Elementary Physics Course Notes
Department of Physics
Weber State University
[Note: These notes are based on a collection of different lectures and classes, not all of which you may have been in.]
The bowling ball pendulum of death sat suspended in midair, the tension of the supporting cable analogous to the tension in the air. Is it art or science, this bowling ball? What secrets of the natural world lay trapped inside this bowling ball pendulum, and how would such secrets become revealed?
And why would anyone in his right mind suspend a bowling ball from the ceiling? Surely, this was the work of a madman. This was the work of Adam Johnston.
The junior faculty member stepped into class with only the slightest hint of fear hiding behind his calm exterior as he asked his students to consider the idea of "work."
Adam continued, introducing the concept of "work." He pointed out that he could exert the same force on something, but if he exerted the force through a greater distance, we seemed to be getting more for the same force exerted. This quantity that we get from pushing on something through a distance is known as work, or W=F*d. The distance and the force must be in the same direction, but usually that's the case anyway.
Okay, so we "do" some work. What's that gain us? Why do we care? Well, this is just the beginning. Work is a quantity that is conserved; that is, the work done to a system (like a machine) should be the same work that the system spits out. This will lead us to conservation of energy.
Sure, you can exert a force on something, but what have you really done? The measure of work (a force through a distance) takes into account exactly what the force has done to change the world. The idea is that this amount of work done on a system is equal to the amount of work which the system can then spit back out. This means that you can have simple machines that require little force over a large distance, but spit out large forces over smaller distances. The work is the same on each side, but just seen in different forms. A pulley system, lever system, etc. are all examples of this idea.
What if I lift a rock up? I've done work to the rock, so what good is this? The rock is higher in the sky, and you can imagine that if I drop the rock, it will do more damage to my toes from this great height than it would have done had it just fallen from the tabletop. So, doing work seems to privilege the rock. It has more potential to break my toe. In the same way, I might do work to get the rock to project across the room. So, doing work can also get an object to move.
We are talking about the idea of energy. Energy comes in different forms (such as the potential to fall down, or in the motion of a thrown object), but all forms of energy are conserved. This is why we think energy is such a great quantity of nature: It's easy to keep track of (because what it was before is what it should always be) and knowing the energy of a system tells us what kinds of things it can do. Analyzing the energy of a system can tell us the same kinds of things that analyzing Newton's Laws might, but for systems with large numbers of objects, we are too lazy to describe all the forces, accelerations, velocities, etc. Energy conservation is an easy (and reliable) trick, due to the fact that energy is conserved.
This brings us to demos. The bowling ball pendulum of death shows different forms of energy quite nicely. To sum up, its energy goes from potential (gravitational potential energy in this case) to kinetic (energy of motion) over and over again. We can identify exactly where all the energy is at any given instant, and if we know the total energy at any time, we know the total energy for all time ever after for this system. (This presumes that the pendulum doesn't interact with the outside environment (such as air, etc.), but we know that this isn't exactly true.) If I know the energy of the system and I know that it is conserved, I can have some faith in standing in front of the bowling ball pendulum of death . . . The demo which ensued from this premise terrified everyone, most especially Dr. Johnston. (You had to be there.)
The demo is similar to the "bungee jump!" animation on the energy animations page. (The bungee jumper, however, has elastic potential energy adding to the total, in addition to kinetic energy and gravitational potential energy.)
The specifics of kinetic and gravitational potential energy were described. An analysis of these describes how to stop your car. Specifically, if you consider the kinetic energy of your car and the work that your brakes must do to stop your car, it can be shown that if your car is moving twice as fast as normal, you need four times the stopping distance. . . . three times as fast as normal, you need nine times the stopping distance.
This is shown very nicely in a virtual demo/animation called "two-car slide" on the linear motion animation page. Adam might suggest that we get rid of speed limits and start imposing kinetic energy limits on traffic. ("Why should we?" you might ask yourself, for it could be a great test question.)
Energy shows up in all kinds of forms: Light, electricity, chemical reactions, etc. We'll cover most all of these as the course continues to spiral out of control.
For some more virtual examples of energy conservation, link here for the list of energy demos/animations.
Collisions can come in one of two extreme forms (or some combination of the two, but we won't complicate matters): Elastic collisions (both momentum and kinetic energy are conserved) or inelastic collisions (momentum is conserved, but not kinetic energy). Elastic collisions are "bouncy," while inelastic collisions are "sticky." This distinction helps us when we think back to conservation of momentum and the demos that were associated with that topic.
"So what?!!" protested a consumer conscious taxpayer and student. Johnston suddenly began to glow bright green as his superhero powers sprang to life. The luminous professor then picked up the student and hurled him across the room, into the wall. "THAT'S what," he responded. "And, that's also a nice example of an inelastic collision," referring to the non-bouncy nature of the student-in-the-wall and the fact that energy had been transferred out of the system, as evidence by the giant hole in the plaster wall. The class grew silent.
That didn't really happen.
Instead, Adam was playing with the Newton's Cradle again. The issue he pondered was why, when the rack was collided into by one ball, did only one ball come out the other side? Conservation of momentum would allow two balls at half the original velocity to emit from the opposite side, but this NEVER happens. Then, in a stunning show of mathematical prowess, Johnston showed that, since this was an elastic collision, kinetic energy also had to be conserved. And, if the K.E. is conserved, it was shown how this limits what the system can do, and it is simply not allowed to throw out two balls at half the original velocity -- this doesn't conserve the K.E.