physics uos ch1 ppt hs
TRANSCRIPT
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In t roduct ion and
Mathematical Concepts
Chapter 1
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1.1 The Nature of Phys ics
Physicshas developed out of the efforts
of men and women to explain our physical
environment.
Physics encompasses a remarkable
variety of phenomena:
planetary orbits
radio and TV waves
magnetismlasers
many more!
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1.1 The Nature of Phys ics
Physics predicts how nature will behave
in one situation based on the results ofexperimental data obtained in another
situation.
Newtons Laws Rocketry
Maxwells Equations Telecommunications
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1.2 Units
Physics experiments involve the measurement
of a variety of quantities.
These measurements should be accurate and
reproducible.
The first step in ensuring accuracy and
reproducibility is defining the unitsin which
the measurements are made.
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1.2 Units
SI unitsmeter (m): unit of length
kilogram (kg): unit of mass
second (s): unit of time
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1.2 Units
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1.2 Units
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1.2 Units
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1.2 Units
The units for length, mass, and time (as
well as a few others), are regarded asbaseSI units.
These units are used in combination to
define additional units for other important
physical quantities such as force andenergy.
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1.3 The Role of Units in Problem So lv ing
THE CONVERSION OF UNITS
1 ft = 0.3048 m
1 mi = 1.609 km
1 hp = 746 W
1 liter = 10-3m3
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1.3 The Role of Units in Problem So lv ing
Examp le 1 The Worlds Highest Waterfall
The highest waterfall in the world is Angel Falls in Venezuela,
with a total drop of 979.0 m. Express this drop in feet.
Since 3.281 feet = 1 meter, it follows that
(3.281 feet)/(1 meter) = 1
feet3212meter1
feet281.3meters0.979Length
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1.3 The Role of Units in Problem So lv ing
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1.3 The Role of Units in Problem So lv ing
Reasoning Strategy: Converting Between Units
1. In all calculations, write down the units explicitly.
2. Treat all units as algebraic quantities. When
identical units are divided, they are eliminatedalgebraically.
3. Use the conversion factors located on the page
facing the inside cover. Be guided by the fact that
multiplying or dividing an equation by a factor of 1
does not alter the equation.
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1.3 The Role of Units in Problem So lv ing
Example 2 Interstate Speed Limit
Express the speed limit of 65 miles/hour in terms of meters/second.
Use 5280 feet = 1 mile and 3600 seconds = 1 hourand
3.281 feet = 1 meter.
second
feet95
s3600
hour1
mile
feet5280
hour
miles6511
hour
miles65Speed
second
meters29
feet3.281
meter1
second
feet951
second
feet95Speed
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1.3 The Role of Units in Problem So lv ing
DIMENSIONAL ANALYSIS
[L] = length [M] = mass [T] = time
2
2
1 vtx
Is the following equation dimensionally correct?
TLTT
LL
2
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1.3 The Role of Units in Problem So lv ing
Is the following equation dimensionally correct?
vtx
LTT
LL
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1.4 Tr igonometry
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1.4 Tr igonometry
h
hosin
h
hacos
a
o
h
htan
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1.4 Tr igonometry
m2.6750tan o
h
m0.80m2.6750tan oh
a
o
h
h
tan
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1.4 Tr igonometry
h
ho1sin
h
ha1cos
a
o
h
h1tan
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1.4 Tr igonometry
a
o
h
h1tan 13.9m0.14
m25.2tan 1
1 4 T i t
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1.4 Tr igonometry
222
ao hhh Pythagorean theorem:
1 5 S l d V t
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1.5 Scalars and Vectors
A scalar quantity is one that can be described
by a single number:
temperature, speed, mass
A vector quantity deals inherently with both
magnitude and direction:
velocity, force, displacement
1 5 S l d V t
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1.5 Scalars and Vectors
By convention, the length of a vector
arrow is proportional to the magnitude
of the vector.
8 lb4 lb
Arrows are used to represent vectors. The
direction of the arrow gives the direction ofthe vector.
1 5 S l d V t
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1.5 Scalars and Vectors
1 6 V t A ddi t i d S bt t i
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1.6 Vector A ddi t ion and Subtract ion
Often it is necessary to add one vector to another.
1 6 Vector A ddi t ion and Subtract ion
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1.6 Vector A ddi t ion and Subtract ion
5 m 3 m
8 m
1 6 Vector A ddi t ion and Subtract ion
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1.6 Vector A ddi t ion and Subtract ion
1 6 Vector A ddi t ion and Subtract ion
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1.6 Vector A ddi t ion and Subtract ion
2.00 m
6.00 m
1 6 Vector A ddi t ion and Subtract ion
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1.6 Vector A ddi t ion and Subtract ion
2.00 m
6.00 m
222 m00.6m00.2 R
R
m32.6m00.6m00.2 22 R
1 6 Vector A ddi t ion and Subtract ion
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1.6 Vector A ddi t ion and Subtract ion
2.00 m
6.00 m
6.32 m
00.600.2tan
4.1800.600.2tan 1
1 6 Vector A ddi t ion and Subtract ion
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1.6 Vector A ddi t ion and Subtract ion
When a vector is multiplied
by -1, the magnitude of the
vector remains the same, but
the direction of the vector isreversed.
1 6 Vector A ddi t ion and Subtract ion
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1.6 Vector A ddi t ion and Subtract ion
A
B
BA
A
B
BA
1 7 The Compon ents of a Vector
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1.7 The Compon ents of a Vector
.ofcomponentvectortheand
componentvectorthecalledareand
r
yx
y
x
1 7 The Compon ents of a Vector
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1.7 The Compon ents of a Vector
.AAA
AA
A
yx
thatsoyvectorialltogetheraddand
axes,andthetoparallelarethatandvectors
larperpendicutwoareofcomponentsvectorThe
yxyx
1 7 The Compon ents of a Vector
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1.7 The Compon ents of a Vector
It is often easier to work with the scalar components
rather than the vector components.
.of
componentsscalartheareand
A
yx AA
1.magnitudewithrsunit vectoareand yx
yxA yx AA
1 7 The Compon ents of a Vector
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1.7 The Compon ents of a Vector
Example
A displacement vector has a magnitude of 175 m and points at
an angle of 50.0 degrees relative to thexaxis. Find thexand y
components of this vector.
rysin
m1340.50sinm175sin ry
rxcos
m1120.50cosm175cos
rx
yxr m134m112
1.8 Add i t ion o f Vectors by Means o f Components
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1.8 Add i t ion o f Vectors by Means o f Components
BAC
yxA yx AA
yxB yx BB
1.8 Add i t ion o f Vectors by Means o f Components
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1.8 Add i t ion o f Vectors by Means o f Components
yxyxyxC
yyxx
yxyx
BABA
BBAA
xxx BAC yyy BAC