Physical Quantities, Units and Prefixes (and a bit on taking measurements too!)

One of these images shows measurements that is‘accurate, but not precise’

and one shows measurements that are‘precise, but not accurate’

Which is which?

We will revisit this later in the lesson.

A B

Mr. Mason Lessons: Wednesday P1&2, Friday P5&6

Mr. Mason Mr. Gillett

Mechanics Electrons, Waves & Photons

Practical Skills 1

You will need a folder to keep your current work and assessments in.

To get the best grades you can, youll need to do work at home beyond homework.

Before each class, you must have read the double page spread in the textbook.

http://www.physics-oasis.co.uk/timetable_ASphysics.html

If you need any help, my room is C5 (Here!) Or email me on nick.mason@oasisenfield.org

Candidates should be able to: (a) explain that some physical quantities consist

of a numerical magnitude and a unit; (b) use correctly the named units listed in this

specification as appropriate; (c) use correctly the following prefixes and their

symbols to indicate decimal sub-multiples or multiples of units: pico (p), nano (n), micro (μ), milli (m), centi (c), kilo (k), mega (M), giga ,(G), tera (T);

(d) Make suitable estimates of physical quantities included within this specification.

Lesson 2 Objectives from 1.1.1 Physical quantities and units

Physical Quantities

PHYSICAL QUANTITIES

Physics is a fascinating science. It deals with times that range from less than 10-22 s, the half-life of helium 5 to 1.4 x1010 years, the probable ’age’ of our Universe.

TemperaturesPhysicists study temperatures from within a billionth of a degree above absolute zero to almost 200 million degrees, the temperature in the plasma in a fusion reactor

Mass and lengthAn investigation of the mass of a quantum of FM radio radiation (2.3x10-42 kg) and the ‘size’ of a proton (1.3x10-15 m) all fall within the World of Physics!

It is vital to realise that all the quantities mentioned above contain a number and then a unit of measurement.

Without one or other the measurement would be meaningless.

Imagine saying that the world record for the long jump was 8.95 (missing out the metres) or that the mass of an apple was kilograms (missing out the 0.30)! 

Number and Unit

In 60 Seconds, List as many units as you can!

All units used in Physics are based on the International System (SI) of units which is based on the following seven base units.

7 base units

Mass - measured in kilograms The kilogram (kg): this is the mass equal to that of the

international prototype kilogram kept at the Bureau International des Poids et Mesures at Sevres, France.

 Length - measured in metres The metre (m): this is the distance travelled by

electromagnetic waves in free space in 1/299,792,458 s.

Time - measured in seconds The second: this is the duration of 9,192,631,770

periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of caesium 137 atom.  

The base units the first 3

Electric current - measured in amperes. The ampere: this is that constant current which, if maintained in

two parallel straight conductors of infinite length and of negligible circular cross section placed 1 metre apart in a vacuum would produce a force between them of 2 x 10 -7 N.

Temperature - measured in Kelvin The Kelvin: this is 1/273.16 of the thermodynamic temperature of

the triple point of water.  Luminous intensity - measured in candelas The candela: this is the luminous intensity in a given direction of a

source that emits monochromatic radiation of frequency 540x1012 Hz that has a radiant intensity of 1/683 watt per steradian

 Amount of substance - measured in moles The mole: this is the amount of substance of a system that

contains as any elementary particles as there are in 0.012 kg of carbon-12.

The last 4

Quantity Unit

Mass kg (kilograms)

Length m (metres)

Time s (seconds)

Electric Current A (amperes)

Temperature K (Kelvin)

Amount of substance mol (moles)

Luminosity cd (Candela)

The base units

How many are there?

How many of what? It's simply a collection of different animals -

you cannot add them together! 

You should be asking

It is most important to realise that these units are for separate measurements – you can’t add together quantities with different units.

For example five kilograms plus twenty-five metres has no meaning.

Adding units

Units can be multiplied just like quantities. For example:

Mass x Length (kg) x (m)

(kg m)

Multiplying units

Dividing Units works just the same For example:

Speed = Distance / Time Distance is measured in (m) Time is measured in (s)

= (m) / (s) = (m/s) or (ms-1)

Speed is measured in (ms-1)

Dividing Units Remember: 1/s = s-1

1) Area = Length (m) x Width (m). What are the units of Area?

2) Acceleration = Velocity (ms-1) / Time (s) What are the units of acceleration?

3) Charge = Current (A) x time (s). What are the units for charge in base units?

Practice Questions

Check that the following are dimensionally correct

1. s=ut + 1/2 at2

Dimensions of s= Dimensions of ut = Dimensions of 1/2 at

2 =

2. Show that F= mv2/r is dimensionally homogeneous for the movement of mass m in a circle.

3. Show that E= mc2 is dimensionally homogeneous .

Answers

1) (m) 2) (kg m s-2) 3) (kg m2 s-2)

Some physical quantities consist of a numerical magnitude and a unit

You can only add/ subtract similar units. Units can be multiplied or divided Seven base units. This means they cannot

be expressed in any other combination of units.

Use correctly the named units listed in this specification as appropriate

Summary

Powers of Ten

In Physics we often deal with very small or very large numbers and it is important to understand how these may be represented.

http://htwins.net/scale2/  

Powers of ten

Prefi x Factor of 10 pico (p) 10-12 nano micro milli centi (c) deci (d) kilo (k) mega giga (G) tera (T)

Prefixes are used with the unit symbols to indicate decimal multiples or submultiples.

What would these mean if you found them in front of a unit ?

It is important to understand how to use your own calculator; they can all be slightly different. This is especially true when dealing with powers of ten.

Remember that 5.4x104 is keyed in as 5.4 EXP 4 but that 105 (One followed by FIVE noughts) is keyed in as 1 EXP 5 and NOT 10 EXP 5.

(Some calculators have an EE key in place of the EXP)

Use of your calculator.

Distance a finger nail grows in 1s 10-9 m Distance across an atom 10-10 m Wavelength of yellow light 6x10-7 m Diameter of a human hair 5x10-6 m World record long jump (man 2007) 8.95 m Height of an adult 1.75 m Length of a marathon (approximately) 40 000 m

Extension: Find out what prefix would be most suitable for these measurements Distance light travels in a year 1016 m Radius of the observable universe 1025 m ‘Diameter’ of a sub nuclear particle 10-15 m

Use the most suitable prefix

How Science works:

Takingmeasurements

Taking measurementsWhen you take measurements there may be some variation in the readings.

If you time the fall of a paper parachute over a fixed distance, the times may vary slightly.

10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.4 s

Let’s look at these results more closely.

Why is there a difference between these results?

For example:

Taking measurements

The results were:

10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.4 s

What is the Range of these results?

Taking measurements : Range

The results were:

10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.4 s

and the maximum value

Range = max – min = 10.4 – 9.9 = 0.5 s

Find the minimum value

Taking measurements : Mean

The results were:

10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.4 s

What is the mean (or average) of these results?

Taking measurements : Mean

The results were:

10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.3 s

Add up the 5 numbers:

10.1+10.2+9.9+10.0+10.4 = 50.6

There are 5 items, so divide by 5:

Mean (or average) =

= 50.6

5

= 10.1 s

Why is the mean recorded to 3 significant figures?

Taking measurements : Mean

The results were:

10.1 s, 10.2 s, 9.9 s, 10.0 s, 10.4 s

Why is it a good idea to calculate the mean of your results?

Because it improves the reliability of your results.

Your results will be more reliable.

Accuracy & Precision

Definitions Accuracy and Precision …sound the same

thing…

…is there a difference?

?

One of these images shows measurements that is‘accurate, but not precise’

and one shows measurements that are‘precise, but not accurate’

Which is which?

.

A B

.

A B

‘accurate, but not precise’

‘precise, but not accurate’

Definitions : AccuracyIn your experiments, you need to consider the accuracy of your measuring instrument.

For example:

It is also likely to be more sensitive.So it will respond to smaller changes in temperature.

An expensive thermometer is likely to be more accurate than a cheap one.

It will give a result nearer to the true value.

As well as accuracy, precision is also important.

For example:

Precision is connected to the smallest scale division on the measuring instrument that you are using.

Definitions : Precision

For example, using a ruler:

Definitions : Precision

A ruler with a millimetre scale

will give greater precision than a ruler with a centimetre scale.

For example:

A precise instrument also gives a consistent reading when it is used repeatedly for the same measurements.

Definitions : Precision

For example, 2 balances:

A

B

A beaker is weighed on A, 3 times:The readings are: 73 g, 77 g, 71 g

It is then weighed on B, 3 times:The readings are: 75 g, 73 g, 74 gSo the Range is:

= 2 g

= 6 g

Balance B has better precision.

Its readings are grouped closer together.

Definitions : Precision

So the Range is:

Accuracy compared with PrecisionSuppose you are measuring the length of a wooden bar:

0

The length has a true value

truevalue

Let’s look at 3 cases…

And we can take measurements of the length, like this:

Accuracy compared with Precision

0

truevalue

0

0

Precise (grouped) but not accurate.

Accurate (the mean) but not precise.

Accurate and Precise.

• The meaning of ‘variation’ and ‘range’,

• How to calculate the mean (or average),and why this improves the reliability of your results,

• The difference between ‘accuracy’ and ‘precision’.

Learning Outcomes

You should now understand:

This is a method of comparing experimental values of a quantity to the accepted precise measurement

Percentage difference= (experimental value-accepted measurement) x100% accepted measurement

It tells you how accurate you were E.g. g = 9.81m/s2 , measured 10.82 m/s2

Percentage difference = (10.82-9.81)/9.81 x 100%= 10.3% Not very accurate.

Percentage Difference

Greater than 20% - rubbish Greater than 10%, less than 20% Poor Greater than 5% less than 10% very good Less than 5% - excellent.

How did you do?