Topic 1 – Physics and Physical measurement

Use the syllabus particularly when

studying for examinations

Ranges of sizes, masses and times

Order of magnitude

We can express small and large numbers using exponential notation

The number of atoms in 12g of carbon is approximately

600000000000000000000000

This can be written as 6 x 1023

Order of magnitude

We can say to the nearest order of magnitude (nearest power of 10) that the number of atoms in 12g of carbon is 1024

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

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.

Size

The smallest objects that you need to consider in IB physics are subatomic particles (protons and neutrons).

These have a size (to the nearest order of magnitude) of 10-15 m.

Size

The largest object that you need to consider in IB physics is the Universe.

The Universe has a size (to the nearest order of magnitude) of 1025 m.

Mass

The lightest particle you have to consider is the electron. What do you think the mass of the electron is?

10-30 kg!(0.000000000000000000000000000001 kg)

Mass

The Universe is the largest object you have to consider. It has a mass of ….

1050 kg

(100000000000000000000000000000000000000000000000000 kg)

Time

The smallest time interval you need to know is the time it takes light to travel across a nucleus.

Can you estimate it? (Time = distance/speed)

10-24 seconds

Time

The longest time ? The age of the universe.

12 -14 billion years

1018 seconds

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 (mass of 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.

Estimate the following:

1. The mass of an apple

(to the nearest order of magnitude)

Estimate the following:

1. The mass of an apple

2. The number of times a human heart beats in a lifetime.

(to the nearest order of magnitude)

Estimate the following:

1. The mass of an apple

2. The number of times a human heart beats in a lifetime.

3. The speed a cockroach can run.

(to the nearest order of magnitude)

A fast South American one!

Estimate the following:

1. The mass of an apple 10-1 kg

2. The number of times a human heart beats in a lifetime.

3. The speed a cockroach can run.

(to the nearest order of magnitude)

Estimate the following:

1. The mass of an apple 10-1 kg

2. The number of times a human heart beats in a lifetime. 70x60x24x365x70=109

3. The speed a cockroach can run.

(to the nearest order of magnitude)

Estimate the following:

1. The mass of an apple 10-1 kg

2. The number of times a human heart beats in a lifetime. 70x60x24x365x70=109

3. The speed a cockroach can run. 100 m.s-1

(to the nearest order of magnitude)

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, but not their definitions.

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.

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.

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.

Note that the Coulomb is NOT a base unit.

The kelvin

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

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.

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.

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!

SI Base Units

Quantity Unit

distance metre

time second

current ampere

temperature kelvin

quantity of substance mole

luminous intensity candela

mass kilogram

You HAVE to learn these!

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

PrefixesPower 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 data 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

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

Errors/Uncertainties

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!)

4.20 ± 0.05 cm

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 estimate the uncertainty by finding the difference between the highest and lowest measurement and divide by two.

Repeated measurements - Example

Pascal 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 = (1567 – 1558)/2 = 4.5 mm

Length of table = 1563 ± 5 mm

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

Precision and Accuracy

The same thing?

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.

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)

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)

Precision and Accuracy

• Precise – High number of significent figures. Repeated measurements are similar

• Accurate – Near to the “real” value

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 error/uncertainty.

Systematic/zero errors

This is normally caused by not measuring from zero. For example when you all measured Mr Brockman’s height without taking his shoes off!

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

Uncertainties

In 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%

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 fractional) 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.

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

Error bars

• X = 0.6 ± 0.1• Y = 0.5 ± 0.1

Gradients

Minimum gradient

Maximum gradient

y = mx + c

Hooke’s law

• F = kx

F (N)

x (m)

y = mx + c

• Ek = ½mv2

Ek (J)

V2 (m2.s-2)

Which of the following is the odd one out?

MassSpeedForce

TemperatureDistanceElephant

DO NOW!

Which of the following is the odd one out?

MassSpeedForce

TemperatureDistanceElephant

DO NOW!

Scalars

Scalar quantities have a magnitude (size) only.

For example:

Temperature, mass, distance, speed, energy.

Vectors

Vector quantities have a magnitude (size) and direction.

For example:

Force, acceleration, displacement, velocity, momentum.

Representing vectors

Vectors can be represented by arrows. The length of the arrow indicates the magnitude, and the direction the direction!

Representing velocity

Velocity can also be represented by an arrow. The size of the arrow indicates the magnitude of the velocity, and direction...well represents the direction!

When discussing velocity or answering a question, you must always mention the direction of the velocity (otherwise you are just giving the speed).

Adding vectors

When adding vectors (such as force or velocity) , it is important to remember they are vectors and their direction needs to be taken into account.

The result of adding two vectors is called the resultant.

Adding vectors

For example;

6 m/s 4 m/s 2 m/s

4 N

4 N 5.7 N

Resultant force

Resultant force

How did we do that?

4 N

4 N

5.7 N

4 N

4 N

Scale drawing

You can either do a scale drawing

4 cm

4 cm

1 cm = 1N

θ = 45°

θ

Or by using pythagorous and trigonometry

4 N

4 N

Length of hypotenuse = √42 + 42 = √32 = 5.7 N

Tan θ = 4/4 = 1, θ = 45°

Subtracting vectors

For example;

6 m/s 4 m/s 10 m/s

4 N

4 N 5.7 N

Resultant velocity

Resultant force

Subtracting vectors

For example;

4 N

4 N

5.7 N

Resolving vectors into components

It is sometime useful to split vectors into perpendicular components

Resolving vectors into components

Tension in the cables?

10 000 N

?? 10°

Vertically 10 000 = 2 X ? X sin10°

10 000 N

?? 10°

? X sin10° ? X sin10°

Vertically 10 000/2xsin10° = ?

10 000 N

?? 10°

? X sin10° ? X sin10°

? = 28 800 N

10 000 N

?? 10°

? X sin10° ? X sin10°