Raymond A. Serway
Chris Vuille
Chapter One
Introduction
Outcomes
•Determine area and volume of different shapes and
figures.
•Identify physical quantity and applicable SI unit.
•Convert units.
•Apply basic trigonometry principles in everyday life.
•Interpret relations from graphs.
•Distinguish between scalars and vectors.
•Calculate resultant and equilibrant.
Theories and Experiments
• Physics is the natural science that involves the study
of matter and its motion and behaviour through
space and time
• Physics has been developed to explain our physical
environment.
• The theory makes predictions about how a system
should work, then experiments check the theories’
predictions
• Every theory is a work in progress
Basic Maths for Physics
 In science we encounter a lot of numbers that may
be :
too small - a lot of preceding zeros
e.g. 0,000000000000000000023
too large - a lot of trailing zeros
e.g. 23000000000000000000
 To simplify these numbers we write them in scientific
notation
Scientific Notation
 Move the decimal place until you have a number
between 1 and 9.
 Multiply by a power of 10, equal to the number of
places the decimal point has been moved.
 If the decimal point is moved to the left, the power
of 10 is positive
 If the decimal point is moved to the right the
power of 10 is negative
Example
In scientific notation
1. 2 890 000 000,00 = 2,89 x 109
2. 118000,0 = 1.18 x 105
3. 0,00008 = 8 x 10-5
4. 0,0000158 = 1,58 x 10-5
Activity 1
1.Write the following numbers in Scientific notation
(a) 58000 (b) 0.0026 (c) 70.6 (d) 0.3 (e) 2 400 000
(f) 0.000 000 684 (g) 0.0704 (h) 0.260 (i) 17600
(j) 0.04080 (k) 0.000500 (l) 357 000 000 000
2.Express the ff values in full
(a) 2.76 x 10-3
(b) 4 x106
(c) 1.2x10-2
add/subtract in Scientific Notation
Self-Study
• To add/subtract in scientific notation, the
exponents must first be the same.
Example:
Find the sum of 3.0 x 102 and 6.4 x 103
solution
3.0  10  6.4  10
2
3
 3.0  10 2  64  10 2
or 0.30 103  6.4 103
 67  10 2  6.7  103
• 67.0 x 102 is mathematically correct, but a number in standard scientific
notation can only have one number to the left of the decimal, so the
decimal is moved to the left one place and one is added to the exponent.
Scientific Notation
• Example 2
• Find the sum of 3.0 x 102 and 6.4 x 106
solution
3.0  10 2  6.4  10 6
 3.0  10 2  64000  10 2
?
= 6400300
= 6.4003 x 106
= 6.4 Mm
Activity 2
Find the sum of the following
numbers
1. 4.5 x 10-4 + 5.2 x 103
1. = 5.2 x 103
2. 6.1 x 105+ 1.2 x 10-3
2. = 6.1 x 105
3. 4.5 x 104 + 5.2 x 103
3. = 5.02 x 104
4. 6.1 x 10-5+ 1.2 x 10-3
4. = 1.261 x 10-3
Scientific Notation
Self-study
Multiplication
Division
3.4  10  4.2 x 10
6
 3.4  4.2  10
 14.28  10
 1.428  10
9
10
63
3
3.2  103
5.7  10 -2
3.2

 103( 2 )
5.7
 0.562  10 5
 5.62  10 4
Powers of Exponentials
(6.53 x 10-3)2 = (6.53)2 x 10(-3)x2
= 42.64 x 10-6
= 4.26 x 10-5
Activity 3
Calculate the ff
1. (4.5 x 10-4) x (5.2 x 103)
2. (6.1 x
105)/(1.2
x
10-3)
1. 23.4 x 10-1 = 2.34
2. 5.08 x 108
3. (3.74 x 10-3)4 3. (3.74)4 x 10 (-3)x4 = 1.96 x 10-10
Basic Maths for Physics
 In science we encounter a lot of numbers that may
be :
too small - a lot of preceding zeros
e.g. 0.000000000000000000023
too large - a lot of trailing zeros
e.g. 23000000000000000000
 To simplify these numbers we write them in powers
(exponents) of 10
Basic Maths for Physics
10  1 10
1
100 = 1 10
2
1000 = 1 10
3
10000 = 1 10
?
100000  1 10
?
1
 0.1  1  10 1
10
1
2
 0.01  1  10
100
1
 0.001  1  10 3
1000
1
 ?  1  10 ?
1000000
Prefixes
• Prefixes correspond to powers of 10
• Each prefix has a specific name
• Each prefix has a specific abbreviation and a
symbol
• See table 1.4 – text book
Prefixes
Examples
1)
2)
3)
4)
5)
6)
7)
8)
6
1 megameter =1 Mm = 1 x 10 m
1 kilogram =1 kg = 1 x 103 g
-2
1 centimeter =1 cm = 1 x 10 m
1.4 kilometer=?=?
0.3 nanometer =?=?m
?=1.7 mg =?g
-6
6 ? = 6 x 10 s=?
5 nanogram =?=?
Units
• Physics experiments involve the measurement of a
variety of quantities.
• To communicate the result of a measurement for a
quantity, a unit must be defined.
Examples of various units
measuring a quantity
International System of Units
• SI Units
– The International System of Units is the modern
form of the metric system, and is the most widely
used system of measurement.
– Agreed to in 1960 by an international committee
Section 1.1
Other Systems of Measurements
• cgs – Gaussian system
– Named for the first letters of the units it uses for
fundamental quantities
• US Customary
– Everyday units
– Often uses weight, in pounds, instead of mass as a
fundamental quantity
Section 1.1
International System of Units
• The International System of Units (SI) defines seven units
of measure as a basic set from which all other SI units
can be derived.
• The SI base units and their physical quantities are
• the meter (m) for measurement of length
• the kilogram (kg) for mass
• the second (s) for time
• the ampere (A) for electric current
• the kelvin (K) for temperature
• the candela (cd) for luminous intensity
• and the mole (mol) for amount of substance.
International System of Units
Base quantity
Symbol for
quantity
SI unit
SI unit symbol
length
l
metre
m
mass
m
kilogram
kg
time
t
second
s
electric current
I
ampere
A
temperature
T
kelvin
K
amount of
substance
n
mole
mol
luminous
intensity
Iv
candela
cd
Fundamental Quantities
• Mechanics uses three fundamental quantities
– Length (m)
– Mass (kg)
– Time (s)
• Other physical quantities can be constructed
from these three
Introduction
Length
• Units
– meter, m
• The meter is currently defined in terms of the
distance traveled by light in a vacuum during a
given time
•
Section 1.1
Mass
• Units
– kilogram, kg
• The kilogram is currently defined as the mass
of a specific cylinder kept at the International
Bureau of Weights and Measures in a vault at
France
Section 1.1
Standard Kilogram
Section 1.1
Time
• Units
– seconds, s
• The second is the SI base unit for time. It
is defined by 9 192 631 770 oscillations of the
radiation corresponding to the transition
between two levels of the caesium atom
Section 1.1
Units in Various Systems
System
Length
Mass
SI
meter
kilogram
cgs
centimeter gram
US
foot
slug
Customary
Section 1.1
Time
second
second
second
Conversions
• When units are not consistent, you may need to
convert to appropriate ones
• See the inside of the front cover for an extensive list
of conversion factors
• Units can be treated like algebraic quantities that can
“cancel” each other
• Example:
Section 1.5
Conversions
1 ft = 0.3048 m
1 mi = 1.609 km
1 hp = 746 W
1 liter = 10-3 m3
Conversions
Example 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 
Length  979.0 meters 
  3212 feet
 1 meter 
Conversions
Example 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.
feet
 miles  5280 feet  1 hour 
Speed   65

95



hour  mile  3600 s 
second

feet  1 meter 
meters

Speed   95

29


second
3.281
feet
second



Activity 8
SI Unit
Scientific notation
120 km/h
33.33 m/s
3.333 x 101 m/s
2.03 g/cm3
2030 kg/m3
2.030 x 103 kg/m3
25 liters
0.025 m3
2.50 x 10-2 m3
3200 µg
3.20 x 10-6 kg
3.20 x 10-6 kg
25.9 nm2
2.59 x 10-17 m2
2.59 x 10-17 m2
Activity
(a) Find a conversion factor to convert from miles per hour to
kilometers per hour. (b) For a while, South African law mandated
that the maximum highway speed would be 74,58 mi/h. Use the
conversion factor from part (a) to find the speed in kilometers per
hour. (c) The maximum highway speed has been raised to 80,8
mi/h in some places. In kilometers per hour, how much of an
increase is this over the 74,58 mi/h limit?
(d) Convert the following numbers into the units given in brackets
6,25 x 10-5 kg
(i) 62,5 mg
(kg)
62,5 x 10-6 kg
(ii) 567,90 ns
(μs)
567,9 x 10-3 μs
5,679 x 10-1 μs
(iii) 12,6 g/cm3 (kg/m3) 12600 kg/m3
1,26 x 104 kg/m3
Areas, volume & Circumference of
different objects
 about shapes and their properties.
 To discover patterns, find areas, volumes, lengths
and angles, and better understand the world
around us.
Trigonometry Review
Section 1.8
More Trigonometry
• Pythagorean Theorem
– r2 = x2 + y2
• To find an angle, you need the inverse trig
function
– For example, q = sin-1 0.707 = 45°
Section 1.8
Degrees vs. Radians
• Be sure your calculator is set for the
appropriate angular units for the problem
• For example:
– tan -1 0.5774 = 30.0°
– tan -1 0.5774 = 0.5236 rad
Section 1.8
Example
ho
tan q 
ha
ho
tan 50 
67.2m

ho  tan 50 67.2m   80.0m
Activity
• The two hot-air balloons in the drawing are
48.2 and 61.0 m above the ground. A person
in the left balloon observes that the right
balloon is 13.3° above the horizontal. What is
the horizontal distance x between the two
balloons?
• Answer: 54.1 m
Activities
1.Using your calculator, find, in scientific notation with appropriate
rounding,
(a) the value of (2.437 × 104)(6.5211 × 109)/(5.37 × 104)
(b) the value of (3.14159 × 102)(27.01 × 104)/(1 234 × 106).
2. The radius of a circle is measured to be 10.5 m. Calculate
(a) the area and (b) the circumference of the circle
3. A house is 50.0 ft long and 26 ft wide and has 8.0-ft-high ceilings.
What is the volume of the interior of the house in cubic meters and in
cubic centimeters?
Activities
1. The base of a pyramid covers an area of 13.0 acres (1 acre = 43 560
ft2) and has a height of 481 ft (Fig. below). If the volume of a
pyramid is given by the expression V = bh/3, where b is the area of
the base and h is the height, find the volume of this pyramid in
cubic meters.
2. In a certain right triangle, the two sides that are perpendicular to
each other are 5.00 m and 7.00 m long. What is the length of the
third side of the triangle?
Problem Solving Strategy
Section 1.9
Problem Solving Strategy
• Problem
– Read the problem
• Read at least twice
• Identify the nature of the problem
– Draw a diagram
• Some types of problems require very specific types of
diagrams
Section 1.9
Problem Solving cont.
• Problem, cont.
– Label the physical quantities
• Can label on the diagram
• Use letters that remind you of the quantity
– Many quantities have specific letters
• Choose a coordinate system and label it
• Strategy
– Identify principles and list data
• Identify the principle involved
• List the known(s) (given information)
• Indicate the unknown(s) (what you are looking for)
– May want to circle the unknowns
Section 1.9
Problem Solving, cont.
• Strategy, cont.
– Choose equation(s)
• Based on the principle, choose an equation or set of
equations to apply to the problem
• Solution
– Solve for the unknown quantity
– Substitute into the equation(s)
• Substitute the data into the equation
• Obtain a result
• Include units
Section 1.9
Problem Solving, final
• Check
– Check the answer
• Do the units match?
– Are the units correct for the quantity being found?
• Does the answer seem reasonable?
– Check order of magnitude
• Are signs appropriate and meaningful?
Section 1.9
Quantities in Motion
• A study of motion will involve the introduction
of a variety of quantities that are used to
describe the physical world.
• Examples of such quantities include distance,
displacement, speed, velocity, acceleration,
force, mass, momentum, energy, work, power,
etc. All these quantities can by divided into
two categories - vectors and scalars.
Vector and Scalar Quantities
A scalar quantity is one that can be described
by magnitude only:
Example: temperature, speed, mass
A vector quantity deals inherently with both
magnitude and direction:
Example: velocity, force, displacement
Vector and Scalar Quantities
• Vector quantities need both magnitude (size)
and direction to completely describe them
 Generally denoted by boldfaced type and an
arrow over the letter
 + or – sign for direction is sufficient for this
chapter
• Scalar quantities are completely described by
magnitude only
Section 2.1
Components of a Vector


x and y are called the x vector component

and the y vector component of r.
Components of a Vector

The vector components of A are two perpendicu lar


vectors A x and A y that are parallel to the x and y axes,
 

and add together vectoriall y so that A  A x  A y .
Components of a Vector
Example
A displacement vector has a magnitude of 175 m and points at
an angle of 50.0 degrees relative to the x axis. Find the x and y
components of this vector.
sin q  y r


y  r sin q  175 m sin 50.0  134 m



x  r cos q  175 m cos 50.0  112 m

r  112 mxˆ  134 myˆ
Vector Addition Using Components
Example
• The magnitudes of the four displacement vectors shown in
the drawing are A=16,0 m, B=11,0 m, C=12,0 m and
D=26,0 m.
(a) Describe the direction of each vector.
(b) Determine the magnitude and directional angle for the
resultant that occurs when these vectors are added
together.
R  Rx2  R y2 =
q  tan
1
 Ry

 Rx
 8.1 m 2   10.3 m 2
= 13 m

1  10.3 m 
  tan 
  52

8.1
m



Activity
Three forces are applied to an object, as indicated in
the drawing. Force F1 has a magnitude of 21.0 N and is
directed 30.0° W of N. Force F2 has a magnitude of
15.0 N due east. What must be the magnitude and
direction of the third force F3 such that the vector sum
of the three forces is 0 N?
Answer:
2
2
F3  F3 x  F3 y 
q  tan
1 
 4.5 N 2   18.2 N 2
F3 y 
1  18.2 N 

  tan 
  76
F

4.5
N


 3x 
 18.7 N
Activities
• A sailboat race course consists of four legs, defined by the
displacement vectors A, B, C and D as the drawing indicates. The
magnitudes of the first three vectors are A = 3.20 km, B = 5.10 km
and C = 4.80 km. The finish line of the course coincides with the
starting line. Using the data in the drawing, find the distance of the
vector D and the angle θ.
Activities
1. Three vectors are acting at a point as shown in Figure below. Their magnitudes are given in
arbitrary units. Calculate the resultant (magnitude and direction) of the three vectors.