Transcript Document

Physics for Dentistry and
Medicine students
PHYS 145
Text book
Physics; John D. Cutnell and Kenneth W.
Johnson; 7th edition; Wiley; 2007.
Chapter 1
Introduction and
Mathematical
concepts
The animation techniques used in the film Star Wars: Episode III—Revenge of the
Sith rely on computers and mathematical concepts such as trigonometry and vectors.
These mathematical tools will also be useful throughout this book in dealing with the
laws of physics. (Lucasfilm/20th Century Fox/The Kobal Collection, Ltd.)
Units of Measurement
System
SI (International
system)
CGS
BE (British
Engineering
system)
Meter (m)
Centimeter (cm)
Foot (ft)
Mass
Kilogram (kg)
Gram (g)
Slug (sl)
Time
Second (s)
Second (s)
Second (s)
Length
Meter
• Originally, the distance measured along the
earth’s surface between the north pole and the
equator.
• Eventually, the meter became the distance
between two marks on a bar of platinum–iridium
alloy (Figure) kept at a temperature of 0 °C.
• Today, the meter is defined as the distance that
light travels in a vacuum in a time of 1/299 792
458 second.
(The speed of light is a universal constant that is
defined to be 299 792 458 m/s)
The standard platinum–iridium meter bar.
(Courtesy Bureau
International des Poids et Mesures, France)
kilogram
• Originally, the kilogram was expressed in
terms of a specific amount of water.
• Today, one kilogram is defined to be the
mass of a standard cylinder of platinum–
iridium alloy, (Figure 2).
The standard platinum–iridium
kilogram is kept at the
International
Bureau of Weights and
Measures in Sévres, France.
This copy of the standard
kilogram is housed at the
National Institute of Standards
and Technology. (Sissy
Riley, Information Services
Division/National Inst of
Standards and Technology)
Second
• Originally, the second was defined according to
the average time for the earth to rotate once
about its axis, one day being set equal to 86 400
seconds. The earth’s rotational motion was
chosen because it is naturally repetitive,
occurring over and over again.
• Today, we use the electromagnetic waves
emitted by cesium-133 atoms in an atomic clock
like that in (Figure 3). One second is defined as
the time needed for 9 192 631 770 wave cycles
to occur.
This atomic clock, the
NIST-F1, is considered
one of the world’s
most accurate clocks.
It keeps time with an
uncertainty of about
one second in
twenty million years.
(© Geoffrey Wheeler)
Standard Prefixes Used to Denote
Multiples of Ten
Prefix Symbol Factor
Prefix Symbol Factor
Prefix Symbol Factor
tera
T
1012
Giga
*G
109
Mega
M
106
Kilo
k
103
Hecto
h
102
Deka
da
101
deci
d
10-1
centi
c
10-2
milli
m
10-3
micro
μ
10-6
nano
n
10-9
pico
p
10-12
femto
f
10-15
The Conversion of Units
• Example: Body Mass Index (BMI)
The body mass index (BMI) takes into
account your mass in kilograms (kg) and your
height in meters (m) and is defined as follows:
Massin kg
BMI = Heightin m
Determine the expression for the BMI of a
person who has a mass of 180 lb. and a height of
71 in.
(1 kg corresponds to 2.205 lb, and 1 ft = 12 in.,
1 m = 3.281 ft.; 1 in. = 2.54 cm)
2
1 kg
X kg
1m
2.205 lb
180 Ib
X = 81.6 kg
3.281 ft
39.372 in.
Xm
71 in.
X = 1.8 m
MBI 
81.6
 25.1 kg / m 2
2
1.8
BMI (Kg/m2)
Evaluation
Below 18.5
Underweight
18.5–24.9
Normal
25.0–29.9
Overweight
30.0–39.9
Obese
40 and above
Morbidly obese
Scalars and Vectors
• A scalar quantity is one that can be
described with a single number
(including any units) giving its size or
magnitude.
Examples: temperature, mass, volume, energy
and time.
• A vector quantity is a quantity that deals
inherently with both magnitude and
direction.
• displacement vector, velocity, force,
weight and acceleration.
A vector quantity has a magnitude and a direction.
The colored
arrow in this drawing represents a displacement
vector.
Vectors Addition and
Subtraction
  
R  A B

R  275m, dueeast  125m, dueeast  400m, dueeast



R  A B
R
 A2  B 2
B

 A
  t an1 

R  275m, dueeast  125m, duenorth
R
275m 2  125m 2
 302m
 125m 
o


24
.
4
north of east

 275m 
  t an1 
(a) The displacement vector for a woman
climbing 1.2 m up a ladder is D . (b) The
displacement vector for a woman climbing

1.2 m down a ladder is  D
The Components of a Vector
Ax  A cos
Ay  A sin 
Example:
Finding the
Components of a Vector
• A displacement vector has a magnitude of r =
175 m and points at an angle of 50.0° relative to
the x - axis in the figure. Find the x and y
components of this vector.

 112m
y  r sin   175m sin 50.0  134m
x  r cos  175m cos50.0
o
o
Example: Using Components
to Add Vectors
• The figure shows three displacement
vectors A, B, and C. These vectors are
arranged in tail-to-head fashion, because
they add together to give a resultant
displacement R, which lies along the x
axis. Note that the vector B is parallel to
the x axis. What is the magnitude of the
vector C?
   
A B C  R
Ax  Bx  C x  Rx
Ay  B y  C y  R y


A  20 m  sin 60.0  17.3 m
B  10 m  cos 0  10.0 m
B  10 m  sin 0  0 m
R  35.0 m  cos 0  35.0 m
R  35.0 m  sin 0  0 m
Ax  20 m  cos60.0 o  10.0 m
o
y
o
x
o
y
o
x
o
y
C x  Rx  Ax  Bx  15.0 m
C y  Ry  Ay  By   17.3 m
C  15   17.3  22.9 m
2
  tan1
2
 17.3
  49.07o south of east
15
Questions
• Are two vectors with the same magnitude
necessarily equal? Give your reasoning.
• (a) Is it possible for one component of a
vector to be zero, while the vector itself is
not zero? (b) Is it possible for a vector to
be zero, while one component of the
vector is not zero? Explain.
• Can two nonzero perpendicular vectors be
added together so their sum is zero?
Explain.
Problems
• Azelastine hydrochloride is an antihistamine
nasal spray. A standard size container holds
one fluid ounce (oz) of the liquid. You are
searching for this medication in a European
drugstore and are asked how many milliliters
(mL) there are in 1 oz. Using the following
conversion factors, determine the number of
milliliters in a volume of one fluid ounce:
1 gallon (gal) = 128 oz.;
3.785 x 10-3 m3 = 1 gal; 1 mL = 10-6 m3.
Problem
• At a picnic, there is a
contest in which hoses are
used to shoot water at
a beach ball from three
directions. As a result, three
forces act on the ball, F1, F2,
and F3. Where F1 = 50.0 N and F2 = 90.0 N.
Determine (a) the magnitude of F3 and (b) the
angle θ such that the resultant force acting on
the ball is zero.
Problem
• Vector A points along the +y-axis and has
a magnitude of 100.0 units. Vector B
points at an angle of 60.0° above the + xaxis and has a magnitude of 200.0 units.
Vector C points along the + x-axis and has
a magnitude of 150.0 units. Which vector
has (a) the largest x component and (b)
the largest y component?
Problem
• Soccer player #1 is 8.6 m
from the goal. If she kicks the
ball directly into the net, the
ball has a displacement
labeled A. If, on the other hand,
she first kicks it to player #2,
who then kicks it into the net,
the ball undergoes two successive
displacements, Ay and Ax. What are the
magnitudes and directions of Ax and Ay?