Science Notes:
Measuring Matter, Force, and Energy
Matter,
force, and energy are common terms that have scientific meanings close
to the common use of the words. Matter is the stuff of which everything
is composed, and force is something that is capable of changing the motion
of an object. Energy is a property that tells us how much work we can
get out of the object that possesses that energy. In keeping with the
fact that science is based on measurements and observations, all of these
entities are described in terms that we can observe and measure. Therefore,
we first discuss these entities by examining and measuring their effects.
Matter
and force are the two fundamental entities of which the universe
is composed. All that exists can be classified in these terms. All environmental
phenomena occur because of the interactions between matter and transformations
of matter in space and time. As the arrangements between forces and masses
change, the change is manifested in terms of energy. Table 4 gives the
abbreviations for the physical qualities and their definition and units.
Physical
Quantity

Definition,
Unit

mass
m

quantity
of matter, kilogram

distance
d

linear
dimension of space, meter

time
t

dimension
of time, second

speed,
velocity, v

distance
per time, m/sec

acceleration,
a

velocity
change per time, m/sec^{2}

force
F

mass
times acceleration, kg . m/sec^{2} = Newton,
nt

Work,
energy W, E

force
times distance, nt.m = Joule, J


Table
4: Summary of physical quantities and
units.

Matter is
discussed in terms of the quantity of matter. This is called the mass.
The unit we will use to measure mass is the kilogram (gram, milligram)
in the MKS system that is globally adopted as the scientific system of
units. For most engineering applications, and for common trade in the
United States, the British system is used, in which the unit of mass is
the pound.
Force is
a more complicated concept. We experience or observe force through its
action on matter (as a push or pull). When a force acts on matter, it
changes the way that quantity of matter is moving (Newton's first law).
So we measure force by its capacity to produce acceleration in a mass.
Acceleration is a measure of change of motion, measured by how much speed
(m/sec) changes in a second. So the units for acceleration are meter per
second per second, or, m/sec^{2}. (Newton's second law: F
= ma). Thus the unit to measure force is a composite of the measure
of mass, and of acceleration. The unit is called a newton (kg.m/sec^{2}),
written as NT or N. So a onenewton force can change the acceleration
of a 1 kg mass by 1 m/sec^{2}.
When a force
(F) is applied to an object and moved through a distance (d,
measured in meters, m) in the direction of the force, we define
the work (W) done as: Work = Force * Distance moved in the direction
of the force, or symbolically,
W
= F · d
(Joules, J = NT · m)
When F
is measured in newtons (NT, or N) and distance in meters, the resulting
quantity of work is expressed in Joules. So, a force capable of producing
an acceleration of 2.3 m/sec^{2} by acting on a mass of 3 kilograms
is a 6.9 NT force. The weight of an object of mass m on Earth is
the force due to Earth's gravitational pull on that object. The gravitational
acceleration of the Earth is about 9.8 m/sec^{2}. (This means
that the gravitational force exerted by the Earth on a 1 kg object is
9.8 nt.). Thus the weight of a 5kilogram object on Earth is 5 kg * 9.8
m/sec^{2}, or 49.0 nt.
A 2.5 NT
force moving something through a distance of 4 m (meters) in its direction
does a work of 2.5 nt * 4 m, or 10 Joules. When a 5 kg object falls a
distance of 4 m, the work is done by the Earth's gravitational force.
As the gravitational force on 5kg is 49 NT, the work done by the Earth
on the 5 kg object in pulling it down by 4 m is 49 nt * 5 kg = 245 ntm
= 245 Joules.
Measuring
Energy: Work, Energy, Heat, and Power
All phenomena involve transformations of energy between potential and
kinetic forms. We discuss some transformations and calculations involving
energy in the next section. Before we do that, we need to understand some
definitions of different means of measuring energy.
Due to historical
reasons, different measures of energy were developed and used in physics
and chemistry. In the early times, physics dealt mainly with motion 
of bodies such as planets and stars, as well as smaller masses. Thus
forces and motion were the focal points of early physics^{[1]}.
Physics measured energy by means of the force required to change the state
of motion. The units of physics dominated the emerging fields of engines
as well, where forces were used to produce motion. How much energy could
be produced every second was the question in designing engines. The amount
of energy per unit of time is defined as power. Thus power has
the units of Joules (energy) per second, also known as a watt. One watt
is one Joule per second. We also have the Horsepower, which is the unit
in the British system. It is understandable that with the horse as one
of the important "animal engines," the early engines were compared
to the power of a horse to move things.
Chemistry
started as the study of changes in the nature of substances^{[2]}.
Heat was a common method used to change substances. Temperature, or the
feel of heat, was used to measure the amount of heat in a substance. Thus
heat energy was measured by chemists in terms of the energy required to
change the temperature of a common substance  water. Thus the unit of
energy (heat) most used by chemists was the calorie, defined as the amount
of heat required to change the temperature of one gram of water by one
degree Celsius. Of course, there are also two different measures of temperature
depending on whether you follow the British or the Metric system. We will
confine ourselves to the Metric system, and hence to degrees celsius (or
centigrade). Count Rumford (Benjamin Thompson) and James Joule, scientists
in the eighteenth century, were among the earliest to show that mechanical
energy and heat could be changed into each other, primarily by noting
that when mechanical work is done, the friction produces heat.
Joule
in fact determined that 4.18 Joules of mechanical work is equivalent to
1 calorie of heat^{[3]}. In practice, a calorie
is a very small amount of heat, and so a kilocalorie, also written as
Calorie (or kcal) is used. A kilocalorie is therefore 4,180 Joules. The
units of energy, heat, and power are summarized in Table 5. Because of
the different origins of the ways of measuring energy, and the numerous
manifestations of energy, there are several units for measuring energy.
Units also vary depending on the practices in different fields, and on
the type of energy being measured. This can be confusing at times. The
tables below summarize most of the units and contexts.
Physical
Quantity and Definition

Units

Metric
system

British
system

Energy,
work (mechanical) = force * distance

nt.m = J

ftlbs 
Energy
(chemical, heat) = energy to change temperature 
calorie (cal)

British
thermal unit (BTU)
1BTU = 778 ftlbs 
Power
= work/energy per unit time 
J/sec = Watt
1000 Watts = 1 KW

horsepower
(HP)
1 HP = 550 ft.lbs/sec
1 HP = 746 watts 
Energy
= power * time 
kilowatt
* hour = (kwh) kilowatthour

no
equivalent 

Table
5:
Physical Quantity, Definition, and Units.

Work and
energy transform into one another. They are measured in the same units.
So a "Joule" is also a unit for measuring energy. As described
in more detail later, all energy is either stored (potential energy) or
is in the process of causing motion of an object (kinetic energy). Thus
we can represent the energy work relationship in a continuous state of
mutual transformation in a system, including the energy that is "lost"
(has become unavailable).
Potential
Energy

Work

Kinetic
Energy

+

Unavailable
Energy

Depending
on the context, the different units above are used in physics or mechanical
engineering:
 Physics/mechanical:
work = force * distance = lb * ft^{2}/sec^{2}, kg * m^{2}/sec^{2} (Joule)
 electrical
energy: kilowatts * hour = kilowatt hour (KWh)
 hydraulics/fluids:
energy head = equivalent distance in feet, or meters
 chemical
process energies: energy head and calorific content = calorie
For physics,
mechanics, and engines, the work is typically stated in terms of moving
something in a unit of time, e.g., energy per second, with power (watts)
in terms of joules per second. For chemistry, the work is changing the
nature of substances, therefore the units are in terms of the amount of
heat needed to change the temperature of water (calorie).
Name
of Unit

Symbol

Value
in calories

Value
in Joules

Measures

kilocalorie 
kcal
or Cal

1000

4184

Scientific
work unit for nutritional requirements and heat 
calorie 
cal

1

4.184

Scientific
work 
British
Thermal Unit 
BTU

252

1054

Engineering
Technology, heating, a/c 
Joule 
J

.24

1

Standard
unit especially for mechanical energy 
Kilowatthour 
kwh

8.6
x 10^{5}

3.6
x 10^{6}

Standard
Unit for Electrical Engineering 
Quad 



Used
for large quantities of Energy 

Table
7: Units of Energy and conversion factors.

Exercises: 
1. 
Look
at the following appliances to get an idea of the power they
generate: a hair dryer, a toaster, a clothes dryer, a light
bulb. For frame of reference, we receive about 1,400 watts of
solar energy for every square meter of the Earth. 
2. 
Each
kilogram of water at Niagara Falls falls through a height of
184 ft. (or approximately 56 m). What is the amount of work
done by the force of gravity on the 1 kg of water? What happens
to this work? 
3. 
You
use a force of 19.6nt to raise a rock (of mass 2 kg) vertically
through a distance of 3 m from the ground.
 Why
vertically?
 What
force are you working against?
 What
is providing the energy for that work? How?
 How
many Joules of work is done?
Now,
assume the rock is kept at the level of 3 m above ground.
How many Joules of (stored) potential energy does it have?
Potential energy will be released if the rock is allowed to
fall. For example, suppose the rock falls squarely on the
top of a nail head held vertically on a piece of wood, and
the nail has to overcome a force of friction of 9.8 nt to
be driven into the wood.
 How
far can the rock theoretically drive the nail in?
 What
assumptions have you made in answering this?

4. 
A
block is pushed 1 meter along a horizontal surface by a horizontal
force of 60 nt. The opposing force of friction is 10 nt.
 How
much work is done by the 60 nt force?
 What
is the work of the friction force?
 Where
does the work go?
 What
is the role of gravity in this situation?

5. 
Power
is the energy released (work done) per unit time, or the rate
that is, power is the rate of releasing energy (or,doing work).
It is measured in watts (Joules per second).
Thus
a coal burning power plant of 1000 megawatts (MW) releases
__________ Joules every second. Where
does the power come from?
If
the power plant were a hydroelectric plant instead, generating
power using the Niagara waterfalls, how much water (in kilograms)
will have to fall every second if the water falls through
the 56 m to release the same amount energy?
In
the operation of the Niagara power plant, 102,000 cu.ft. of
water falls through 56 m every second. If all this
energy could be connected to electricity, how many megawatts
of power would be produced?

6. 
A
skier who weighs 700 nt skis down a hill that is 60 m long and
20 m high. If 1000 J of energy is lost in overcoming friction,
what is his kinetic energy at the bottom of the hill? 

[1]Physics derives its name
from the Greek word "Physis," meaning the nature of things;
and the field was given its name by Aristotle.
[2]Chemistry
derives its name from "Cheo," which means "to pour.
[3]There
is an anecdote that Joule did this experiment for the first time by
noting the temperature difference between the bottom and top of a beautiful
waterfall in Switzerland while he was on his honeymoon there!
