Topic 1 – Physics and physical measurement

Use the syllabus and this REVISION POWERPOINT

when studying for examinations

Order of magnitude

The number of atoms in 12g of carbon is approximately 600000000000000000000000

We can say to the nearest order of magnitude that the number of atoms in 12g of carbon is 1024

(6 x 1023 is 1 x 1024 to one significant figure)

This can be written as 6 x 1023

Small numbers

Similarly the length of a virus is 2.3 x 10-8 m. We can say to the nearest order of magnitude the length of a virus is 10-8 m.

Ranges of sizes, masses and times

You need to have an idea of the ranges of sizes, masses and times that occur in the universe.

You have to LEARN these!

Size10-15 m to 1025 m (subatomic particles to the

extent of the visible universe)Mass

10-30 kg to 1050 kg (electron to the mass of the Universe)

Time10-23 s to 1018 s (time for light to cross a

nucleus to the age of the Universe)

A common ratio – Learn this!

Hydrogen atom ≈ 10-10 m

Proton ≈ 10-15 m

Ratio of diameter of a hydrogen atom to its nucleus

= 10-10/10-15 = 105

Estimation

For IB you have to be able to make order of magnitude estimates.

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

SI Base Units

Quantity Unit

distance metre

time second

current ampere

temperature kelvin

quantity of substance mole

luminous intensity candela

mass kilogram

Can you copy this please?

Note: No Newton or Coulomb

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)

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)

Guess what

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.

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

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.

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

Individual measurements

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

19.16 ± 0.01 V

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.

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)

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.

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.

Systematic/zero errors

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

Systematic/zero errors

This is normally caused by not measuring from zero. For example when you all measure Ms. Mink’s height without taking her shoes off!

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

Uncertainties

If the average height of students at CGHS 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%

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.

Combining uncertainties

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

Combining uncertaintiesExample: 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

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.

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

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)

Error bars

• X = 0.6 ± 0.1

• Y = 0.5 ± 0.1

Gradients

Minimum gradient

Maximum gradient

y = mx + c

y = mx + c

• Ek = ½mv2

y = mx + c

• Ek = ½mv2

Ek (J)

V2 (m2.s-2)

Period of a pendulum

T = 2π l g

Period of a pendulum

T = 2π l g

T (s)

l½ (m½)

Period of a pendulum

T = 2π l g

T2 (s)

l (m)