Monday, October 23, 2017

Summary of Atomic Theory

The 21st Century understanding of atomic theory is very effective in helping explain and predict how substances interact. It is the result of a growing body of knowledge that dates back centuries.


In the middle of the 5th Century BCE, Democritus proposed ideas that were correct in many ways. Democritus believed that all matter consisted of extremely small particles that could not be divided. He called these particles atoms from the greek word transliterated as atomos, which means "uncut" or "indivisible." 
He thought there were different types of atoms with specific sets of properties for the different substances in creation. The atoms in liquids, for example, were round and smooth, but the atoms in solids were rough and prickly. 
Though Democritus's ideas didn’t catch on, he was surprisingly accurate in his assumptions. Scientist of the 21st Century eventually concluded that many of Democritus’s ideas were correct, and they extended the understanding of atomic theory in stages that led to the current model.

John Dalton

Dalton proposed the theory that all matter is made up of individual particles called atoms, and in it, he identified several things that have lasted into the modern atomic theory:
  • All elements are composed of atoms.
  • All atoms of the same element have the same mass, and atoms of different elements have different masses.
  • Compounds contain atoms of more than one element.
  • In a particular compound, atoms of different elements always combine in the same ratios.

J. J Thompson
Thompson's experiments provided the first evidence that atoms are made of even smaller particles that have positive and negative charges.

Ernest Rutherford
Rutherford's model extended what was previously understood by identifying that atoms have a central, relatively dense (compared to the entire volume of an atom) nucleus around which electrons move. 

Niels Bohr

  • In Bohr's model, electrons move with constant speed in fixed orbitals around the nucleus.
  • Electrons must orbit the nucleus in one of several fixed, specific orbits, and each orbit represents a specific energy level.
  • The first orbital represents the lowest electron energy level, and the other orbitals represent progressively higher and higher energy levels.

Electron Cloud Model

  • Evidence following Bohr's work led to the understanding that the electrons do not orbit the nucleus like a planet.
  • While they do exist at specific energy levels and occupy orbitals, their position in the orbital is never 100% certain. They are somewhere in the orbital, but exactly where cannot be known specifically. Each orbital can be, therefore, conceived as an electron cloud. 

The progression of Atomic Theory in the modern era took place in various steps and stages. The resulting body of understanding results in a model of atoms that is highly effective and useful in understanding and predicting the behavior of substances.

Thursday, October 5, 2017

Solving Science Word Problems (and any other kind of word problem, too.)

Updated 2019-08-16

Throughout science, there inevitably comes a time when it is necessary to use some "known relationship" to figure out what happened or what might happen. In physics and chemistry, especially, this is the case, but sciences like sociology use "known relationships," such as population growth models, to explain or predict certain happenings. Business science looks at factors such as supply and demand or production cost vs sales price as means of maximizing profit.

In many, many cases, the "known relationship" is expressed as a mathematical equation. The relationship between the rate something happens and the amount of something produced is very common, so this discussion will use a couple of rate problems as its example.

In most general terms, the amount of something produced is equal to the rate of production times the amount of time production took place. For instance, in a displacement problem, rate is how far something moves in a given time and motion of an object is produced. In a general form a rate problem might look like this: 
O = R•t 
where O is the output, R is the rate, and t is the time.

So what is this process of solving science problem that will use rate problems as its example?

There are three steps to solving ANY science problem (or word problem of any kind, for that matter).

The following two examples will be used as the steps are discussed:

EXAMPLE 1: A baker's oven will hold only 1 pan of cookies, and each pain has space for 12 cookies. The baking time on cookies (including putting the dough on the pan) is 20 minutes. Therefore, the rate cookies are baked is 12 cookies per 20 minutes. How many cookies can be baked in 80 minutes? 
EXAMPLE 2: A car travels at an average rate of 20 MPH for 3 hours. How far does it go.

The first step is to write down what is asked for.  What are you supposed to find?
Example 1:
LOOKING FOR "How many cookies"
Example 2:
LOOKING FOR "How far does it go"
A student familiar with physics motion problems would see Example 2 as a "distance" problem and would use the distance equation variables. In such a case, R would be velocity, v, t would be time, t, and LOOKING FOR would be distance, d (or in some cases, s). 
The second step is to write down what's given and  find an equation that relates to the question.

Example 1:

Rate of baking  (R) = 12 cookies/20minutes
time (t) = 80 minutes

Intuition and general math instruction will lead you to a formula where…

Number of Cookies = R • t

Example 2:

Rate of motion (v) = 20 MPH
time (t) = 3 hours

Intuition or a quick Google search will reveal a formula (the distance formula) that related velocity and time of motion.

d = vt

From time to time, it is necessary to rearrange an equation so that it yields the answer you are trying to find. For example, if you trying to find time in Example 2 above, you will need to isolate the t variable. MANY TIMES it is easier to do the algebra BEFORE you plug in the numbers and units!

d = vt               (To find t divide both sides by v.) 
d/v = vt/v           (The v on the right side cancels.)
d/v = t
Once you have an equation in the form you need, you are ready for the next and final step.

The third step is to plug in what was given and solve. Assuming the second step was completed, the following solutions would emerge:

Example 1:
Cookies = R•t
Cookies = 12 Cookie/20 min • 80 min
Cookies = 960 Cookie•min / 20 min
Cookies = 48 Cookie 

Example 2:
d = vt
=  20 mi/hr * 3hr
d = 60 (mi•hr)/hr
d = 60 mi

For additional examples and a video explanation, check this out:

Scan for Video

Scan for Video

Example 3 (All together)

A car ball rolls at a constant rate of 20 m/s. How far will it roll in 8 seconds?

Using df as final distance rolled, v as the velocity, and t as time… 
Find df where
v = 20 m/s
t = 8 s
df = vt
df = (20 m/s) (8 s)
df = 160 m


There are three steps to solving problems.

1: Write down what is asked for.
2: Write down what is given and find a relevant equation.
2b: Rearrange the equation so that it yields the answer you want.
3. Plug in and solve.

The same thing expressed as five steps:

1 Write down what is being asked for.
2. Write down what is given.
3. Identify a relevant equation.
4. Plug in.
5. Solve.

Tuesday, August 1, 2017

Physical Quantities: Equivalency and Conversion

Objects in the physical world can be described according to various physical properties, such as length, volume, mass (or weight). Since the beginning of humanity, people have come up with ways to measure things in a standard way.

Standards and Units

Measurements were usually created to compare to some reference object or other agreed-upon standard. For instance, if trading sea shells, the standard would be… a seashell. One sea shell equaled one seashell.

Okay… hang in there… keep going…

So, along the way, magic occurred (not really) and people began to equate the word "one" with "unit." So, if you said, "Give me eight units of seashells," since seashells were measured in… themselves… you would get eight seashells.

But suppose a guy sold sand. Selling grains of sand would be… dumb. Suppose (sticking to the beach motif) he had a coconut hollowed out. His thing was, one scoop of sand for one seashell…

So for sand, the unit would be scoops.

A buyer would say, "Give me eight scoops of sand," and would pay eight seashells for it.

It must be time for a definition!

Unita quantity chosen as a standard in terms of which other quantities may be expressed. (Oxford dictionary.

Not very helpful, but in the right direction!

Anne Marie Helmenstine, Ph.D. ( defines it this way:

A unit is any standard used for comparison in measurements.

Going back to strictly intuition, most people already know what units are. "Comparison" is a good word to hang onto, so do that.

Now think about things you already know. Gallons of gasoline. Pounds of lunch meat. Miles to the next town.

Using a standard unit like miles allows us to make reasonable comparisons. A mile is a mile is a mile. So if it is 200 miles to Townville and 400 miles to Villaton, since a mile is a mile is a mile, it must be twice as far to Villaton.

If I have 4 gallons of paint and you have 2, I have twice as much paint, since a gallon is a gallon is a gallon.

So, think about things around you. What are the standard units for them.

Distances between towns?
Soda (pop)?

Chances are, for at least one of those, you thought of different standards. For example, you might find 20 oz bottles of soda as well as 2 liter bottles!

There are times when converting from one standard unit to the other is desirable.

Conversion and Equivalency

The process of converting from one standard unit to another boils down to finding how many of one thing is equal to one thing of the other.

Good news, #1: The math on this is easy.

Good news, #2: You can usually look it up on Google.

Bad news, #1: An explanation follows anyway.

To start with a definition of conversion…

Conversion: The process of finding out how many units from one standard are equal to how many units from another standard.

Suppose you discover that, in a fantasy novel, the people in one town sell milk by the Nallog and in another by the Ecnuo. Some guy has a barrel on which are etched lines for both Nallogs and Ecnuos, and another dude sees that the milk comes to the 2 Nallog mark and also the 256 Ecnou mark.

In the (silly) example, you can see that 2 Nallogs = 256 Ecnous. That is, the two quantities are equivalent.

Finding out how many Ecnous are in a Nallog is easy! Divide the bigger number by the smaller. Bam!

256 ÷ 2 = 128

So 1 Nallog  (the bigger unit) is equivalent to 128 Ecnou (the smaller unit).

In the (silly) example above, the conversion factor is 2.

Conversion factor: A number that, when multiplied will convert one unit to another.

Oxford Dictionary says it like this: an arithmetical multiplier for converting a quantity expressed in one set of units into an equivalent expressed in another.

To find (or derive) a conversion factor for anything, all that is needed is to know how much of something is present in the two different units. Then, to find the conversion factor, divide the larger by the smaller of the quantities. The quotient (number after you push the equal button) will be how many of the smaller thing (the bigger number) are in the bigger thing (smaller number).

No, that's not confusing, is it?


A container has 591.5 milliliters of shampoo in it. The label also says it has 10 clarkens (which are cleverly abbreviated as "Clar"). Find the conversion factor for milliliters and clarkens.

591.5 ml
_______  =   59.15 ml/Clar
10 Clar

Thus, 1 Clar is equal to 59.15 ml.

BAM! Easy math!


It is always best to just measure things in the units you need. But sometimes, that's impossible. Sometimes your most accurate measuring device provides units that you have to convert.

A solid understanding of equivalency and conversion prepares students to face the demands of science and engineering.

About that math…
Use the following link to see an example of how to do the math for unit conversions…

Monday, July 31, 2017

Physical Quantities: Quantities and Units

Where are we going with this? This page will assist in understanding the relationship between units and the quantities they measure.

When looking at the world around, people pretty much automatically attend to physical quantities, pretty much without thinking about them. The youngest child intuitively can judge differences with some skill.

By the time the child reaches school age, the following conversation would seem drastically out of place:

Teacher: "Mary, how far can you run?"
Mary: "I can run six pounds! Very heavy!"

Almost all children would know that far and heavy describe different physical quantities.

As most readers of this would know, one of the jobs of science is to complicate things. No… not that… 
to clarify things by assigning specific words with specific meanings to specific ideas, objects and concepts in order to make discussion precise and accurate (which are both words surrounded by confusion, ironically).

Therefore, with regard to physical quantities, a certain set of words are used to describe specific things.

Included in those sets of words are two sides to every quantity. 

One side is the concept of what is being described. Mary, in the dialog above, gave an answer about one quantity with words used for a different. 

The other side of the concept is, for every quantity, specific ways that it is measured (which are called units). Pounds do not go with a "how far" question!

First what are the things being described?

Types of Physical Quantities

The following list is certainly not all-inclusive. It includes a few very common and familiar quantities that are measured.

Distance: Distance is a measure of… okay, distance is so common it actually has different meanings, so in science, there are different words that are used so in order to be more specific.

Distance (Most General): The measure of how far two points are from each other, as in, "The tip of the antenna was 12 meters from the the surface of the window."
Distance (A specific case) Think Distance Traveled: The length of a path that a moving body takes, as in, "The dog ran from tree to tree through the park until it was at the tree next to the one where it started, covering a distance of 250 yards." Compare with Displacement, next!
DisplacementThe measure in a straight line between where a moving body begins and ends, as in, "The dog ran from tree to tree through the park until it was at the tree next to the one where it started, resulting in a displacement of only 4 yards."
Length, Width, Height: Pretty much what you expect, on this! The measure of how far specific points of an object are from other points on the object.
Other things that would be included in the distance concept are circumference, radius, perimeter, range, altitude, depth… You can probably think of others. But will you?

In general, distance is the measure of how far apart two things are.

Volume: (Not talking about sound, which borrowed from this concept for its own purposes!) This also is pretty much what you expect!

Volume is the space in three dimensions that an object or substance takes up (or holds). If a tank holds 25 gallons of gasoline, then the volume of the gasoline that filled the tank would be (duh) 25 gallons. A bottle of soda holds 20 ounces. A different bottle holds 2 liters.

Mass: Mass is a physical quantity that is the result of how many protons, electrons, and neutrons are all in a given space. It is actually not directly observable, though there are devices (scales and balances) that combine with gravity (or other acceleration) and other laws of physics so that it can be measured. Mass is a measure of the amount of matter an object contains.

If two things with the same volume have different masses, one would feel heavier than the other.

Good news: There are scales that measure mass, so you can just plop things down and get a number!

Weight: Weight is a measure of mass under a particular condition. Many people have heard things like, "Well, on the moon, I'd only weigh 12 pounds."

Weight is a basic concept that people are very familiar with. Weight is the degree of heaviness something has.

Time: This is something people very intuitively understand, but which is actually a very abstract concept. Stop reading and write down a definition of time. Not how time is measured! Try a definition of time that does not use seconds, minutes, hours, days, etc. and see what you come up with!

According to the Oxford dictionary, time is the indefinite continued progress of existence and events in the past, present, and future regarded as a whole. 

Time is a very basic concept in science, and fortunately, our intuitive understanding is enough for us to use it.

How do you measure these quantities?

The list below will connect the quantities above with the SOME OF THE units used to measure them. Common units in science are in bold and "normal" abbreviations for the common units are in parenthesis..

NOTE: Italics units are from the English system

Distance: inches, feet, yards, milesmeters (m), kilometers (km), centimeters (cm), light-years

Volume: gallon, ounce, cup, teaspoonliters (l or lt), milliliters (ml)

Mass: slugsgrams (g or gr), kilograms (kg)

Time: hours (hr), minutes (min), seconds (s)

A few more…

Some units are derived or combined from the basic units but are so common they are worth noting here.

Force: Newtons (n or N), Pounds
Weight (which is a force) is also measured in pounds, newtons
Speed or Velocity: MPH, m/s, cm/s, km/hr
Speed or Velocity is a distance unit divided by a time unit.

Acceleration: (m/s)/s, MPH/s, (km/s)/s, cm/s2  m/s2
Acceleration is a velocity unit divided by a time unit.

And also…

Temperature: Temperature is, within the kinetic theory of matter model, defined as the average kinetic energy of the molecules in a system or substance. How much thermal energy is present? How hot is it? The absence of thermal energy is described as being cold. Temperature is measured in degrees. In science, officially in Kelvin degrees (°K), but often in Celsius degrees (°C). 

SI Units

With so many units, things could get confusing. So… Some smart people made a decision that, a a general best-practice science would be built on seven base units. They also gave it a fancy name:

The International System of Units

Then… they decided they would abbreviate it… from French 

Système international (d'unités)

The seven base SI units and some corresponding constants allow meaningful and uniform dialog about all matters of science.

Tuesday, April 25, 2017

Formula Quick Look

The following page is a list of formulas and very brief explanations.

Density is the ratio of a substance's mass to its volume and can be expressed mathematically as

where D is density, M is mass, and V is volume.


What is the density of an object having a mass of 8 kg and a volume of 2 cubic meters?
D = M/V
D = 8/2
D = 4 kg/m3

In science, we will use Celsius or Kelvin temperature scales to describe temperature.
To convert between Celsius and Kelvin:

Kelvin = Celsius + 273.15
Celsius = Kelvin - 273.15

To convert between Celsius and Fahrenheit:

Fahrenheit = Celsius * (9/5) + 32
Celsius = (Fahrenheit - 32) * 5/9

Gas Laws:

Charles's Law
The volume of a gas is directly proportional to its temperature in kelvins if the pressure and number of molecules are constant.


Boyle's Law
The volume of a gas is inversely proportional to its pressure if the temperature and the number of molecules are constant.


Combined Gas Law
Pressure is inversely proportional to volume, or higher volume equals lower pressure. Pressure is directly proportional to temperature, or higher temperature equals higher pressure.

If a sample of gas initially has a pressure of 2 atm, a volume of 3 liters, and a temperature of 300 K, what would its final volume be if the pressure changed to 1.5 atm and the temperature changed to 290 K? 

(P1V1)/T1=(P2V2)/T(2 • 3)/300 = (1.5 • V)/290
6/300 = 1.5 V/290
290 • (6/300) = 1.5 V
5.8 = 1.5 V
5.8/1.5 = V
3.87 l = V

Ideal Gas Law

When the number of molecules are included in calculations, the following formula can be used:
PV = nRT

This law can be converted into the following form which will allow memorization of only 1 formula for gas law problems:

P1V    P2V2
_____ = _____
n1T1       n2T


Finding final velocity:
vf = vi + at
where vf is final velocity, vi is initial velocity, a is acceleration, and t is elapsed time.

An object is moving at a rate of 3 m/s and accelerates at a rate of 2 (m/s)/s for 5 seconds. What is its final velocity? 
vf = vi + at
vf = 3 + 2 • 5
vf = 3 + 10
vf = 13 m/s

Finding average velocity:
v(ave) = (vf+vi)/2
where v(ave) is average velocity, vf is final velocity, and vi is initial velocity. Also:

v(ave) = ((vi + at) + vi)/2

Finding final position (final distance from a reference point):
df = di + vit + 1/2at2         
where df is the final, total displacement… 
di is the initial displacement. (How far from whatever point of reference is the object when the thing starts accelerating?)…
 vi is the initial velocity of the object at the beginning of the acceleration.
t is the elapsed time from the beginning of the acceleration until the end of the period being observed. 
(vit accounts for the motion of the object based on its starting velocity. It keeps covering distance at the initial rate, and additionally, it accelerates and covers more distance.) 
a is the acceleration and t is elapsed time.

An object begins 10 meters from a mark on a track with an initial velocity of 3 m/s. If it accelerates at a rate of 5 (m/s)/s for 4 seconds, how far from the mark does it end up? 
df = di + vit + 1/2at2 
df = 10 + 3(4) + 1/2(5)(4)^2
df = 10 + 12 + 1/2 (5) (16)
df = 10 + 12 + 40
df = 62 m


Where F is force, a is acceleration, and m is mass, then:

F = ma

Force of Friction—friction always opposes forces that are moving (or trying to move) an object.

Ff = Fnμ
where  Ff  is the force of friction,  Fn  is the normal force, and  μ is the coefficient of friction (a number that is looked up).
The normal force is the portion of weight that is perpendicular to the surface. For a flat surface (the angle between the surface and the horizon is zero, θ = 0):
Fn = mg
where m is mass and g is acceleration due to gravity (9.8 (m/s/)s on earth) 

Work and Energy:

Work is found by

W = Fd
where W is work, F is force applied (not net force!), and d is displacement/distance.

Kinetic energy (KE) is found with this equation:
KE = 1/2 mv2
where KE is kinetic energy, m is mass and v is velocity.

The potential gravitational energy can be found with this equation:
PE = mgh
where PE is potential gravitational energy, m is mass, g is acceleration due to gravity, and h is height.

On earth, acceleration due to gravity is 9.8 (m/s)/s

The amount of elastic potential energy is determined by how hard it is to compress or stretch something and how far it is stretched or compressed.

The equation to find this is:
PE = 1/2kd2
where PE is potential elastic energy, k is a constant specific to a particular stretchy thing (spring, rubber band, etc.) and d is the distance that it is stretched or compressed (sometimes x is used instead of d, as in the illustration)

Heat/Energy Transfer

Now to find heat, we can use the formula:
Q = mcΔT
Where Q is heat or thermal energy, m is mass, c is a number called specific heat that you either look up or calculate, and ΔT is the change in temperature.


How much heat is absorbed by 200 grams of water that starts at 25C and ends up at 30C, given that the specific heat of water is 4.2 J/g°C?

Q = mcΔT
Q = 200•4.2•(30-25)
Q = 200•4.2•5
Q = 4200 J

What is the specific heat of a metal that has a mass of 50 grams and changes temperature from 100C to 30C and gives off 4200 J of thermal energy?

Q = mcΔT
4200 = 50•c•(100-30)
4200 = 50•70•c
4200 = 3500c
4200/3500 = c
1.2 = c


Given the following information, find the work done on a 6.5 kg object after 4 seconds:

A = 16 N
B = 4 N
C = 14 N
D = 9 N

 STEP 1: Find Net Force by resolving the UpDown forces, resolving the LeftRight forces, and then using the Pythagorean Theorem:

F(net)2 = UpDown2 + LeftRight2

F(net)2 = (16 - 4)2 +(14 - 9)2
F(net)2 = (12)2 + (5)2
F(net)2 = 144 + 25
F(net)2 = 169
F(net) = 13 N

STEP 2: Find Acceleration where the force is the net force on the object:

F = ma

13 = 6.5a
13/6.5 = a
2 (m/s)/s  =  a

STEP 3: Find the distance through which the force acted due to the net force.

df = 1/2at2

df = 1/2 • 2 • 42
df = 16 m

STEP 4: Find the work done by the net force through the calculated distance.

W = Fd

W = 13 • 16
W = 208 J

To find the final velocity in the above:

Do Step 1 above.

Do Step 2 above.


Vf = at

Vf = 2 • 4
Vf = 8 m/s

To find final kinetic energy, first find the final velocity (above), and then:

KE = 1/2mv2
KE = 1/2•6.5•82
KE = 1/2 • 6.5 • 64
KE = 208 J

Tuesday, April 18, 2017

The Transfer of Thermal Energy

Thermal energy is a relatively easy concept to grasp. Objects in nature have a temperature, and that is (by definition) the average kinetic energy of the molecules of the object. The higher the temperature, the higher the average kinetic energy. Naturally, the larger the object, the more molecules, which means more kinetic energy.

So, thermal energy is a function of how many molecules are present as well as what the temperature of those molecules are. For any given substance, the total thermal energy can be easily found. 

The total thermal energy would be how much energy could be given off if the object's temperature dropped to absolute zero. This theoretical idea is not practical

Instead, thermal energy is generally defined as the amount of energy given off or taken in as a result of some change in temperature. 

The formula for finding thermal energy given a temperature change is actually very easy, EXCEPT it relies on the idea of change in temperature. It is common to use T for temperature and likewise common (though it is possibly something new to many introductory students) to use the Δ as a symbol for "change."

Thus, Δis the symbol for change in temperature.

So, if something starts off at 100 C and ends up at 80 C, what is ΔT?

ΔT = Ti - Tf
ΔT = 100 - 80

Finding Δis more about getting used to the symbol than anything else; it is the difference between starting and ending (initial and final) temperatures.

Now to find heat, we can use the formula:

Q = mcΔT

Where Q is heat or thermal energy, m is mass, c is a number called specific heat that you either look up or calculate, and Δis the change in temperature.

So, what is specific heat? Different materials require different amounts of energy to change temperature. Specific heat is a measure of that difference. Specific heat is the amount of energy needed to raise one unit of mass (grams, for instance) one degree (usually Celsius). The energy is usually measured in Joules or Calories. 


How much heat is absorbed by 200 grams of water that starts at 25C and ends up at 30C, given that the specific heat of water is 4.2 J/g°C?

Q = mcΔT
Q = 200•4.2•(30-25)
Q = 200•4.2•5
Q = 4200 J

What is the specific heat of a metal that has a mass of 50 grams and changes temperature from 100C to 30C and gives off 4200 J of thermal energy?

Q = mcΔT
4200 = 50•c•(100-30)
4200 = 50•70•c
4200 = 3500c
4200/3500 = c
1.2 = c


Thermal energy transfer is a fairly simple concept. When (two or more) things are in the same environment (which we will call being in the same system) the molecules of the things will bump into each other until all of them have the same kinetic energy.

What does that mean? Those things with higher energy will give off their energy to the things with lower energy. After a period of equalization, everything in the system will have the same average kinetic energy.

So, suppose a hot piece of metal is put into a cup of cool water… The energy from the metal will be transferred into the water. The metal will cool off. The water will warm up.

The amount of energy given off will be equal to the amount of energy absorbed. This is a major law of physics! Energy cannot be destroyed. It can change forms, or be transferred from one thing to another, but it cannot just go away.

Therefore, if hot metal is put into cool water, the quantity of the energy lost is equal to the quantity of the energy gained. Thus, Qlost = Qgained.

SO… if you know how much energy was gained, then you know how much energy was lost. 


Suppose you put a sample of hot metal (for which you know the starting temperature) into water. If you know the mass of the water and you know the temperature change of the water, using the known quantity for water's specific heat (4.2), you can calculate how much energy was gained. Then, if you know the energy gained by the metal, the mass of the metal, and the change of temperature of the metal, you can then calculate the specific heat.


  • Q = mcΔT
  • In a system, once equilibrium is reached everything in the system will have the same kinetic energy (temperature).
  • Energy lost from objects in a system will equal energy gained by other objects in the system until all of the objects have equal temperature.


The following video presents a lab exercise in which the process of heat exchange is discussed and used.

Here is a link to the companion lab sheet: CLICK HERE 

Sunday, April 16, 2017

Concepts of Force, Work, and Energy

The concepts of force, work, and energy are closely related, and they are often tied to motion. To begin understanding of how they interact, it is important to start with a firm grasp of the basic concepts.


The starting place for understanding how force, work, and energy interact is to quickly review concepts related to force.

Force is a push or a pull that acts on something in creation.

Forces are the result of four fundamental forces found in creation: gravitational force, electromagnetic force, and the strong and weak forces associated at the atomic level.

At any given time, an object in the universe is subjected to many forces. Forces on an object add up as vectors (direction and magnitude), and if the net force is NOT zero, then the object will be accelerated at a rate given by Newton's second law:

F = ma

where F is the net force on an object, m is the mass of the object, and a is the resulting acceleration.

Force is measured in Newtons (the symbol is N), which is the potential to accelerate a 1 kg object at a rate of 1 meter per second per second. that is:
1 N = 1 (kg • m/s)/s = 1 kg • m/s2
It is important to remember that an object can be moving, but that the net force on it is zero. This does not mean there are no forces at work. It just means that it is moving at a steady rate (constant velocity) because all of the forces are balanced out. For example:
Pedaling a bicycle at a steady rate requires that the force of the tires pushing against the ground is equal to the wind resistance opposing the motion of the bike. 
When a box is pushed across the floor at a steady rate, the force pushing against the box is equal to the oppositional force of friction.
Consider the box example further. The force of gravity pulls the box toward the center of the earth, causing it to press against the floor. The solid nature of the floor opposes the force of gravity, keeping the box from moving downward. The "up and down" forces are in balance, and they create the resistance of friction that opposes the force exerted on the box to push it. If the pushing force is greater than the frictional force, then the box accelerates. If they pushing force is equal, the box moves at a steady rate. If the pushing force is less than the force of friction, the box slows down or does not start moving.


Extending the concept of force to motion, the idea of work emerges. 

In the context of physics, work is a very specific concept. Work is the quantity that represents the application of a force through a distance. This means that work is done when a force is exerted and when motion occurs. Pushing against a wall does no work, though it requires a lot of effort (which is a loosely used term related to work, force, and motion.

Work can be calculated as the product of force and distance/displacement:

W = Fd

where W is work, F is force applied (not net force!), and d is displacement/distance.

Work is measured in Newton-meters (the symbol is Nm or N-m) meaning that a Newton was applied through a distance of one meter.

So, back to the box example above, if the force to push the box causes it to move some distance, then work is done. If the force does not cause it to move, then effort was spent, but no work was done.

Assume the force needed to balance friction and move the box at a constant velocity is 5 N and that the box is pushed 10 m. In that case how much work was done?
W = Fd
W = 5N • 10 m
W = 50 Nm
It is vital to remember that work is done, not as a result of the net force, but rather as a result of the applied force through a distance. In the case of a box moving at a steady rate (constant velocity) the net force on the box is zero, but the applied force is used to find work done.

To make things slightly confusing, in many cases, (because of what is discussed below about energy), work will given the unit of joules (J). To extend the above example with this concept,

W = Fd
W = 5N • 10 m
W = 50 Nm
W = 50 J


Going to the next concept, energy, is not terribly difficult. Energy can be defined as the potential to do work.

There is, thus, a direct relationship between work and energy. However, where work is often described with the unit of Newton-meters, energy is generally described with the equivalent unit, joules (the symbol is J).

A joule is the energy needed to do 1 Newton-meter of work. So:
1 J = 1 Nm
An example will help clarify the relationship between work and energy. Think about this:

If "Cash" is the potential do "pay" and energy is the potential do work, then…
Q: If you paid $20.00 for something, how much cash did you spend?
A: You spent $20.00 
Q: If you did 20 Nm of work, how much energy did you spend?
A: You spent 20 Nm (or 20 J)
Thus, once you have calculated the amount of work done, you know how much energy was used to do it.


Up to this point, energy has been looked at in terms of motion and the potential to cause motion. However, energy exists on other forms. It is important to understand that energy can change forms.

Energy exists in different forms. Though it is still the potential to do work, as different forms of energy are examined, the idea of moving something through a distance can get lost. That should not be a distraction, though. Just cling to the idea that energy is the potential to do work.

Mechanical Energy—This is the form of energy that has been discussed up to this point.

Mechanical energy is the energy associated with the motion and position of everyday objects.

There are three TYPES of Mechanical Energy

In the sections that follow, three types of mechanical energy will be explored:

  • Kinetic energy
  • Gravitational potential energy
  • Elastic potential energy
Kinetic Energy—the energy of motion is called kinetic energy.

The amount of energy a moving object has can be found based on the mass and velocity of the object that is moving. Kinetic energy (KE) is found with this equation:
KE = 1/2 mv2
where KE is kinetic energy, m is mass and v is velocity.

Potential Energy—energy that is stored as a result of position or shape.

Potential energy (PE) is a little more broad than kinetic energy. Potential energy can be thought of as how much motion could occur if the stored energy was released.

For instance, a hot wheel car at the top of the track is not moving, but if it is released, because of its position, gravity will cause it to start. The car will accelerate (overcoming friction of the track and in the bearings of the wheels) and move down the track.

Another type of potential energy relates to the shape of something. When you stretch a rubber band, because of its shape, it has stored, potential energy. Likewise a compressed or stretched spring, because of its shape, also has potential energy.

Two types of potential energy will  be examined more specifically.

Gravitational Potential Energy—the potential to create motion based on position within gravity and on the mass of the object.

Imagine hanging a heavy weight over a pulley and attaching to a car. Letting the weight go would create tension in the rope and that tension would create a force on the car causing it to accelerate. The higher the weight, the more potential it would have. The heavier the weight, likewise, the more potential it would have.

The potential gravitational energy can be found with this equation:
PE = mgh
where PE is potential gravitational energy, m is mass, g is acceleration due to gravity, and h is height.

On earth, acceleration due to gravity is 9.81 (m/s)/s.


Elastic Potential Energy—the potential energy of an object that is stretched or compressed.


The amount of elastic potential energy is determined by how hard it is to compress or stretch something and how far it is stretched or compressed.


The equation to find this is:
PE = 1/2kd2
where PE is potential elastic energy, k is a constant specific to a particular stretchy thing (spring, rubber band, etc.) and d is the distance that it is stretched or compressed (sometimes x is used instead of d, as in the illustration)

Regarding Potential Energy and Kinetic Energy, remember that they both deal with either the potential to create motion or deal with the actual motion.
Thermal Energy—the total potential and kinetic energy associated with the motion of all the molecules in an object.

Understanding thermal energy relies on what was learned about the kinetic theory of matter: all objects are made up of particle that are in constant motion. When temperature increases, the molecules move faster (and take up more room).
Thermal energy is the sum of all the kinetic energy of all those molecules.

The molecules of different types of material act differently in reaction to thermal energy, but working with thermal energy is fun and relatively easy. This will be addressed later in detail.

Chemical Energy—the energy stored in the chemical bonds of a substance.

If the bonds can be broken, the energy is released. Burning is the process of creating a chain reaction of bonds breaking and giving of energy—the chemical energy is converted into light and heat.

Electric Energy—the energy associated with electric charges.

Electric energy can be converted (through use of a motor) into mechanical energy. Mechanical energy can be converted (through a generator) into electric energy. Electric energy can be converted into light and heat by a light bulb.

Electromagnetic Energy—a form of energy that travels through space as a wave.

Light is electromagnetic energy.

Nuclear Energy—the energy stored in atomic nuclei.

It takes energy to slam protons and neutrons together in a nucleus. Once the nucleus is formed, that energy is stored in the nuclear bonds. Breaking those bonds (fission) releases the energy.


There is a close relationship between force, work, and energy. Energy is the potential to do work, and can be seen in different forms.

Definitions and content from:

New Oxford American Dictionary

Physical Science Concepts in Action, Pearson