Lecture 3: From Pennies to Kilowatts: Getting the Force on Your Side!

Note: this lecture discusses material in Chapters 4, 5, and 6. I suggest that you read through this lecture, and then read the chapters, and then read the lecture again. By that time, I may have added something, and this may all make some sense! I'm taking a top down approach here, while the text sensibly discusses the concepts in turn. Between these two sources, it may just work for you (you'll get the pun later, I suspect)…


Power and Money

image of lightbulb

When you get your electric bill, your bottom line looks something like this:

330 kw-hr at $.10/kw-hr for a total bill of $33.00.

One way to read this is:

Power x money = more money!

But actually, you should read this as:

Power x time = Energy............... (kilowatts x hours = kilowatt-hours)


Energy x price /(unit energy) = money (kilowatt-hours x price/kw-hr = total price)

In jest, I often say that power x time = money is the most important equation in all of physics. Perhaps after this section, you can decide if I'm right. Before we get too deep into the truth of this statement, lets ask a simple economic question:

is $.10/kw-hr a good price for your electric power?

Well, a kilowatt is obviously 1000 watts and all of you know what a 100 watt bulb is like, so 1 kilowatt (1kw) is the same power as (10) 100 watt bulbs. Okay, you might ask, "so what is a watt?" Well, 100 watts is the energy radiated into space by your bulb each second (about 10% is in the form of visible light, and 90% is infra-red heat if you are using an incandescent bulb). So a watt is an amount of energy/sec. So far so good, but what are the units of energy?

Energy units (in this case) are called Joules. Simply put, a 100 watt bulb radiates 100 joules of energy into space each second.

So...... before we go further, lets define the kilowatt- hour (that pesky term on your electric bill) in terms of joules, since they are both energy units:

1 kw-hr = 1000 watts x 1 hr = 1000 joules/s x 3600 s = 3,600,000 joules!

Thus, you pay the power company about a dime for nearly four million joules of energy!

(a) energy is very cheap,

(b) a joule is a very small amount of energy

(c) both of the above

To figure out which is, we need to know what a joule is, and to understand that, we need to discuss the relationship between Force and Energy.

Force at Work

Imagine for a moment that you lift your physics book over your head. Lets say the mass of your book is one kilogram. How much force do you need to apply to lift the book?

From Newton's second law, Force = mass x acceleration. Note that if you simply drop your book, it accelerates at about 10m/s2 (or simply "g"). Thus the force on it due to gravity must be mass x acceleration of gravity, or simply:

W = mg, where W is the downward force due to gravity, or the Weight of the object

On The other hand, if you don't want it to accelerate downward, you need to apply an upward force to counteract gravity, so the force you apply equals the Weight:


image of Eric with a book that is laying on his palm that is faced upward toward the ceiling

The downward arrow is the force of gravity, while the upward arrow is the force that you apply.


Question (1)...Okay, so how much force do you have to apply to hold the book over your head?

Let do some work!

Now if you push the book one meter in the air, then you do Work against gravity. Work is a form of energy. Now since you expend more energy if the book is very massive, or if you lift it very high, then we can define Work as follows:

Work = Force x distance

image of eric with book on the palm of his hand raised above his head

In this case, the force equals mg or 10N, and the distance is the height (h) you lift the book or one meter, so

W = mg x h = mgh = 10N x 1 m = 10 N-M = 10 Joules!

Ah Ha…we have our definition of the joule…it’s the energy you must expend to lift your physics book a small distances in the air!


If 10 Joules is how much energy you must expend to lift the book one meter, how far do you have to lift it to expend one joule of energy?





While we are on the subject, why do some scales measure Kilograms, and others pounds, and you almost never see a scale that measures Newton's?

image of newton calibrating his scale

The answer is the some scales are simply calibrated to measure kilograms. Stick a one kilogram mass on top of the scale, and wherever the dial reads, write "one kilogram" in front of it. Stick two kilogram masses on the scale, and write "two kilograms" where the dial points. The scale is merely responding to the force that the mass exerts on it. Take your scale to the moon, for example, and your mass readings will be way of!


question (2) ...How much will a one kilogram mass weigh of you bring it, and the scale to the moon?

Okay, so if you do lift your book one meter in the air, you expend 10 joules of energy. Do this a few times, and count Joules…they will seem quite real to you! To expend one kilowatt hour of energy (to do 3,600,000 joules of work) you need to either lift your physics book 360,000 meters in the air, or lift it one meter 360,000 times.

Imagine for a moment that you are equipped with an apparatus that converts all of the work that you do to electrical power and delivers it to my house. At the going rate, I will pay you a dime for your Herculean labor!

Okay, so you probably get the point…$.10/kw-hr is cheap, cheap, cheap…so how can the kind, hard working folks at the power company stay in business, much less drive SUV's, and vacation where there is lots of solar energy in the winter? Well, its complicated in an economic sense, but on the physics side of things, its pretty straight forward: They get gravity and Sunshine to do the work for them. Lets discuss these in turn:

Energy for Free?

image of california hydro plant

Now that you've got your physics book one meter in the air, let it go…Note that it hits the table with a pretty loud smack. In fact, if you dropped the book from one meter, gravity did work = force x distance = 10 joules of work. Since you weren't holding the book this , it sped up gaining a type of energy known as kinetic energy. Now imagine that 1 kilogram of water falls 100 meters from the top of a hydroelectric plat to the bottom. Gravity does 1000 joules of work on the water (1 kilogram x 10m/s2 x 100 meters = 1000 joules).

Now since water flows over the falls, it might be more reasonable to calculate the rate at which gravity does work. If 1 kilogram/second passes over the top, and falls one hundred meters to the bottom, then gravity does 1000 joules/second of work. Since a joule/s is a watt, this means that gravity is doing work at a rate of one kilowatt (1 kw). Of course, 1kg/s is not a very high flow rate, so you can see this can be an effective way to generate power -- we'll discuss how you convert the energy of the water to electrical energy later in the course…its not that hard!

image of of hoover power plant

On the other hand, gasoline releases about 50 million joules for every liter that is burned (combusted) in your car. Lower grade fuel used in power plants probably releases something like 36 million joules/liter or 36 MJ/L. Quick question (3): how many liters of gasoline must a power plant burn to produce one kilowatt-hour of energy?

(3) The answer requires a bit of math: 36 MJ/L x 1 kw-hr/3.6 MJ = 10 liters. I'm actually doing a bit of approximation here, but I'm probably correct within 20% or so. Since power plants are not 100% efficient, less than half of the energy released can be turned into electrical energy. Thus at least 20 liters must be burned to produce one kilowatt-hour of energy. This means that you pay only a few cents per gallon of fuel consumed at the power plant! No wonder alternative energy sources have such a hard time competing with the traditional methods!

A point worth remembering in all this is how much energy there is available in chemical bonds. When we burn something, we break the bonds that hold atoms and molecules together--these bonds are actually much stronger than the forces between massive objects, such as your book and the earth, and breaking them releases tremendous amounts of energy relative to the amount of mass involved. We'll see how this works a bit later as well.

Since you don't get something for nothing, where did this energy stored in the chemical bonds of the fuel come from? Well, the fuel is basically compressed plant life…and the planets get their energy from the sun, so the energy stored is basically sunlight!


Different forms of energy: Kinetic and Potential

There is another way to look at energy besides work and power. They are two forms: potential and kinetic energy, but you may well be out of energy at the moment (I know I am), we'll pick this concept up in part two…



Answer(1): Well, if the book has a mass of one kilogram, then it weighs 10 Newton's..and that's how much force you have to apply......

........ (W = mg = 1 kg x 10m/s2 = 10 kg-m/s2 = 10 N).


Note that A Newton is a unit of force, just like pounds, only smaller. One Newton is about 1/4 pound (actually .225 lbs.). To hold the book over your head, you need to apply 2.25 lbs!


Answer 1b: The answer is one tenth of a meter or 10 cm.



Answer (2): In fact a one kilogram mass will register as 1/6 of a kilogram on the moon, even though the amount of mass hasn't changed at all. Similarly, you weigh about 1/4 lb. (about one Newton!) less at the equator than the at the poles because the earth's rotation throws you off the scale a bit!


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