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Wednesday, October 28, 2009

How to Define and Find Derivatives

Especially for the benefit of those students who are in trig this year, this is a quick review of what a derivative is and how we find them. Remember a derivative is nothing more than the slope of a tangent line. We can use the result as the instantaneous slope at a point. Here, we use the simple curve, y = x^2. Keep in mind that, fundamentally, we start with the normal, usual slope equation you have used for years: slope = (y2 - y1) / (x2 - x1). Check it out, and I hope it helps.

Saturday, October 24, 2009

How to Do Gauss's Law with NON-Conducting Materials

The previous video dealt with Gauss's law and conductors, where, when in electrostatic equilibrium, the electric field = 0 inside. Any net charge sits on the outer surface of a metal chunk. But, when we move to NON-conducting materials, things are more involved since there are NO de-localized electrons. It is OK to have net charge inside the material, spread throughout the volume, and therefore it is OK to have an electric field inside these materials. There would still just be static charge, and no currents. This is also the case where we would have charge densities. Check out how to do this for uniform charge densities, and I hope it helps while you review this topic.

Sunday, October 18, 2009

How to Do Gauss's Law with Conducting Materials

Conducting materials separate themselves from non-conductors due to the metallic bonds. Those delocalized electrons that are free and drifting randomly throughout a metal are forced to move when an electric field is present, and currents are formed. However, with Gauss's law, remember we only can apply it to electrostatic situations. This is why charges, through polarization, rearrange and give NO E-field inside when we have static charge. Any net charge sits on the outer surface; this is the only way to have equilibrium. Check it out or review it.

How To Deal With Air Friction Mathematically - Hockey Puck

Air friction is a different creature compared to static or kinetic friction. Static and kinetic frictions are forces between two solid surfaces, whereas air friction is between a solid surface and a fluid. Something like water friction behaves similar to air friction, where these friction forces depend on how fast you try to move through the fluid (think about how it is actually tougher to try and run in water than to walk in water). Check out how to handle this fluid friction is certainly more involved than dealing with static or kinetic friction, which we treat as constant forces. Air friction is non-constant, and calculus must be used to find an exponential behavior with time.

Saturday, October 17, 2009

2009 Nobel Prize in Physics

The Nobel Prize in Physics for 2009 has been given to three American scientists, for their work over the past few decades in fiber optics and the technology responsible for digital photography, which lies in something called a charge coupled device (CCD). The scientists are Charles Kao, Willard Boyle, and George Smith.

An enormous chunk of modern technology we take for granted exists only because of their work. For example, much of the ETHS computer network backbone is fiber optics, and new lines put in globally to expand the Internet backbone is fiber optic, as well as phone lines that are put in the ground (yes, your voice is ultimately transmitted as light!). There are fiber optic computers being developed, and particle and nuclear physicists have used fiber optics in detectors for some period of time. The CCD is in every digital camera, cell phone, telescope, and numerous types of satellites. CCDs are able to take photons falling on them and convert it into electrical signals, which can then be used to digitize data. Because we see final products as 'black boxes,' most people do not understand how modern electronic devices and the Internet work...this prize and the publicity it generates will help educate people a bit more so they can hopefully better appreciate the role science plays in our lives.

Thursday, October 15, 2009

Einstein's View of Gravity in General Relativity

We know a bit about gravity, and the fact that all masses attract all other masses. Newton figured this out in the 17th century. However, Newton never understood where gravity came from. We had to wait nearly 300 years before Einstein proposed the General Theory of Relativity, and the notion of 'warped space-time.' Check out this clip from Brian Greene's Elegant Universe.

Classic footage from Moon - Hammer vs Feather

A classic experiment, done by Apollo astronauts on the moon, proved that, minus air friction, even a feather has the same acceleration due to gravity as heavier objects, such as a hammer. You can even notice that the acceleration is less than on earth by watching the fall. The acceleration of gravity on the moon is about 1/6 the earth's value of 9.8 m/s^2, which puts it at about 1.6 m/s^2.

How to do Tension Problems with Systems of Objects

Here is an example of how to do a problem where we have a system of objects tied together, and need to find acceleration and a couple tension forces. These tend to be confusing when we first learn the process of applying the 2nd law, but with some practice and using the same strategy every time for a system, we'll get it down. The strategy is to draw the force diagram (always!), do F = ma for the entire system to get the acceleration, then isolate individual objects and do F = ma on those to get internal forces. Check it out!