a kilogram metre per second squared, [N] [kg m s–2]

2 mol H2 1 mol O2

2 mol H2O

Amount of Substance

The mole is defined as the amount of substance that contains NA entities

(e.g. atoms or molecules).

The same amount of substance for different materials can have a different mass or occupy a different volume

Avogadro's number,

1 mol H atoms + 1 mol H atoms

= 1 mol H2 molecules

2g 2g 32g

18g 18g

2 mol H2 + 1 mol O2 = 2 mol H2O

Dimensional AnalysisEach of the 7 base units is given a dimensional symbol, i.e.

Base SI UnitsQuantity Name Symbol Dimension

SymbolMass kilogram kg MLength metre m LTime second s TElectric Current ampere A ITemperature kelvin K θLuminous Intensity candela cd JAmount of Substance mole mol N

When writing the “dimensions of ” we use square brackets, e.g.

“Dimensions of mass” is written as [m], so [m] = M

It is generally accepted that the unit symbol can be used instead of the dimension symbol, i.e. [m] = M or [m] = kg

Sometimes we define units purely in terms of their base units, e.g.

[ v ]=¿−1=m s−1

Dimensional Analysis

velocity=displacement

time⇒ v=

st

∴ [ s ][ t ]

= LT

=L×1T

=L ×T −1=¿− 1

[s] = L (length) or m (metre)[t] = T (time) or s (second)

¿[ s ][ t ]

=ms=m ×

1s=m × s− 1=ms− 1

Derived SI Units

To find the dimensions of force, [F], we know that,

SI unithertzjoulenewtonwattpascalcoulombvoltohmfaradweberhenryteslabecquerelsievertgraylumenlux

We use a lot more than the 7 base units, e.g.

Using a similar process we can show that,

This tells us that the newton, N is actually kgms–2 in base units or has dimensions of MLT–2

[] = M (kg), [] = LT–1 (ms–1) and [] = T (s)

𝐹=𝑚𝑎∧𝑎=𝑣𝑡⇒𝐹=

𝑚𝑣𝑡

Voltage is the energy per unit charge and charge is the product of current and time, so the volt is kgm2s–3A–1 (dimensions ML2T–3I–1)

Work done (Energy changed) = force × distance, so the joule is kgm2s–2 (dimensions ML2T–2)

Dimensional Analysis of Derived UnitsThe reason why we do this analysis is that it can help us see if our equations are correct,

e.g. which is the correct equation for the period of a pendulum,

.

Both of these fit the form, where n = 1 or ½.

Using dimensional analysis gives:

2π has no units – it is dimensionless.[period, T] = T; [length, l] = L; [acceleration, ] = LT–2;

.

∴T=( LL T− 2 )

𝑛

¿ ( 1T− 2 )

𝑛

⇒T =(T 2 )𝑛 so ⇒T =(T 2 )1 /2=T

Example:Which of the following is correct for the relationship between energy and momentum, or

mass (kg); energy (J); velocity, , (m s–1)

kg m2 s–2 kg × kg m2 s–2 kg2 m2 s–2

The 2 is ignored as it is dimensionless

𝑝=𝑚𝑣⇒ [𝑝 ]=[𝑚 ][𝑣 ] kg × m s–1 kg m s–1

⇒ [𝑝2]=¿(kg m s–1)2 kg2 m2 s–2

∴2𝑚𝐸=𝑝2

Prefixes

Average distance to the Moon 385000000 m

How to express measurements of very different magnitudes

Length of e-coli is about 0.000002 m

There are two ways to represent large and small numbers

1. Average distance to the Moon 3.85 × 108 m

1. Length of e-coli is about 2.0 × 10–6 m

2. Average distance to the Moon 385000 km

2. Length of e-coli is about 2 μm (micrometer)

1 = standard form2 = prefix

12345678

1 2 3 4 5 6

+ve exponent

–ve exponent

What do these prefixes mean?

2TB (2 Terabyte) drive

3.2 GHz CPU

Microchip

= 2,000,00 0,000,000 bytes

Nano particles

3,200,000,000 Hz =

= 0.000,001 m

0.000,000,001 m =

Nothing scary, just a way to eliminate a lot of zero's

Multiplication Prefixes   

Multiplication FactorPrefix

Symbol

1012 = 1,000,000,000,000. Tera T109 = 1,000,000,000. Giga G106 = 1,000,000. Mega M103 = 1000. Kilo K100 = 1.    10–3 = .001 milli m10–6 = .000,001 micro 10–9 = .000,000,001 nano n10–12 = .000,000,000,001 pico p10–15 = .000,000,000,000,001 femto f

Notation and Precision

• Prefixes get rid of non-significant zero’s• Loughborough in London Loughborough University by road is 198,000

m.• The zero’s are not significant as we have only measured to the nearest km so

we could just say 198 km.• If we want to show greater precision than this we would need to quote 198.0

km. This zero is now significant as it implies a more precise measurement – to the nearest 100m.

A route that avoids a nasty junction increases the distance to 200 km.

How do we know that this is to the nearest 1km and not to the nearest 10 or 100 km?

Notation and Precision

• In physics we rarely need anything more than 2 or 3 sf.

• 200,000 m = 2 × 105 (1 significant figure, 1sf – nearest 100km)

2.0 × 105 (2sf – nearest 10km)

2.00 × 105 (3sf – nearest 1km)

2.000 × 105 (4sf – nearest 100m)

2.0000 × 105 (5sf – nearest 10m)

2.00000 × 105 (6sf – nearest 1m)

For best practice use standard form rather than prefixes in any calculation.

This is where standard form is required.

1. Make sure all values are given without prefixes.

E.g. what is the volume of a rod that is 1.2m long 14cm wide and 15mm deep?

Numbers in Calculations

2. Make sure all values are given in the same units and that these are SI units.

E.g. It took 2 hours and 55 minutes to travel the 200 km, what was the average speed?

𝑣= 2 ×105 m1.05 × 104 s

=19 ms−1

¿2.5× 10−3 ×106¿2.5× 103 cm3

¿2.5× 106 mm3¿2.5× 10−3 ×109

Converting between different units

What would (a) 20J be in eV and (b) 65eV be in J?

(a) multiply 20J by a fraction that is equal to 1 but has mixed units, eV on top and J on the bottom. This means J will cancel out leaving eV as the unit.

1 eV =1.6 ×10−19 J

electronvolts → joules:

joules → electronvolts:

¿1eV ×20 J

1.6 ×10−19 J20 J ×

1 eV

1.6 ×10−19 J(b) as above but the fraction should now have J on top and eV on the bottom to cancel, leaving J as the unit.

¿1.3×1020 eV

65eV ×1.6× 10−19 J

1eV

Converting factor is therefore,

¿ 1.6×10−19 J × 65eV1eV ¿1.04× 10−17 J

E.g. electronvolts joules where⇆

Review Objectives1. Know what the S.I. system of measurement is and explain why it is

required.

2. Recognise the term Dimensional Analysis and apply it correctly to scrutinize equations.

3. Explain how a prefix is used and how it is related to writing a measurement using standard form to an appropriate number of significant figures.

4. Demonstrate how values can be converted between non S.I. and S.I. units.