physics for scientists and engineers - university of … paik p. 3 classical physics mechanics and...
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Spring, 2008 Ho Jung Paik
Physics for Scientists and Engineers
Chapter 1Concepts of Motion
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PhysicsFundamental science
concerned with the basic principles of the Universefoundation of other physical sciences
Divided into six major areasClassical MechanicsThermodynamicsElectromagnetismOpticsRelativityQuantum Mechanics
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Classical PhysicsMechanics and Electromagnetism are basic to all other branches of classical physics
Classical physics were developed before 1900Our study will start with Classical Mechanics.
Also called Newtonian Mechanics
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Classical Physics, contIncludes Mechanics
Major developments by Newton, and continuing through the latter part of the 19th century
Thermodynamics
Optics
ElectromagnetismAll of these were not developed until the latter part of the 19th century
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Modern PhysicsBegan near the end of the 19th century
Phenomena that could not be explained by classical physics
Includes Theories of RelativityQuantum Mechanics
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Classical Mechanics TodayStill important in many disciplines
Wide range of phenomena can be explained with classical mechanics
Many basic principles carry over into other phenomena
Conservation Laws apply directly to other areas
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Objective of PhysicsTo find the fundamental laws that govern natural phenomena
To express the laws in the language of mathematics
To use these laws to develop theories that can predict the results of future experiments
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Theory and ExperimentsShould complement each other
When a discrepancy occurs, theory may be modified
Theory may apply to limited conditionse.g. Newtonian Mechanics confined to objects
1) traveling slowly with respect to the speed of light2) larger than atoms
Try to develop a more general theory
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Model BuildingA model is often a simplified system of physical components
Identify the components
Make predictions about the behavior of the system
The predictions will be based on interactions among the components and/orBased on the interactions between the components and the environment
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Models of Matter
Atoms has a central nucleus surrounded by electrons
Nucleus contains protons and neutrons
Protons and neutrons are made up of quarks
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The fundamental constituents of matter are considered to be particles that have zero size
e.g. electrons, quarks, photon, etc.
An extended object can be modeled as a mass at a single point in space and time
when its internal motions can be ignored
More complex objects can often be modeledas a collection of particles
“Particle” Model
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Quantities UsedIn Mechanics, three basic quantities are used
LengthMassTime
Will also use derived quantitiesThese are other quantities that can be expressed in terms of basic quantities
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Systems of MeasurementsUS System of measurement
Length in feet (ft)Time in seconds (s)Mass in slugs
Commonly, in pounds (lb)
SI – Systéme InternationaleAgreed to in 1960 by an international committeeMain system used in this text
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LengthSI Unit: meter, m
1 in = 2.54 cm ⇒ 1 m ≈ 3.28 ft
Previously defined in terms of a standard meter bar
Now defined by the distance traveled by lightin a vacuum during a given period of time
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MassSI Unit: kilogram, kg
1 lb = 0.45359237 kg⇒ 1 kg ≈ 2.20 lb
Based on a metal cylinder kept at the International Bureau of Standards, Paris
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TimeSI Unit: second, s
Previously defined based on a mean solar day
Now defined in terms of the oscillation of radiation from a cesium atom
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PrefixesPrefixes correspond to powers of 10
They are multipliers of the base unit
Examples:2 mm = 2 x 10-3 m3 g = 3 x 10-3 kg
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Derived QuantitiesCombinations of the fundamental quantities of length, mass and time
Example: Density It is defined as mass per unit volume
Units are kg/m3
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Densities
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Average Density of Earth?From Earth’s radius RE = 6.37 x 106 m,
Earth’s mass is ME = 5.98 x 1024 kg, therefore
The density of granite is 2.75 x 103 kg/m3
What does this tell us about the interior of Earth?
3213634 m1008.1)1037.6(π ×=×=EV
33321
24
kg/m1054.5m1008.1kg1098.5
×=××
==E
EE VMρ
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Atomic MassThe atomic mass is the total number of protons and neutrons in the element
Often measured in atomic mass units, u (or amu), the mass of a proton
1 u = 1.6605387 x 10-27 kgNote electron masses are negligible compared with 1 amu
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DimensionsBy dimensions, we mean how a quantity depends on L,M & T
denotes the physical nature of a quantity, not its size
Dimensions are denoted with square bracketsLength [L]Mass [M]Time [T]
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SymbolsThe symbol used for a quantity is not necessarily the symbol used for its dimension
Some quantities have one symbol used consistently
e.g. time is t virtually everywhere
Some quantities have many symbols used, depending upon the situation
e.g. lengths may be x, y, z, r, etc.
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Dimensional AnalysisTechnique to check the correctness of an equation or to assist in deriving an equation
Dimensions (length, mass, time) can be treated as algebraic quantities
add, subtract, multiply, divide
Both sides of equation must have the same dimensions!
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Dimensional Analysis, contGiven the equation: x = 1/2 at 2
Check dimensions on each side to see if it might be correct:
The equation is dimensionally correctThere are no dimensions for the constant 1/2
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Conversion of UnitsWhen units are not consistent, you may need to convert to appropriate ones
e.g. ft to m
Units can be treated like algebraic quantities that can multiply or cancel each other out
See the inside of the front cover for an extensive list of conversion factors
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Conversion of Units, contMultiply original value by a ratio equal to one, e.g., 12 in/1 ft = 1
Example, 15.0 in = ? cm
Always include units for every quantity in your answer
1 in = 2.54 cm, cm 1.38in 1
cm 2.54in 0.15 =×
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Reasonableness of ResultsWhen solving a problem, check your answer to see if it seems reasonable
e.g. a car going at 106 m/s is not reasonable
Make an order of magnitude “guess” to estimate what the answer should be
Order of magnitude is the closest power of 10Order of magnitude of 20 ⇒ 10Order of magnitude of 700 ⇒ 103
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How Many Ping Pong Balls?The average room size is ~20 ft x 15 ft x 8 ft
⇒ Vroom ≈ 103 ft3
The diameter of a ping pong ball is ~1 inch⇒ Vball ≈ (.1 ft)3=10-3 ft3
The ballpark estimate for the number N of balls that could fit in a room is:
N Vball≈ Vroom ⇒ N ≈ 106
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Significant FiguresA significant figure is one that is reliably known
Zeros may or may not be significantThose used to position the decimal point are not significantTo remove ambiguity, use scientific notation
In a measurement, the significant figures include the first estimated digit
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Significant Figures, examples0.0075 m has 2 significant figures
The leading zeros are placeholders onlyScientific notation: 7.5 x 10-3 m
10.0 m has 3 significant figuresThe decimal point gives information about the reliability of the measurement
1500 m is ambiguousUse 1.5 x 103 m for 2 significant figuresUse 1.50 x 103 m for 3 significant figures
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Significant Figures, operationsMultiplying or dividing: The number of significant figures is the same as the lowest number of significant figures in any factor
e.g. 25.57 m x 2.45 m = 62.6 m2
Adding or subtracting: The number of decimal places is equal to the smallest number of decimal places in any term
e.g. 135 cm + 3.25 cm = 138 cm
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Rounding Off NumbersLast retained digit is increased by 1, if the last digit dropped is ≥ 5
e.g. 1.36 ⇒ 1.4
Last retained digit remains as it is, if the last digit dropped is < 5
e.g. 1.34 ⇒ 1.3
Saving rounding until the final result will help eliminate accumulation of errors
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Measurement UncertaintyWhen measurements are made, there is always an uncertainty
Example: a rectangular plate is measured to have dimensions
L = 5.5 ± .1 m, W = 6.4 ± .1 m
This can be expressed as percentagesL = 5.5 m ± 1.8%, W = 6.4 m ± 1.6%
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Propagation of UncertaintyMultiplying or dividing: The percentage uncertainties are added
L x W = (5.5 m ± 1.8%)(6.4 m ± 1.6%)= 35 m2 ± 3.4%
Adding or subtracting: The absolute uncertainties are added
W - L = (6.4 m ± 0.1 m) - (5.5 m ± 0.1 m)= 0.9 m ± 0.2 m
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KinematicsDescribes motion while ignoring the agents (forces) that caused the motion
For now, will consider motion in one dimension
Along a straight line
Will use the particle modelInfinitesimal size, but has a finite mass
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Position
Defined in terms of a frame of reference (coordinate system)
The object’s position is its location with respect to the frame of reference
A = 28 m, B = 50 mC = 36 m, D = 0 m, E = −40 m, F = −55 m
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Position-Time Graph
Shows the motion of the particle (car)
The smooth curve is a guess as to what happened between the data points
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1-D DisplacementDefined as the change in position during some time interval
Represented as Δx; Δx = xf – xi SI units are meters (m) Δx can be positive or negative
Is independent of the frame of reference
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2-D Displacement
Example: A particle travels from A to B along the path shown
The distance traveled is the total length of the curve and is a scalar
The displacement is the solid line from A to B and is a vector
Independent of the path taken between the two points
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Scalars and VectorsScalar quantities are completely described by magnitude only
e.g. distance, speed, mass, temperature
Vectors quantities need both magnitude (numerical value) and direction to completely describe them
e.g. displacement, velocity, acceleration, force
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Adding Vectors
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Subtracting Vectors
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2-D Displacement, cont
rΔrr rrr+= 01
Final position Initial position Displacement
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Speed and VelocitySpeed is the distance traveled (scalar) divided by the time interval spent
, has no direction
Velocity is the displacement (vector) divided by the time interval spent
, has a direction
ΔtΔ
vavgl
=
ΔtrΔ
vavg
rr
=
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Velocity Vectors
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Relating Position to Velocity
ΔtvrrΔtrΔ=v
rrr
rvr
rr
rrr
+=
−=Δ
12
12
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Acceleration
ΔtvΔar
r=avg
Acceleration is the velocity change (vector)divided by the time interval spent
, has a direction
Acceleration occurs whenthe magnitude of velocity (speed) changes,the direction of the velocity changes, orboth the speed and direction change
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Acceleration in Circular Motion
Δtavvvv=vΔ
ΔtvΔa
if
ifrrr
rrr
rr
+=
−
=
Uniform circular motionOnly the direction of velocity changes
⇒ Centripetal acceleration
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Acceleration due to Gravity
Δtavvvv=vΔ
ΔtvΔa
if
ifrrr
rrr
rr
+=
−
=
Projectile motionBoth the directionand magnitude of velocity changes