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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/sec2

force F

mass times acceleration, kg . m/sec2 = 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/sec2. (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/sec2), written as NT or N. So a one-newton force can change the acceleration of a 1 kg mass by 1 m/sec2.

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/sec2 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/sec2. (This means that the gravitational force exerted by the Earth on a 1 kg object is 9.8 nt.). Thus the weight of a 5-kilogram object on Earth is 5 kg * 9.8 m/sec2, 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 nt-m = 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

Metric system
British system
Energy, work (mechanical) = force * distance

nt.m = J

Energy (chemical, heat) = energy to change temperature

calorie (cal)

British thermal unit (BTU)
1BTU = 778 ft-lbs
Power = work/energy per unit time

J/sec = Watt
1000 Watts = 1 KW

horse-power (HP)
1 HP = 550 ft.lbs/sec
1 HP = 746 watts
Energy = power * time

kilowatt * hour = (kwh) kilowatt-hour

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).



Depending on the context, the different units above are used in physics or mechanical engineering:

  • Physics/mechanical: work = force * distance = lb * ft2/sec2, kg * m2/sec2 (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
Value in calories
Value in Joules
kcal or Cal
Scientific work unit for nutritional requirements and heat
Scientific work
British Thermal Unit
Engineering Technology, heating, a/c
Standard unit especially for mechanical energy
8.6 x 105
3.6 x 106
Standard Unit for Electrical Engineering

Used for large quantities of Energy
Table 7: Units of Energy and conversion factors.



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?

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?

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?

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!



  ©Copyright 2003 Carnegie Mellon University
This material is based upon work supported by the National Science Foundation under Grant Number 9653194. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.