SCIENCE SKILLSIB PHYSICS | UNIT 1 | SCIENCE SKILLS

UnitsIB PHYSICS | UNIT 1 | SCIENCE SKILLS

1.2

Two Types of Observations

Quantitative “How Many” / “How Much”Numerical

Qualitative Description

Provide some examples of each

Measurement

How can you quantify a measurement?

Systems and Units

Length Meter m

Mass Kilogram kg

Time Second s

Electric Current Ampere (amp) A

Temperature Kelvin K

Amount of Substance Mole mol

Luminous Intensity Candela cd

Fundamental S.I. Units:

Example IB Question

FYI: IBO (International Baccalaureate Organization expects you to memorize the fundamental units

Units are Arbitrary

1790 - The length of a pendulum that swings

half of its maximum distance in one second

1791 - The length of one ten-millionth of the

distance between the North Pole and the equator

1795 - The length of an official bar of brass

fabricated to be exactly one meter as determined in 1791

1799 - The length of an official bar of platinum,

measured from the brass bar and stored at the French

National archives

1889 – The distance between two lines on an official bar of platinum-

iridium alloy, measured at 0°C

1983 – The length traveled by light in a vacuum during 1/299,792,458 of a second

1/10,000,000th

What’s ‘the standard’?

The “second” is defined as the interval required for 9,192,631,770 vibrations of the cesium-133 atom measured via an atomic beam clock

All of our base SI units are grounded in some “standard” that helps maintain consistency.

Some of these units even reference each other…

Definition of the Second

Primary and Secondary Colors

Primary Colors Secondary Colors

Fundamental vs Derived

Length m

Mass kg

Time s

Fundamental S.I. Units

Derived Units

Velocity:

Acceleration:

Force:

Τ𝑚 𝑠

ൗ𝑚 𝑠2= ൗ

Τ𝑚 𝑠𝑠

𝑁 = 𝑘𝑔 × ൗ𝑚 𝑠2

Welcome to IB Land!

Since this course is International all of the units must be in the “European” format rather than the “American” format

This means that instead of writing units with a fraction slash, we must use negative exponents

7 m/s m s-1

9.81 m/s2 m s-2

87 g/cm3 g cm-3

6.67 Nm2

kg2N m2 kg-2

2.2 J

KJ K-1

8.31J

K×molJ K-1 mol-1

The Metric System*T

aken

dir

ectl

y fr

om

th

e IB

Phy

sics

Dat

a B

oo

klet

The Metric System

P T G M k m μ n p fh da d c

The value given is the number of places the decimal moves

Please make sure that you go in the correct direction!

900 nm = 900,000,000,000 m

or

900 nm = 0.0000009 m

The Metric System

P T G M k m μ n p fh da d c

900 nm → _______________ m0.0000009

900 × 10-9 m

base

9

The Metric System

Prefix Abbreviation Power

giga- G 109

mega- M 106

kilo- K 103

hecto- h 102

deca- da 101

Base

deci- d 10-1

centi- c 10-2

milli- m 10-3

micro- μ 10-6

nano- n 10-9

Conversions:250 g = kg

0.00325 kg = μg

54 mm = km

0.25

3,250,000

0.000054

3

6

33

3

The Metric System | Try These

65 μC = CPrefix Abbreviation Power

giga- G 109

mega- M 106

kilo- K 103

hecto- h 102

deca- da 101

Base

deci- d 10-1

centi- c 10-2

milli- m 10-3

micro- μ 10-6

nano- n 10-9

12 MW = W

0.000065

12,000,000

6

6

The Metric System

There’s more…

Dimensional AnalysisIB PHYSICS | UNIT 1 | SCIENCE SKILLS

1.3

Warm Up

Convert 0.004 km to m

Convert 130 cm to m

Convert 764 ns to s

0.004 × 103 = 4 m

0.000000764 s

764 × 10-9 =

130 × 10-2 = 1.3 m

Conversions

Convert the Following:

26.2 miles → kilometers 1 Mile = 1.609 Kilometers

26.2 mi ×1.609 km

1 mi= 𝟒𝟐. 𝟐 𝐤𝐦

Conversions with fractions

Convert the Following:

35 mi hr-1→m s-1 1 Mile = 1609 meters

35 mi

1 hr×1609 m

1 mi×

1 hr

60 min×1 min

60 s= 𝟏𝟓. 𝟔 𝐦 𝐬−𝟏

Conversions with Exponents

How many cm2 are there in 1 m2?

How many cm3 are there in 1 m3?

100 × 100 = 1002 = 𝟏𝟎, 𝟎𝟎𝟎 𝐜𝐦𝟐

100 × 100 × 100 = 1003 = 𝟏, 𝟎𝟎𝟎, 𝟎𝟎𝟎 𝐜𝐦𝟐

Conversions with Exponents

Convert the Following:

0.05 km2→m2

0.05 km2 ×1000 m

1 km×1000 m

1 km= 𝟓𝟎, 𝟎𝟎𝟎𝐦𝟐

0.05 km2 ×1000 m

1 km

2

= 𝟓𝟎, 𝟎𝟎𝟎𝐦𝟐

Conversions with Exponents

Convert the Following:

5 m2→ ft2

5 m3→ ft3

1 meter = 3.28 feet

5 m2 ×3.28 ft

1 m

2

= 𝟓𝟑. 𝟖 𝐟𝐭𝟐

5 m3 ×3.28 ft

1 m

3

= 𝟏𝟕𝟔. 𝟒 𝐟𝐭𝟑

Dimensional Analysis

Start with the formula and substitute units in for variables

v = d / t

d = at

Is this formula valid?

𝑚

𝑠=

𝑚

𝑠

𝑚 =𝑚

𝑠2𝑠

𝑚 =𝑚

𝑠

not valid

Dimensional Analysis

We can use equations with units that we know to find units that we don’t.

𝑝 = 𝑚 × 𝑣Variable Unit

Momentump kg m s-1

Massm

Kilogram[kg]

Velocityv

Meters per second[ms-1]

= kgm

s

Dimensional Analysis

Constants have units too! That’s what makes our equation valid

𝐹 = 𝐺𝑚1𝑚2𝑑2

Variable Unit

ForceF

Newton[N]

Massm1 and m2

Kilogram[kg]

Distanced

Meter[m]

Universal Gravitation Constant

GN m2 kg-2

𝐺 =𝐹𝑑2

𝑚1𝑚2=

N m 2

kg kg

=N m 2

kg 2

Example IB Question

𝐹 → N → kg × m s−2

𝑣 → m s−1

𝑘 =𝐹

𝑣2=

kg × m s−2

m s−1 2=kg × m s−2

m2 s−2

=kg

m= 𝐤𝐠𝐦−𝟏

Normalized Scientific Notation

Helpful for very big numbers

89,000,000 =

750,000,000,000 =

8,759,000,000 =

8.9 × 107 8.9E7or

8.759 × 109 8.759E9or

7.5 × 1011 7.5E11or

Normalized Scientific Notation

Helpful for very small numbers

0.00125 =

0.0000008255 =

0.00000082550 =

1.25 × 10-3 1.25E-3or

8.2550 × 10-7 8.2550E-7or

8.255 × 10-7 8.255E-7or

Orders of Magnitude

If I have $144 in my pocket and you have $24 in your pocket, how many times larger is my wealth?

144

24= 6 𝑡𝑖𝑚𝑒𝑠 𝑙𝑎𝑟𝑔𝑒𝑟

Orders of Magnitude

How do we compare numbers in scientific notation?

8.9 × 107 and 7.3 × 1015

7.3 × 1015

8.9 × 107≈ 108

15 − 7 = 8

Orders of Magnitude

Mass of universe 10 50 kg

Diameter of universe 10 25 m

Diameter of galaxy 10 21 m

Age of universe 10 18 s

Speed of light 10 8 m s-1

Diameter of atom 10 -10 m

Diameter of nucleus 10 -15 m

Diameter of quark 10 -18 m

Mass of proton 10 -27 kg

Mass of quark 10 -30 kg

Mass of electron 10 -31 kg

Planck length 10 -35 m

Example IB Question

104

10−2≈ 106

4 − (−2) = 6

UncertaintyIB PHYSICS | UNIT 1 | SCIENCE SKILLS

1.4

Precision/Accuracy

Precision: The degree of exactness in a measurement

Accuracy: The closeness of a measured value to the standard

*Repeatability

Precision/Accuracy

High Precision ✔️ ✔️

Low Precision ✔️ ✔️

High Accuracy ✔️ ✔️

Low Accuracy ✔️ ✔️

Example IB Question

Types of Error

RandomError

SystematicError

“Human

Factor”

Error/Offset

in the

instrumentation

Example IB Question

Uncertainty Game Show

Question Answer Uncertainty Actual Points

1

2

3

4

5

6

7

8

Total

Measurement Precision

Analog:Estimate to one digit beyond the smallest marking

Digital:Only go the least significant digit’s place

0 1

1 cm 1 mm

Estimating Uncertainty Range

Analog Scale

0 1

Uncertainty

± (half the smallest division)

Digital Scale ± (the smallest division)

Other General Rules

Your uncertainty should typically only have one significant digit (two are okay in some situations)

Your precision in the measurement and uncertainty MUST match

i.e. Same number of decimal places

Report these Measurements!

5.27 ± 0.05

90.0 ± 0.1

8.78 ± 0.10

19.99 ± 0.01

Significant Digits

How many significant digits?

3.45 cm 3

226.5 cm 4

2.50 cm 3

0.025 cm 2

12060 m 4

0.0000250 km 3

25.0 mm 3

25000 mm 2

2.50 × 104 mm

*IB will give full credit as long as your answer is within 1 sig fig

Recommendation for IB Exam:Round all answers to 3 sig figs

unless otherwise stated

Uncertainty in CalculationsIB PHYSICS | UNIT 1 | SCIENCE SKILLS

1.5

Estimating Uncertainty Range

When you have repeated measurements, report the average with an uncertainty of ± (half of the range)

Trial 1 2.01 s

Trial 2 1.82 s

Trial 3 1.97 s

Trial 4 2.16 s

Trial 5 1.94 s

Average = 1.98 s

Range = 2.16 – 1.82 = 0.34 s

Uncertainty = 0.34/2

= ± 0.17 s

Three ways to Report

AbsoluteUncertainty ± 0.3 g

Fractional Uncertainty

𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒

𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡=0.3

2.0= 0.15

PercentageUncertainty

𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙 × 100% = 15%

2.0 ± 0.3 g

Three ways to Report

AbsoluteUncertainty

0.385 ± 𝟎. 𝟎𝟎𝟏 𝐕

Fractional Uncertainty

0.001

0.385= 𝟎. 𝟎𝟎𝟐𝟔

PercentageUncertainty

0.0026 × 100% = 𝟐𝟔%

Example IB Question

Absolute: Percent:

± 0.02 A 0.02

2.00× 100% = 1%

Uncertainty in Calculations

Adding or Subtracting

If y = a ± b then Δy = Δa + Δb

To find the uncertainty in a sum or difference you just add the uncertainties of all the ingredients.

Absolute Uncertainty

Always Add

Try This

A 9.51 0.15 meter rope ladder is hung from a roof that is 12.56 0.07 meters above the ground. How far is the bottom of the ladder from the ground?

12.56 − 9.51 = 3.05 m

0.15 + 0.07 = 0.22 m

3.05 ± 0.22 m

Uncertainty in Calculations

Multiplying or Dividing

If y = a × b ÷ c then Δy/y = Δa/a + Δb/b + Δc/c

To find the uncertainty in a product or quotient you just add the percentage or fractional uncertainties of all the ingredients.

Percent or Fractional Uncertainty

Always Add

Try This

A car travels 64.7 0.5 meters in 8.65 0.05 seconds. What is its speed?

𝑣 =𝑑

𝑡=64.7

8.65= 7.48 m s−1

0.5

64.7× 100% = 0.77%

0.05

8.65× 100% = 0.58%

0.77% + 0.58% = 1.35%

7.48 m s−1 ± 1.35%

7.48 × 0.0135 = 0.1 m s−1

7.48 ± 0.1 m s−1

This is in the Data Booklet ☺

Example IB Question

0.10 ± 0.01 A

0.01

0.10× 100% = 10%

𝐼2 = 𝐼 × 𝐼

10% + 10% = 20%

Example IB Questions

4𝜋𝑟3

Exact Values𝑟 × 𝑟 × 𝑟

2%+ 2%+ 2% = 𝟔%

𝐿3 = 𝐿 × 𝐿 × 𝐿3%+ 3%+ 3% = 𝟗%

0.3

10.0× 100% = 3%

103 = 1000 cm3 1000 × 0.09 = 𝟗𝟎 𝐜𝐦𝟑