introduction and mathematical concepts chapter 1 1.1 the nature of physics physics predicts behavior...
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Introduction and Mathematical Concepts
Chapter 1
1.1 The Nature of Physics
Physics predicts behavior of nature applications
Newton’s Laws → Rocketry
Maxwell’s Equations → Telecommunications
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1.2 Units
units
meter (m): unit of length
kilogram (kg): unit of mass
second (s): unit of time
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1.3 The Role of Units in Problem Solving
CONVERSION OF UNITS
1 ft = 0.3048 m
1 mi = 1.609 km
1 hp = 746 W
1 liter = 10-3 m3
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1.3 The Role of Units in Problem Solving
Example 1 The World’s 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
feet 3212meter 1
feet 281.3meters 0.979 Length
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1.3 The Role of Units in Problem Solving
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1.3 The Role of Units in Problem Solving
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 hour and 3.281 feet = 1 meter.
second
feet95
s 3600
hour 1
mile
feet 5280
hour
miles 6511
hour
miles 65 Speed
second
meters29
feet 3.281
meter 1
second
feet951
second
feet95 Speed
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1.3 The Role of Units in Problem Solving
DIMENSIONAL ANALYSIS
[L] = length [M] = mass [T] = time
221 vtx
Is the following equation dimensionally correct?
TLTT
LL 2
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1.4 Trigonometry
h
hosin
h
hacos
a
o
h
htan
h
ho1sin
h
ha1cos
a
o
h
h1tan
222ao hhh
Pythagorean theorem:
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1.4 Trigonometry
a
o
h
h1tan 13.9m0.14
m25.2tan 1
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1.5 Scalars and Vectors
A scalar a single number:temperature, speed, mass
A vector magnitude and direction:velocity, force, displacement
8 m/s4 m/s
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1.6 Vector Addition and Subtraction
5 m 3 m
8 m
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1.6 Vector Addition and Subtraction
2.00 m
6.00 m
222 m 00.6m 00.2 R
R
m32.6m 00.6m 00.2 22 R
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1.6 Vector Addition and Subtraction
2.00 m
6.00 m
6.32 m
00.600.2tan
4.1800.600.2tan 1
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1.6 Vector Addition and Subtraction
A
B
BA
A
B
BA
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1.7 The Components of a Vector
yx AAA
scalar components Vector components
yxA ˆˆ yx AA
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1.7 The Components of a Vector
Example
A displacement vector has a magnitude of 175 m and points atan angle of 50.0 degrees relative to the x axis. Find the x and ycomponents of this vector.
rysin
m 1340.50sinm 175sin ry
rxcos
m 1120.50cosm 175cos rx
yxr ˆm 134ˆm 112
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1.8 Addition of Vectors by Means of Components
yxA ˆˆ yx AA
yx
yxyxC
ˆˆ
ˆˆˆˆ
yyxx
yxyx
BABA
BBAA
xxx BAC
yyy BAC
BAC
yxB ˆˆ yx BB