1.2 Measurement in Experiments

Learning Objectives

List basic SI units and quantities they describe

Convert measurements to scientific notation

Distinguish between accuracy & precision

Use significant figures in measurements & calculations

Numbers as Measurements

In science, numbers represent measurements

Numbers involve three thingsMagnitude how much?Dimensions length, mass,

timeUnits of what?

The SI system

The standard measurement system for science

Base unitsBasic units that are not a combination

of some other units Derived units

Are combinations of base units

Base UnitsPhysical Quantity

(Dimension)

Unit Abbreviation

Mass Kilogram kg

Length Meter m

Time Second s

Electric current Ampere A

Temperature Kelvin K

Luminous intensity

Candela cd

Amount of substance

Mole mol

Derived units

Derived units are combinations of base units

Base Unit Derived Unit

m (length) m3 (volume)

kg (mass)

m (length)

s (time)

N (newton) for force

1N = 1 kg∙m

s2

Prefixes indicate orders of magnitude (powers of 10)

Power Prefix Abbrev Power Prefix Abbrev

10 -18 atto- a 10 -1 deci- d

10 -15 femto- f 10 1 deka- da

10 -12 pico- p 10 3 kilo- k

10 -9 nano- n 10 6 mega- M

10 -6 micro- μ 10 9 giga- G

10 -3 milli- m 10 12 tera- T

10 -2 centi- c 10 15 peta- P

Converting Prefixes & Units

The main idea: multiply the given unit by a conversion factor yielding the desired unit

Conversion factor: a ratio of two units that is an equivalent to 1.

Example: convert millimeters to meters1 mm x 10-3 m = 1 x 10-3 m

1 mm

Practice 1A, #1-5

Converting units of area and units of volume

How many cm2 are in 1 m2? How many cm3 are in 1 m3? How many in3 are in 1 L?

Scientific Method

http://www.sciencebuddies.org/science-fair-projects/overview_scientific_method2.gif

A way of thinking and problem solving

A group of related processes and activities

Scientific Method: Important Terms

Law vs. Theory Fact / Observation Hypothesis Experiment

Accuracy & Precision

AccuracyNearness of a measurement to the

true value Precision

Degree of exactness or refinement of a measurement

Repeatability of a measurement

Precision

describes the limit of exactness of a measuring instrument

Significant figures reflect certainty of a measurementAre figures that are known because

they are measured

Significant Figures

Represent numbers known with certainty plus one final estimated digit

Reflect the precision of an instrument or measurement

Must be reported properly Require special handling in

calculations

Rules to determine significant digits

1. All non-zeros ARE

2. All zeros between non-zeros ARE

3. Zeros in front of non-zeros ARE NOT

4. Final zeros to right of decimal ARE

5. Final zeros without a decimal ARE NOT

How many significant figures?

50.3 20.001 3.0025 3426 0.892 210 0.0008 6.58 x 103

57.00 1.534 x 10-4

2.000000 2.00 x 107

1000 5000. 20. 30

Rules of calculating with significant figures

1. When adding & subtracting, final answer must have fewest decimal places present in the calculation.

2. When multiplying & dividing, final answer must have fewest significant digits present in the calculation.

3. Number of figures in a constant are ignored wrt sig figs.

1.3 Language of Physics

Physical quantities often relate to one another in a mathematical way

Data is collected in a table form Data is graphed

to show relationship of independent & dependent variables

When time is a variable it is usually the independent (x) variable

Manipulated & responding variables

Data Table and Graph

Determining k through displacement

x (m)Force

(N)mass

(kg)

0.00 0.00 0.00

0.01 0.49 0.05

0.03 0.98 0.10

0.06 1.47 0.15

0.09 1.96 0.20

Hooke's Law

0.00

0.50

1.00

1.50

2.00

2.50

0.00 0.02 0.04 0.06 0.08 0.10

Displacement (m)

Forc

e (N

)

Equations

Equations indicate relationships of variables

2)(2

1tatvx

tavvt

xv

i

if

Evaluating Physics Equations: Dimensional Analysis

Can give you clues how to solve a problem Can help check many types of problems

because… Dimensions can be treated as algebraic

quantities Example: derive a formula for speed Example: How long would it take a car to

travel 725 km at a speed of 88 km/h?

Order of Magnitude Estimates Physics often uses very large and very

small numbers Using powers of ten as estimates of the

numbers can help estimate and check your answers

Example: from the previous problem,

hhkm

km

speed

disttime 10

10

10

/88

7252

3