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Physics. A Mathematical Science. Science. An organized way of studying our surroundings. Technology. Applied science Using discoveries to create useful products. Physics. Study of matter and energy and their relationships Experimental Research using equipment Theoretical - PowerPoint PPT Presentation
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Physics
A Mathematical Science
Science
An organized way of studying our surroundings
Technology
Applied scienceUsing discoveries to create useful products
PhysicsStudy of matter and energy and their relationships Experimental
Research using equipment Theoretical
Construction of theory using mathematics to explain experimental data
Basic to all other sciences Chemistry, engineering, architecture,
medicine A few laws describe most physical
relationships
Traits Helpful to a Physicist:
KnowledgeInsightCreativityImaginationPatience
Scientific Method
Recognize the
ProblemForm a
Hypothesis
Test the Hypothesis
Draw Conclusions
Use observations
Conduct the experimentDesign an experiment
Collect data
Make predictions
Revise/ repeat experiment
Measurement
Definition of the base unit
SI Base Unit
Other common units
Length: distance light travels in 1/300,000,000s
meter km, cm, mm
Mass: mass of a Pt-Ir cylinder
gram kg, mg
Temperature:
0 K = -273 °C Kelvin
Time: period of radiation of Cesium-133
second
ms, min, h
Data Analysis
Chapter 2
Measurement
quantitative description Requirements: Know property attempting to measure Must have a standard for comparison Must have a method of comparison
International System of Measurement
SICreated by the French in 1795Used by most countriesUnits are related to powers of 10No fractions are used
Powers of ten
Peta - 1015 Tera - 1012 Giga - 109
Mega - 106
Kilo - 103
Hecto - 102
Deka - 101
Deci – 10-1
Centi – 10-2
Milli – 10-3
Micro – 10-6
Nano – 10-9
Pico – 10-12
Femto - 10-15
SI base units Unit Quantity Instrumen
t
Meter Length – distance between two points
meter stick
Kilogram
Mass – amount of matter
balance
Kelvin Temperature – how hot or cold an object is relative to others (avg. KE of particles)
thermometer
Second Time – interval between two events
clock
SI base units
Unit Quantity Instrument
Mole Amount of a substance(6.02 x 1023)
Count (calculated from mass)
Candela
Light Intensity – amount of light that falls on 1 m2 of surface
Light meter
Ampere
Electrical current – number of charges moving past a point in 1 second
Ammeter
Derived units
made from basic units Volume: amount of space occupiedVolume may determined by: Calculating from dimensions Graduated cylinder – if liquid Water displacement – if irregular in shape
Acceptable units: L, mL, m3, cm3, dm3
Determining Volume from Dimensions
V = l x w x h
= 1 dm3 = 1 L
1000 cm3 = 1000 mL
1 cm3 = 1 mL
1 dm1 dm
1 dm
Other Derived UnitsDensity – mass per unit volume D = m/V units: g/cm3
can be used to identify an unknown sample of matter
Weight – measure of force of gravity between 2 objects W = mg Newton (kg·m/s2) Measured with a spring scale
Scientific Notation
way to express extremely large or small numbers as powers of ten
M x 10n M = # between 1 and 10
n = any whole number
+n – # is larger than 1
-n – # is smaller than 1
Examples:
123456778 = 1.23456778 x 108
0.0000456 = 4.56 x 10-5
Operations:
To add or subtract, exponents must be the same. Adjust exponents
and decimal place Add or subtract M’s Keep n the same Adjust exponent and
decimal on final answer if needed
Example: 2 x 102 + 3 x 103
2 x 102 30 x 102
= 32 x 102
= 3.2 x 103
Operations
To multiply: multiply M’s Add n’s
To divide: Divide M’s Subtract n’s
Example: (2.0 x 102)(3.0 x
103)
= 6.0 x 10(2 + 3)
= 6.0 x 105
Using a Calculator for Scientific Notation
Locate or This stands for “x 10”Example: (2.0 x 102)(3.0 x 103) Enter “2.0 EE 2 times 3.0 EE 3 = ” 6.0 x 105 should appear on the display
Use the +/- key to enter negative exponentsIf the answer does not appear in sci. not., check the mode or punch SCI.
EE EXP
Solving Problems Using Dimensional Analysis
AKA: factor-label method, conversion factors, bridge methodUnits are treated as factors Multiply by a series of factors to cancel the unwanted unitsNo need to memorize lists of formulas You do have to know the conversion factors
Factors are equivalent.
1 m or 1 min
100 cm 60 s
Ex: ? m = 500 cm
? m = 500 cm
100 cm
1 m
= 5 m
Arrange factors to cancel unwanted unitsMultiply by numbers on the top of the barDivide by numbers on the bottomIf the units match on each side of the =, the problem should be correct.
Uncertainties of Measurement:
All instruments are subject to external forces and interpretation by people
Accuracy and Precision:
Describe the reliability of a measurementAccuracy: how close a measurement is to the correct value May be expressed as percent error
% error = accepted value – experimental value x 100
accepted value
Accuracy and Precision:
Precision: how close repeated measurements are to each other Depends on the exactness of the
instrument scale Measurements are recorded using
the correct number of significant digits
Parallax
Apparent shift in position of an object when viewed from various angles Meter reading Graduated cylinder reading
Significant digits
All definitely known digits plus one estimated digit.The number of sig. digs. should be observed in all calculations using measurements.Rules for determining number of sig digs in a recorded measurement are on page 39. Nonzero digits Captured zeroes Zeros after a decimal and after a number
Examples
300 m 1 sig dig303 m 3 sig digs3030 m 3 sig digs30.0 m 3 sig digs0.3 m 1 sig dig0.0003 m 1 sig dig0.00300 m 3 sig digs0.03030 m 4 sig digs
Reading Instrument Scales
Reading Instrument Scales
Reading Instrument Scales
Reading Instrument Scales
Rounding Off Numbers
If adding or subtracting measurements, round your answer to the least number of decimal places.
If multiplying or dividing measurements, round your answer to the least number of significant digits.
Problems – pages 27-28
Solving Equations Using Algebra
Isolate unknown on the left side of the equation before plugging in known values when possibleRemember the order of operations.Perform same operations to both sides of equationExample: Solve the following expression for b.
3y = 6x + 2ab2
Units in Equations:
Operations performed on numbers are also performed on unitsProper units = correct answer Good check method
Measurements of the same type must have the same units Make conversions using dimensional
analysis Example: 6 cm + 5 m + 2 mm
Representing Data observations →charts → graphs
→equationsGraph – visual display Circle – parts of a whole (percents) Bar – how one quantity varies with another Line – (same as bar)
Determine relationship (verbal or equation) Determine slope (rate of change of y to x) Interpolate – read between data points Extrapolate – read beyond data points (predict)
Variables
Independent – one manipulated in an experiment Plotted on the x-axis
Dependent – changes as a result of manipulating independent variable Plotted on the y-axis
Linear Relationships
Data points form a straight lineEquation: y = mx + b Slope (m) = rise/run y-intercept (b) =
value of y when x = 0
Direct relationship: As x increases, y
increases x
Parabolic Relationship
Data forms an upward curve (parabola)Equation: y = kx2
K = constant = y/x2
Power curve: as x increases, y increases more each time
x
y is greater for each increment of x
Root Curve
Data points form a an upward curve which levels offEquation: y = kx
Inverse Relationship
Data points slope downward (hyperbola)Equation: y = k/xAs x increases, y decreases
x
Identify these relationships:
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