WORK: Another word which in physics-speak differs from regular English. If people got paid only for the physics type of work, salaries would change drastically. Garbage collectors would make the big bucks, and doctors, lawyers and executives would make very little. But, I digress.
Work done by a force is the component of the force in the direction of
motion multiplied by the distance traveled. Another way of saying the same
thing is that work is the dot product of force and
displacement. SI unit is the joule = newton∙meter,
J=N∙m. Named after James Joule, most people
pronounce it jewel. A few say jowl, because the Joule family moved from
Say Fx is 10 N and Fy is 5 N and you pull this wagon 8 m. You have done 80 J of work. (Fy is not relevant here because it is ^ to the direction of motion.)
Let's say your job is to move a big pile of concrete blocks from where a truck unloaded them to where they are needed for a building. If the elevations are the same, the total work done on the blocks is zero! In English, you did a lot of work. In physics-speak, you did positive work on a block to lift it, another bit of positive work to get it moving sideways, then negative work to slow it down to a stop, then negative work to lower it to the ground, and the total is zero. (This is neglecting work needed to push air around a little, and assuming the initial and final elevations of the block are the same.)
Work is also energy transferred. If you pull a wagon, you are doing work on the wagon and this transfers energy from you to the wagon. You acquired this energy from a peanut-butter sandwich or something. The peanuts and wheat got it from sunlight. The sun got it by squishing hydrogen nuclei together to form helium (and why that nuclear reaction gives off energy is a long story). So far, everybody is transferring energy to others. What about the wagon? Think about this before reading on.
You cheated- cyberspace is all-knowing and our sensors have detected insufficient thinking. The wagon has friction forces acting on it, and this creates heat which is a form of energy. Also it pushes the air, giving the air kinetic energy. Next question: You know darn well that you use a lot of energy moving concrete blocks sideways (see two paragraphs back), so if the total work done on the blocks is zero, where did the energy go? Think about this before going on. Don't peek.
My web-sense is tingling so I know you cheated again. The end result of all that activity of moving the blocks is the production of heat. You have "burned" a lot of stored energy in your body (chemical potential energy from food) and added the heat to the environment.
The two forms of energy you will play with most are kinetic and gravitational potential energy. Kinetic energy, or energy of motion, turns out to be (1/2)mv2. To derive this, write F = ma, multiply both sides by x. Fx is the work done on a body. From the equation v2 = vo2 + 2ax with vo = 0, we find ax = 1/2v2. Thus we find that to get something up to speed, the work necessary is 1/2mv2, so we call this the kinetic energy.
Similarly with gravitational potential energy.
You raise mass m, and the work you do is mgh where h
is the height raised above a point called the reference point. The mgh formula is for g = constant. This is fine for Earth-bound applications,
where g has negligible changes, but for space flight it turns out that U = -GMm/r, where U is potential energy with respect to a
“point” infinitely far away, G is the universal gravitation constant, M & m
are the two attracting bodies, and r is center-to-center distance. Some
applications of this are found here.
Another energy is potential
energy in a spring. If it is a coil spring, the force is proportional to
the distance stretched or compressed: f = -kx. As you
stretch or compress it, the force increases from zero, so the average f is half
the final. By this reasoning we find that its potential energy is 1/2kx2.
This formula is valid only if f = -kx. In any spring or ball or…, the force is some
function of the amount of stretch or compression, but it may be more complex
than f = -kx.
Power is the rate of doing work or expending energy, and a joule per second is a watt (W, named after James Watt, noted for his improved steam engine). Pulling a wagon, w = Fx∙x, so P = Fx∙x/t = Fx∙v. P is the dot product of force and velocity.
CONSERVATION OF ENERGY in physics-speak means the constancy of energy. The amount of energy does not change if you consider all forms (including mass, but that is a long story: look into mass-energy equivalence near the bottom of this page if you want to find out more about mass-energy). When energy seems to disappear (energy of the gasoline used in the car, electrical energy used in appliances) it usually has been converted to heat energy. If you lived in a thermos bottle, you would need to cut down on the use of appliances to prevent over-heating. Come to think of it, you would need to cut down on your metabolism- your body heat production. Come to think of it some more, you would do exactly that- you would die. But I digress again.
Conservation of energy provides us with a way of looking at the big picture without worrying about the details. It is like looking at the total in and out of a checking account. We use the word system to mean anything- a group of objects, a machine, a person, a planet.... Work done on the system transfers energy into it. Work done by the system transfers energy out of it. There can be other kinds of energy transfers: eating food, putting gasoline in the tank, etc. Let us call input energy positive and output negative, in keeping with checkbook practice. Add these all up and call the result a big W. Then the big equation we get is that the initial energy of our system + W is equal to the final energy. This is just like the checkbook equation, initial balance + W = final balance, where W is the sum of all ins and outs, with the ins positive and the outs negative. You can check out your understanding of this stuff by trying your hand at writing the energy equations for a bunch of different situations. Eo + W = E seems so easy that you might think that you don't need the practice, but you are wrong if you think that.
SUMMARY
Kinetic energy = 1/2mv2 m in kg and v in m/s gives KE in joules (J)
Gravitational potential energy = Ugrav
= mgh m in
kg, g=9.8 m/s2 and h in meter gives U in joules
Uspring = 1/2kx2 k in N/m and x in meter gives PE in joules.
Work is energy input to a system, so Eo +
W = E, where E’s are initial and final energies and W is the sum of all work
done on the system, including negative terms if the system does work on the
outside world.
Every once in a while, someone claims to have invented a device which violates the conservation of energy principle. The Patent Office rejects these things without checking them out. A decade or so ago, a group of mentally impaired folks (Congress) forced the U.S. Patent Office to test such a device, which the inventor claimed was a source of free energy. Naturally it failed the test. Here is a cycle which seems to violate conservation of energy, but when something seems to, look more closely.
An important energy concept that you may not need now is mass-energy equivalence, from relativity theory.
I cannot leave the subject of energy without yacking about fossil fuels. Eventually they will be depleted to the point where they will be too expensive for ordinary use. When? For oil, probably in your lifetime if you are twenty something. So we gotta get into renewables such as solar in a big way. Wind power is competitive with other sources now. There is plenty mo info on the web on renewables and conserving our energy resources; just click on mo info or still more for nice stuff. Good advice for the homeowner who wants to save $ at http://www.rmi.org/sitepages/pid171.php#LibHshldEnEff.
Whatever you do, do not click on back or your way out of the web will suffer a meltdown and you will be forever lost in virtual (non)reality.
My main pages:
mechanics
fluids, heat, electricity and magnetism
vibrations and waves
quantum
index
Comments, questions: fredrick.gram @ tri-c.edu (no spaces)