Transcript Document

CHAPTER 1
INTRODUCTION AND
MATHEMATICAL
CONCEPTS
1.1 The Nature of Physics
Laws of physics:
Describe heat generated by burning match
 Determine star speed
 Assist police with radar

Galileo and Newton

Laws have roots in rocketry and space
travel
1.1 The Nature of Physics
Physics is the core of:
X-rays
 Telecommunication
 Lasers
 Electronics

1.2 Units
System
SI
CGS
BE
Length
Meter (m)
Centimeter Foot (ft)
(cm)
Mass
Kilogram
(kg)
Gram (g)
Time
Second (s) Second (s) Second (s)
Slug (sl)
1.2 Units
Base Units used with laws to define
additional units for quantities
Force
 Energy

Derived Units combinations of base
units
1.3 The Role of Units in
Problem Solving
Conversion of Units
 3.281
ft = 1 m
Ex. 1
Express 979 m in ft
979 m
3.821 ft =
1m
3212 ft
1.3 The Role of Units in
Problem Solving
If units do not combine algebraically to
give desired results  conversion is not
correct
Ex. 2 Express 65 mi/hr in m/s
65 mi
5280 ft
hr
m
29 meter
1 hr
1 mi
3600 s 3.821 ft
sec
 Only quantities with same units can be
added or subtracted
1.3 The Role of Units in
Problem Solving
Dimensional Analysis
Dimension= physical nature of a
quantity and type of unit used to specify
it
 Ex:
Distance Length {L}
used to check validity of equation
1.4 Trigonometry
sinØ= ho/h
cosØ= ha/h
tanØ= ho/ha
h
ho
ø
ha
1.4 Trigonometry
Ex: Trig ho= ??
tanØ= ho/ha
ho= (ha)(tanØ) = (67.2m)(tan50°) = 80m
ho
50°
ha= 67.2 m
1.4 Trigonometry
Inverse Functions
used to find angle if two sides are known
Ø= Sin-1(ho/h)
Ø=Cos-1(ha/h)
Ø=Tan-1(ho/ha)
1.4 Trigonometry
Pythagorean Theorem
Square length of hypotenuse of Right
Triangle is equal to sum of square of
lengths of other two sides
h2= ho2 + ha2
1.5 The Nature of Physical
Quantities: Scalars &
Vectors
Scalar Quantity
One that can be described by a single
number (including units) giving its size or
magnitude
 Answers “How much is there?”
 Ex: Volume, Time, Temperature, Mass

1.5 The Nature of Physical
Quantities: Scalars &
Vectors
Vector Quantity
One that deals inherently with both
magnitude and direction
 Arrows used to show direction

Direction of arrow = Direction of vector
 Length of arrow is proportional to magnitude


All forces are vectors
Force = push/pull
 Magnitude measured in Newtons

1.5 The Nature of Physical
Quantities: Scalars &
Vectors
Main Difference
Scalars do not have direction; vectors do
Negative and positive signs do not
always indicate a vector quantity
Vector has physical direction (east, west)
 Temperatures have (+) and (-) , but no
direction  not a vector

1.6 Vector Addition &
Subtraction
Addition

When adding vectors you must take both
magnitude and direction into account
1.6 Vector Addition &
Subtraction
Colinear
2 or more vectors that point in the same
direction
 Arrange head-to-tail and add length of total
displacement  Gives the resultant vector
 R=A+B

A
B
R

Only works with this type of vector addition
1.6 Vector Addition &
Subtraction
Perpendicular
2 vectors with a 90° angle between them
 Arrange head to tail and use pythagorean
theorem
 R2 = A2 + B2

R
A
B
1.6 Vector Addition &
Subtraction
Not colinear, not perpendicular

Must add graphically
Draw the components head-to-tail
proportionally & accurately
 Measure the resultant

1.6 Vector Addition &
Subtraction
Subtraction
Multiply one of the vectors by –1 to reverse
direction
 Add like before

1.7 The Components of a
Vector
Vector Components
Components of vector can be used in
place of the vector itself in any calculation
in which it is convenient to do so
 Components are any two vectors that add
up vectorally to the original vector
 R= x + y

R
y
x
1.7 The Components of a
Vector
In two dimensions the vector
components of a vector A are two
perpendicular vectors Ax and Ay that
are parallel to the x & y axes
Add together so that A = Ax + Ay
Do not have to be x & y, but it is easier
to use them ( especially with trig )
1.7 The Components of
a Vector
For a vector to be zero, all its
components must be zero
Two vectors are equal if, and only if,
they have the same magnitude and
direction

If they are equal, their components are
equal
1.8 Addition of Vectors by
Means of Components
Components are most convenient and
accurate way to add vectors
If C= A + B
Then Cx = Ax + Bx and Cy= Ay + By
By
C
Ay
Ax
Bx
1.8 Addition of Vectors by
Means of Components
Example: A jogger runs 145 m in a
direction of 20.0° east of north
(displacement vector A) and then 105 m
in a direction 35.0° south of east
(displacement vector B). Determine the
magnitude and direction of the resultant
vector C for these two displacments
1.8 Addition of Vectors by
Means of Components
Vector
A
x Component y Component
Ax=(145m)(sin20.0°)
=49.6m
B
Bx=(105m)(cos35.0°)
=86.0m
C
Ax + Bx = Cx = 135.6 m
Ay= (145m)(coz20.0°)
=136m
By= -(105m)(sin35.0°)
= -60.2m
Ay + By = Cy = 76 m
1.8 Addition of Vectors by
Means of Components
Bx
Ax
35.0°
B= 105 m
Ay
A= 145 m
20.0°
C
By
1.8 Addition of Vectors by
Means of Components
C²= Cx² + Cy² = 155m
Ø=Tan-1(76m/135.7m) = 29°
Vocabulary
Base SI units- units for length (m), mass
(kg), and time (s).
Derived units- units that are
combinations of the base units.
TrigonometrySinθ = ho/h Cosθ = ha/h Tanθ = ho/ha
Vocabulary
Pythagorean Theorem- h^2=ho^2+ha^2
Scalar quantity- A single number giving its
size or magnitude.
Vector quantity- A quantity that deals
inherently with both magnitude and direction.
Resultant vector- the total of the vectors.
Vector components- two perpendicular
vectors Ax and Ay that are parallel to the x
and y axes, respectively, and add together
vectorially so that A=Ax+Ay.
 Mathematical Steps
 Draw vectors (sketch)
 Add Graphically (for estimation)
 Make a chart
 Find Components (Horizontal and
Vertical)
 Check your signs
 Add columns of the chart together
 Draw the resulting components
 Draw the resultant
 Use Trig and the Pythagorean Theorem
to get angle and total length