Module 1

Module 1
PHYSICS FOR ENGINEERS
In this Module
 Measurements in Physics
At the completion of this module, you should be able to:

 Differentiate fundamental quantities from derived quantities
 Convert units from one system to another
Are you ready? Then start the lesson now!
Lesson
MEASUREMENT IN PHYSICS
1
Physics for Engineers, Surigao del Sur State University – Bislig Page | 1
INTRODUCTION
Why do we have to measure? We need to measure because measuring helps
us know more about the things around us. We measure when buying goods in
the market; we measure the temperature of a place to wear appropriate
clothes. Measuring is also important to our health – we need to measure the
dosage of the medicine we take whenever we are sick.
Physics is the study of matter. In a quite literal sense, physics is the greatest
of all natural sciences: it encompasses the smallest particles, such as
electrons and quarks; and it also encompasses the largest bodies, such as
galaxies and the entire universe.
Physics usually involves experiments to support, refute or validate a
hypothesis or a theory. These experiments require measurement.
This module will take you back to the basics and relearn the art of measuring.
It is very important in the pursuit of learning physics because almost
everything relies on accurate measures.
THE MEASURING PROCESS

In order to carry out measurements, a system of standards and a system of
units should be defined. Two systems of units have evolved: the metric
system and the English system.
The metric system has two variations: the mks (meter-kilogram-second) system
and the cgs (centimeter-gram-second) system. The English system is otherwise
known as the fps (foot- pound-second) system.
The International System of Units, abbreviated SI from the French
¿ Système International d ' Unités , is the modern form of the metric system. It is
the system of units that the General Conference on Weights and Measures
has agreed upon and is legally enforced in almost all parts of the world.
Physical quantities may either be fundamental or derived.
Fundamental quantities are basic quantities which are independent of one
another. The SI fundamental quantities are length, mass, time,
thermodynamic temperature, electric current, luminous intensity, and amount
of substance.
Derived quantities are combination of fundamental quantities. For example,
speed may be defined as distance traveled divided by time. Other familiar
examples of derived quantities are acceleration, density, work and energy.
SI Fundamental Units
Symbo
Quantity Unit Definition
l
One meter is the distance traveled by
light in a vacuum during a time
Length meter m 1
interval of of a second
299792458
One kilogram is the mass of the
kilogra standard platinum-iridium cylinder
Mass kg
m kept at the International Bureau of
Weights and Measures in France
One second is the duration of
9192631770 periods of the radiation
Time second s corresponding to the transition
between two hyperfine levels of the
ground state of cesium-133 atoms
1
One kelvin is the fraction of the
Temperature kelvin K 273.16
triple point of water.
One ampere is the constant current
flowing in each of two long parallel
wires, 1.0 m apart, that would produce
Electric current ampere A
between these wires a force equal to
a 2 ×10−7 newton per meter length of
each wire
One candela is the luminous intensity
in a given direction of a source that
emits a monochromatic radiation of
Luminous
candela cd frequency 540 ×1012 Hz and that has a
Intensity
radiant intensity in that direction of
1
watts per steradian.
683
One mole is the amount of substance
Amount of that contains as many atoms or
mole mol
substance molecules as there are atoms in 0.012
kg of carbon-12.
SCIENTIFIC NOTATION AND UNIT CONVERSION

Scientific notation is a convenient and widely used method of expressing large
and small numbers. Any quantity may be expressed in the form
N ×10n ,
where N is any number between 1 and 9, and n is the appropriate power of
10.
To help you with expressing into scientific notation, you can follow these
steps:
1. Identify whether the number is large or small.
2. Move the decimal point.
a. If the number is greater than 10, move the decimal point to the
left to create a new number ranging from 1 to 9.
b. If the number is less than 10, move the decimal point to the right
to create a new number ranging from 1 to 9.
3. Write the base 10 and the exponent n, which signifies the number of
times the decimal point was moved.
4. The exponent n is positive if the decimal point is moved to the left; it is
negative if the decimal point is moved to the right.
SAMPLE PROBLEM 1.1
Express the following in scientific notation.
m
1. The speed of light is approximately 300,000,000 .
s
Solution:
From 300,000,000.0, we move the decimal point to the left (thus positive
exponent) eight times (thus N=3 and n=8).
m 8m
Therefore, 300,000,000 =3 ×10 .
s s
2. The mass of a strand of hair is approximately 0.00000062 kg.
Solution:
From 0.00000062, we move the decimal point to the right (thus negative
exponent) seven times (thus N=6.2 and n=−7).
Therefore, 0.00000062 kg=6.2× 10−7 kg .
Try This
Express (a) 0.000646 and (b) 5,430,000 in scientific notation.
In expressing SI measurements in scientific notation, the SI prefixes are used

to denote decimal multiples and submultiples of the SI units. These prefixes
are listed in the table below.
SI Prefixes
SI Prefix Symbol Multiplier SI Prefix Symbol Multiplier
24
yotta- Y 10 yocto- y 10−24
21
zeta- Z 10 zepto- z 10−21
18
exa- E 10 atto- a 10−18
15
peta- P 10 femto- f 10−15
12
tera- T 10 pico- p 10−12
9
giga- G 10 nano- n 10−9
6
mega- M 10 micro- μ 10−6
3
kilo- k 10 milli- m 10−3
2
hecto- h 10 centi- c 10−2
deca- da 101 deci- d 10−1
The simplest way to convert one unit to another is to form a conversion ratio
with the desired unit on the numerator and the unit to be converted at the
denominator. The original quantity is then multiplied by this conversion ratio.
Sample Problems 1.2 demonstrate how this is done.
Sample Problems 1.2
1. Convert (a) 55 km to meters and (b) 12 g to kilograms. Express your

answers in scientific notation.
Solution:
1000 m
a. 55 km=55 km × =55 ×1000 m=55,000 m .
1 km
55,000 m=5.5 ×10 4 m .
1 kg 12 kg
b. 12 g=12 g × = =0.012 kg.
1000 g 1000
0.012 kg=1.2× 10−2 kg.
2. The SI unit of force is the newton, represented by a capital letter N.

m
One newton of force gives a 1.0 kg body an acceleration of 1.0 2 . 1 N is
s
m
equal to 1 kg 2 . A smaller unit of force is the dyne. 1 dyne is equal to
s
cm
1 g 2 . How many dynes are there in 1 N ?
s
Solution:
m 1000 g 100 cm cm
1 N =1 kg 2 × × =100,000 g 2 =100,000 dynes .
s 1 kg 1m s
5
100,000 dynes=1 ×10 dynes.
mi
3. The world land speed record of 763.0 was set on October 15, 1997,
h
by Andy Green in the jet-engine car Thrust SSC. Express this speed in
meters per second.
Solution:
First we determine the conversion factors needed,
1 mi=1.609 km
1 km=1000 m
1 hr=3600 s
mi mi 1.609 km 1000 m 1h m
763.0 =763.0 × × × =341.019
h h 1 mi 1 km 3600 s s
LESSON TEST
Answer the following problems. Show you solutions in a whole
sheet of paper. Send your answers to my facebook account Toper
Man.
1. A solid peace of lead has a mass of 23.94 g and a volume of 2.10 cm3.
From these data, calculate the density of lead in kilograms per cubic
meter.
2. A rectangular lot has a width of 75.0 ft and a length of 125 ft. Determine
the area of this lot in square meters.
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 cubic
centimeters?

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PHYSICS FOR ENGINEERS

At the completion of this module, you should be able to:

Are you ready? Then start the lesson now!

THE MEASURING PROCESS

SCIENTIFIC NOTATION AND UNIT CONVERSION

Express (a) 0.000646 and (b) 5,430,000 in scientific notation.

In expressing SI measurements in scientific notation, the SI prefixes are used

Sample Problems 1.2 demonstrate how this is done.

Sample Problems 1.2

1. Convert (a) 55 km to meters and (b) 12 g to kilograms. Express your

2. The SI unit of force is the newton, represented by a capital letter N.

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