# Chapter 1 - Silvina Gatica

```ANNOUNCEMENTS
•Students that have purchased a book that includes the access
code to WileyPlus, can submit the homework in WileyPlus
•All students must go once a week to recitation (R 300) and
once a week to Lab (R 305). See the syllabus to know which
day you have lab or rec. or check with your instructor.
•The first homework is posted in WebAssign and WileyPlus.
Deadline is extended until Sep. 4 to allow all students to register
in the system.
Chapter 1
Introduction and
Mathematical Concepts
1.2 Units
SI units
meter (m): unit of length
kilogram (kg): unit of mass
second (s): unit of time
1.2 Units
1.3 The Role of Units in Problem Solving
1.2 Units
The units for length, mass, and time (as
well as a few others), are regarded as
base SI units.
These units are used in combination to
define additional units for other important
physical quantities such as force and
energy.
1.3 The Role of Units in Problem Solving
THE CONVERSION OF UNITS
1 ft = 0.3048 m
1 mi = 1.609 km
1 hp = 746 W
1 liter = 10-3 m3
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,
Length = 979.0 (meters) = 979.0 (3.281 feet) = 3212 feet
1.3 The Role of Units in Problem Solving
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 eliminated
algebraically.
3. Use the conversion factors located on the page
facing the inside cover.
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.
 miles  5280 feet 
feet
Speed  65
 65
 95
 hour   3600 s 
second
feet   (1/3.281) meter 
meters
 Speed  
95
 95
 29
 second  

second
second

1.3 The Role of Units in Problem Solving
DIMENSIONAL ANALYSIS
[L] = length
[M] = mass
[T] = time
Is the following equation dimensionally correct?
x  vt
1
2
2
L  2
L   T  LT
T 
Wrong 
1.3 The Role of Units in Problem Solving
Is the following equation dimensionally correct?
x  vt
L
L   T  L
T 
Right 
1.4 Trigonometry: Review
1.4 Trigonometry
ho
sin  
h
ha
cos  
h
ho
tan  
ha
1.4 Example: how high is the building?
ho
tan  
ha
ho
tan 50 
67.2m

ho  tan 50 67.2m   80.0m

1.4 Trigonometry
 ho 
  sin  
h
1
 ha 
  cos  
h
1
 ho 
  tan  
 ha 
1
1.4 Example: How deep is the lake?
 ho 
  tan  
 ha 
1
 2.25m 

  tan 
  9.13
 14.0m 
1
d  22.0m tan(9.13 ) 3.53
o
1.4 Trigonometry
Pythagorean theorem:
h h h
2
2
o
2
a
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 Scalars and Vectors
Arrows are used to represent vectors. The
direction of the arrow gives the direction of
the vector.
The length of a vector
arrow is proportional to the magnitude
of the vector.
8 lb
4 lb
Example: Car moves on two steps, both due East
3m
5m
8m
Example: Car moves on two steps, first due east, later due north.
2.00 m
6.00 m
R  2.00 m  6.00 m
2
R
2
2
2.00 m  6.00 m
2
2
 6.32m
R
2.00 m
6.00 m
tan   2.00 6.00
  tan
1
2.00 6.00  18.4

6.32 m
2.00 m

6.00 m
When a vector is multiplied
by -1, the magnitude of the
vector remains the same, but
the direction of the vector is
reversed.

B
 
AB

A

A
 
AB

B
1.7 The Components of a Vector


x and y are called the x vector component

and the y vector component of r.
1.7 The 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 .
1.7 The Components of a Vector
It is often easier to work with the scalar components
rather than the vector components.
Ax and Ay are the scalar components

of A.
xˆ and yˆ are unit vecto rs with magnitude 1.

A  Ax xˆ  Ay yˆ
1.7 The 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   y r
y  rsin   175 msin 50.0o134 m

cos   x r
x  rcos  175 mcos50.0o112 m
r
r  112 mxˆ  134 myˆ

1.8 Addition of Vectors by Means of Components
  
C AB

A  Ax xˆ  Ay yˆ

B  Bx xˆ  By yˆ
1.8 Addition of Vectors by Means of Components
r
C  Ax xˆ  Ay yˆ  Bx xˆ  By yˆ
 Ax  Bx xˆ  Ay  By yˆ

Cx  Ax  Bx
C y  Ay  By
```