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Units of length?

Units of length?

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Units of length?. Units of length?. Mile, furlong, fathom, yard, feet, inches, Angstroms, nautical miles, cubits. The SI system of units. There are seven fundamental base units which are clearly defined and on which all other derived units are based:. You need to know these. The metre. - PowerPoint PPT Presentation

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Page 1: Units of length?

Units of length?

Page 2: Units of length?

Units of length?

Mile, furlong, fathom, yard, feet, inches, Angstroms, nautical miles, cubits

Page 3: Units of length?

The SI system of units

There are seven fundamental base units which are clearly defined and on which all other derived units are based:

You need to know these

Page 4: Units of length?

The metre

• This is the unit of distance. It is the distance traveled by light in a vacuum in a time of 1/299792458 seconds.

Page 5: Units of length?

The second

• This is the unit of time. A second is the duration of 9192631770 full oscillations of the electromagnetic radiation emitted in a transition between two hyperfine energy levels in the ground state of a caesium-133 atom.

Page 6: Units of length?

The ampere

• This is the unit of electrical current. It is defined as that current which, when flowing in two parallel conductors 1 m apart, produces a force of 2 x 10-7 N on a length of 1 m of the conductors.

Page 7: Units of length?

The kelvin

• This is the unit of temperature. It is 1/273.16 of the thermodynamic temperature of the triple point of water.

Page 8: Units of length?

The mole

• One mole of a substance contains as many molecules as there are atoms in 12 g of carbon-12. This special number of molecules is called Avogadro’s number and equals 6.02 x 1023.

Page 9: Units of length?

The candela (not used in IB)

• This is the unit of luminous intensity. It is the intensity of a source of frequency 5.40 x 1014 Hz emitting 1/683 W per steradian.

Page 10: Units of length?

The kilogram

• This is the unit of mass. It is the mass of a certain quantity of a platinum-iridium alloy kept at the Bureau International des Poids et Mesures in France.

THE kilogram!

Page 11: Units of length?

Derived units

Other physical quantities have units that are combinations of the fundamental units.

Speed = distance/time = m.s-1

Acceleration = m.s-2

Force = mass x acceleration = kg.m.s-2 (called a Newton)

(note in IB we write m.s-1 rather than m/s)

Page 12: Units of length?

Some important derived units (learn these!)

1 N = kg.m.s-2 (F = ma)

1 J = kg.m2.s-2 (W = Force x distance)

1 W = kg.m2.s-3 (Power = energy/time)

Page 13: Units of length?

Prefixes

It is sometimes useful to express units that are related to the basic ones by powers of ten

Page 14: Units of length?

Prefixes

Power Prefix Symbol Power Prefix Symbol

10-18 atto a 101 deka da

10-15 femto f 102 hecto h

10-12 pico p 103 kilo k

10-9 nano n 106 mega M

10-6 micro μ 109 giga G

10-3 milli m 1012 tera T

10-2 centi c 1015 peta P

10-1 deci d 1018 exa E

Page 15: Units of length?

Prefixes

Power Prefix Symbol Power Prefix Symbol

10-18 atto a 101 deka da

10-15 femto f 102 hecto h

10-12 pico p 103 kilo k

10-9 nano n 106 mega M

10-6 micro μ 109 giga G

10-3 milli m 1012 tera T

10-2 centi c 1015 peta P

10-1 deci d 1018 exa E

Don’t worry!

These will all be in the

formula book you

have for the exam.

Page 16: Units of length?

Examples

3.3 mA = 3.3 x 10-3 A

545 nm = 545 x 10-9 m = 5.45 x 10-7 m

2.34 MW = 2.34 x 106 W

Page 17: Units of length?

Checking equations

If an equation is correct, the units on one side should equal the units on another. We can use base units to help us check.

Page 18: Units of length?

Checking equations

For example, the period of a pendulum is given by

T = 2π l where l is the length in metres g and g is the acceleration due to gravity.

In units m = s2 = s m.s-2

Page 19: Units of length?

Let’s do some measuring!

Page 20: Units of length?

Errors/Uncertainties

Page 21: Units of length?

Errors/Uncertainties

In EVERY measurement (as opposed to simply counting) there is an uncertainty in the measurement.

This is sometimes determined by the apparatus you're using, sometimes by the nature of the measurement itself.

Page 22: Units of length?

Individual measurements

When using an analogue scale, the uncertainty is plus or minus half the smallest scale division. (in a best case scenario!)

4.20 ± 0.05 cm

Page 23: Units of length?

Individual measurements

When using an analogue scale, the uncertainty is plus or minus half the smallest scale division. (in a best case scenario!) 22.0 ± 0.5 V

Page 24: Units of length?

Individual measurements

When using a digital scale, the uncertainty is plus or minus the smallest unit shown.

19.16 ± 0.01 V

Page 25: Units of length?

Repeated measurements

When we take repeated measurements and find an average, we can find the uncertainty by finding the difference between the average and the measurement that is furthest from the average.

Page 26: Units of length?

Repeated measurements - Example

Iker measured the length of 5 supposedly identical tables. He got the following results; 1560 mm, 1565 mm, 1558 mm, 1567 mm , 1558 mm

Average value = 1563 mm

Uncertainty = 1563 – 1558 = 5 mm

Length of table = 1563 ± 5 mm

This means the actual length is anywhere between 1558 and 1568 mm

Page 27: Units of length?

Precision and Accuracy

The same thing?

Page 28: Units of length?

Precision

A man’s height was measured several times using a laser device. All the measurements were very similar and the height was found to be

184.34 ± 0.01 cm

This is a precise result (high number of significant figures, small range of measurements)

Page 29: Units of length?

AccuracyHeight of man = 184.34 ± 0.01cm

This is a precise result, but not accurate (near the “real value”) because the man still had his shoes on.

Page 30: Units of length?

Accuracy

The man then took his shoes off and his height was measured using a ruler to the nearest centimetre.

Height = 182 ± 1 cm

This is accurate (near the real value) but not precise (only 3 significant figures)

Page 31: Units of length?

Precise and accurate

The man’s height was then measured without his socks on using the laser device.

Height = 182.23 ± 0.01 cm

This is precise (high number of significant figures) AND accurate (near the real value)

Page 32: Units of length?

Random errors/uncertainties

Some measurements do vary randomly. Some are bigger than the actual/real value, some are smaller. This is called a random uncertainty. Finding an average can produce a more reliable result in this case.

Page 33: Units of length?

Systematic/zero errors

Sometimes all measurements are bigger or smaller than they should be. This is called a systematic error/uncertainty.

Page 34: Units of length?

Systematic/zero errors

This is normally caused by not measuring from zero.

For this reason they are also known as zero errors/uncertainties. Finding an average doesn’t help.

Page 35: Units of length?

Systematic/zero errors

Systematic errors are sometimes hard to identify and eradicate.

Page 36: Units of length?

UncertaintiesIn the example with the table, we found the length of the table to be 1563 ± 5 mm

We say the absolute uncertainty is 5 mm

The fractional uncertainty is 5/1563 = 0.003

The percentage uncertainty is 5/1563 x 100 = 0.3%

Page 37: Units of length?

UncertaintiesIf the average height of students at BSH is 1.23 ± 0.01 m

We say the absolute uncertainty is 0.01 m

The fractional uncertainty is 0.01/1.23 = 0.008

The percentage uncertainty is 0.01/1.23 x 100 = 0.8%

Page 38: Units of length?

Combining uncertainties

When we find the volume of a block, we have to multiply the length by the width by the height.

Because each measurement has an uncertainty, the uncertainty increases when we multiply the measurements together.

Page 39: Units of length?

Combining uncertainties

When multiplying (or dividing) quantities, to find the resultant uncertainty we have to add the percentage uncertainties of the quantities we are multiplying.

Page 40: Units of length?

Combining uncertainties

Example: A block has a length of 10.0 ± 0.1 cm, width 5.0 ± 0.1 cm and height 6.0 ± 0.1 cm.

Volume = 10.0 x 5.0 x 6.0 = 300 cm3

% uncertainty in length = 0.1/10 x 100 = 1%% uncertainty in width = 0.1/5 x 100 = 2 %% uncertainty in height = 0.1/6 x 100 = 1.7 %

Uncertainty in volume = 1% + 2% + 1.7% = 4.7%

(4.7% of 300 = 14)

Volume = 300 ± 14 cm3

This means the actual volume could be anywhere between 286 and 314 cm3

Page 41: Units of length?

Combining uncertainties

When adding (or subtracting) quantities, to find the resultant uncertainty we have to add the absolute uncertainties of the quantities we are multiplying.

Page 42: Units of length?

Combining uncertainties

One basketball player has a height of 196 ± 1 cm and the other has a height of 152 ± 1 cm. What is the difference in their heights?

Difference = 44 ± 2 cm

Page 43: Units of length?

Who’s going to win?

New York TimesLatest opinion poll

Bush 48%

Gore 52%

Gore will win!

Uncertainty = ± 5%

Page 44: Units of length?

Who’s going to win?

New York TimesLatest opinion poll

Bush 48%

Gore 52%

Gore will win!

Uncertainty = ± 5%

Page 45: Units of length?

Who’s going to win?

New York TimesLatest opinion poll

Bush 48%

Gore 52%

Gore will win!

Uncertainty = ± 5%

Uncertainty = ± 5%

Page 46: Units of length?

Who’s going to win

Bush = 48 ± 5 % = between 43 and 53 %

Gore = 52 ± 5 % = between 47 and 57 %

We can’t say!

(If the uncertainty is greater than the difference)