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Showing posts from February, 2013

### Interference equations

Derivation of the double and single slit interference equations

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### Thin film interference

A description of the inteference pattern generated by light incident on a thin film.

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### Impulse and Momentum

An explanation of the connection between force and rate of change of momentum

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### Physics of Waves

Waves Physics Energy

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### Vectors in Space

This video explains how to sketch vectors in R^3, how to determine the magnitude of a vector and how to determine a unit vector

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### The Unit Vector

This video explains how to determine a unit vector given a vector. It also explains how to determine the component form of a vector in standard position that intersects the unit circle.

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### Q: Is it possible that there are any undiscovered forces? - Milly

Sure, there is always the possibility that there's more going on with matter and energy than we currently know about. In fact, that's the goal of science -- to understand more about nature, and to find another kind of force would really be a big step in our knowledge.

There are limits to what form such a new kind of force could take, given the large amount of experimental evidence currently available on the forces we know about. We have explored very carefully the reactions of matter and energy on "people-sized" scales of energy and distance. The usual forces of gravity and electricity and magnetism are very apparent on these scales. When we explored what goes on inside atomic nuclei, and how individual particles interact at high energies, the weak and strong nuclear forces were discovered and investigated. We now know that the weak nuclear force and electricity and magnetism are all manifestations of the same interaction. We're still working on how gravity and t…

### Q: My physics teacher said that it is imposible to go faster than the speed on light, but if you were standing on a train going at the speed of light and you walked from one end of the train to the other, then would'nt you be going faster than the speen of light relative to the ground? and what would happen if you were going at the speed on light or faster? Theoretically - Daimhin

It may seem like should happen that way. The problem with physics is that it doesn't always work the way that it seems like it should.
You've probably learned that the speed of light is a constant (c). But what if you looked at it from different points of view? For instance, if you're standing on the Earth, then the speed of light is c. But what if you're standing on the train that's moving at half the speed of light? Shouldn't it look like the light is moving at half speed? Well, for all that it certainly seems like it should, it doesn't. The light moves at the same speed whether you're standing on the Earth, or on a speeding train. But whoa! How can the light move at the same speed from the Earth's perspective as from the train's? Because velocity is equal to distance divided by time, and it seems like everybody should agree on the distance traveled and the time elapsed. But do they? According to special relativity (Einstein's…

### Q: What is dark matter and why is it important to our understanding of the universe? - Predrag

Dark matter is matter that is invisible to our normal methods of observing matter in galaxies, yet it still has gravitational effects on visible matter. No one is quite sure what dark matter consists of and it's a topic of a lot of ongoing research.

Dark matter was originally theorized by an astronomer by the name of Fritz Zwicky who saw a large discrepancy between the observed mass of galaxies (the visible matter) and their computed masses (computed from gravitational effects). This discrepancy is known as the "missing mass problem." This missing mass is termed dark matter -- it is "dark" because it's not visually observable.

Understanding dark matter helps us understand the history of the universe. Our current knowledge of the formation of galaxies is not consistent with theories that do not involve dark matter, so the more we know about dark matter, the more we understand how these galaxies originally formed. Also, it helps us understand current behavio…

### Q: How can wave used to cook things such as in a microwave? - Tyu Suat Hong

In a microwave oven, special antennas radiate electromagnetic waves. The typical size of these waves is a few centimeters. The oven is built so that it acts like a resonator for the wave, which means that the waves inside the oven can develop very large amplitudes (and therefore can carry lots of energy).

Electromagnetic wave's forces act on charges, pushing positive charges (+) one way and negative charges (-) the opposite way. The molecules in the food, which have easily separated (polarized) (+) and (-) parts, will therefore oscillate. As they oscillate, they transfer energy to the rest of the food by bumping into other molecules. More oscillations of molecules = heat, and higher temperature. This way the food heats up and cooks.
Water is a good molecule to heat in the microwave because it looks like this
H(+)
(-)O .
H(+)

The charges are separated which means its easier for the wave to make the molecule oscillate.
Another mechanism that is at work when microwaves heat up food i…

### Q: Why exactly is the speed of light constant in vacuum? I know that's what happens, but I want to know why. Relativity simply works under the assumption of light's constant speed, but that doesn't prove it. It's sort of like saying the product of two numbers is equal to the sum of the same two numbers just because 2+2=2x2. A proof requires more than a phenomenon. - Bill

This is an interesting philosophical question. In physics, we don't prove theories to be right, but we do prove theorems about the math used to hold together our theories. Which theories (whole structures, not just little fragmentary claims) are right is in the end determined by mere phenomena. Nobody gave us any book of true assertions, we have to cobble them together out of observation and mathematical logic.

The key logic behind Special Relativity was that Maxwell's equations for electromagnetism looked like exact, universal laws of physics, and their solution gives light waves with a universal speed. Now it was logically possible that those laws were only true in one special reference frame, but by 1905 no experiment (including the famous attempt by Michelson and Morley) provided any evidence that they failed to work in any inertial frame. Einstein showed that there was a logical, consistent framework (Special Relativity) in which Maxwell's equations worked in all inert…

### One of my students asked me, "Why does the electron move at all?" I admitted I didn't know and would like to find out for myself and for her. Thanks - David DeCarli

Awesome question! (Give your student my compliments for thinking it up!) Naturally, one would think that because protons are positively charged, and electrons are negatively charged, the two should attract and stick together. The reason that doesn't happen can't even begin to be explained using classical physics. This was one of the key mysteries that were cleared up right away by the invention of quantum mechanics around 1925.
The picture you often see of electrons as small objects circling a nucleus in well defined "orbits" is actually quite wrong. As we now understand it, the electrons aren't really at any one place at any time at all. Instead they exist as a sort of cloud. The cloud can compress to a very small space briefly if you probe it in the right way, but before that it really acts like a spread-out cloud. For example, the electron in a hydrogen atom likes to occupy a spherical volume surrounding the proton. If you think of the proton as …

### Q: When we use tidal forces to generate energy, that energy has to come from somewhere. Doing this, does it mean that the Earth slowly escapes the sun's attraction since we use the sun's gravity as an energy source? - Anonymous

That's an interesting question. The tides do have effects on orbits, but not quite what you'd guess. For starters, the tides on earth are mostly from the moon, not the sun. Your idea about tidal friction draining energy from other forms is completely correct, however.   So let's start with the effects of the moon tides. The facts are that the moon is moving away from the earth at about 3.8 cm per year and that the earth's days are getting longer at about 2 milliseconds per century. The earth's orbit around the sun changes by only a negligible amount.
These lunar tides mainly can drain energy from two sources: 1. the rotational energies of the earth and (to a much smaller extent ) the moon 2. the orbital energy of the moon.
One effect is to slow the earth's rotation, gradually making days longer. That's what's happening, and that's where energy is actually being drained from.
The other effect is less obvious. Draining energy from the moon'…

### Q: I have a question which has bothered me for quite a number of years and I just have no one to turn to ask. I hope that you can take a few minutes to help me understand. My question has to do with the basic structure of the universe. My understanding is that most physicists buy into the big bang theory - as supported by Hubble's observations of the red light shift indicating that the universe is constantly expanding. However, to put this concept in terms that I can understand, this would mean that from the moment of the big bang to now, the universe would constantly expand from a given point and that all matter would travel outward from that point at some particular speed - as with all explosions. After several billion years, this would create something of a balloon-like structure - relatively empty at the center - but with most matter falling within a certain zone at a constantly expanding radius from that central point - and allowing for differential speeds, collisions, etc. - a fuzzy balloon perhaps. This is the only mechanism I can understand that proves the red light shift is universal. However, it's also my understanding that when the galaxies have been mapped, they suggest the structure of the universe is actually more of a non-ending sponge-like structure with strings and clusters of galaxies linked together with gaps in between. This structure would seem to indicate a steady-state universe over a big bang/fuzzy balloon universe. The obvious conclusion is that the observable universe is completely at odds with the theoretical concept of the big bang. Is there something that ties these two concepts together? Or, if the observation of the sponge-like nature of the universe is correct, is there something fundamentally wrong with the big bang concept? - jeffrey

Yes, it's hard to initially grasp this, but the particular issues you're concerned about actually work out fine in the current picture. Let's look at the key points.

In the BB picture, the universe expands out not from one "given point" but from any given point. Stand anywhere. You'll see the stuff near you moving away, the farther the faster. Think of how things look from somebody else's point of view. They see the same thing.

One illustration often used is a raisin muffin expanding as it cooks. From any raisin's point of view, the other raisins are moving away. There's no particular place that gets especially empty, so there's nothing balloon-like about it. The red light shift is approximately proportional to distance, so it covers a huge range.
As for the current structure of the galaxies, on a fairly large scale it is indeed more spongy and irregular than one would get from well-stirred muffin dough. However, on a very large scale it looks …

### Q: What is the boiling temperature of cooking oil? Using the same amount of heat, cooking oil and water, which liquid will boil first? Why is one liquid boiled before the other? Thanks for your answers. - Kevin Nguyen

A:
One question at a time. Your first question is actually the toughest. This is because it's hard to measure the boiling point of oil. The reason is that well before it reaches its boiling point, oil will start to smoke. This is called the 'smoke point'. The smoke points for some common cooking oils are here:

Safflower - 510 F (266 C)

Soybean - 495 F (257 C)

Corn - 475 F (246 C)

Peanut - 440 F (227 C)

Sesame - 420 F (216 C)

Olive - 375 F (191 C)

(from http://wywahoos.org/wahoos/cookbook/tools.htm)

The exact temperatures will also depend on how pure the oil is.

The boiling point estimates that I've found are pretty sketchy, but a fair estimate for soybean oil (most cheap cooking oil is soybean oil) is about 300 C (or 572 F).

You can compare this to the boiling point of water, which is 100 C (or 212 F). The boiling point of a liquid is the temperature where the liquid will change into a gas. The reason that different liquids boil at different temperatures is because of …

### Hello, I was wondering, what would happen if a cluster of atoms quantum tunneled, and quantum jumped at the same time. I heard that the element anti-hypertritium was able to quantum tunnel. I also learned that if you cool an atom down enough, then hit it with a laser, it would be able to quantum leap. So in theory, if I was to do this procedure on anti-hypertritium, what would happen? Many Thanks, zAk

All sorts of quantum systems show tunneling, which means the leaking of a wavefunction through a region in which its kinetic energy is negative. Typical radioactive decays involve tunneling. Many electrical devices require electron tunneling through barriers.

Quantum "leaps" are a fictional process introduced in the early days of proto-quantum theories. In modern quantum mechanics, the quantum state always evolves via a continuous process.There's some mystery involved in the "measurement" aspect of the process, in which we see only a portion of the resulting quantum state, but so far as we know no "leap" ever occurs. If you wish to look up more on this measurement process, a key search term is "decoherence".

### Q: I heard that in space, if you don't have a rope attach you to the space ship, you will just float/fly away. Why does that happen? and what kind of force is it? Derek

Actually, while we're on the subject of gravity, let's consider the case in which the space ship is in orbit around the Earth. The Earth's gravity weakens as you go away from the center of the Earth, inversely proportional to the square of the distance. If an astronaut is separated from his spaceship by a tiny distance, then the acceleration due to gravity will be slightly different and they will follow slightly different orbits, drifting apart.

If the astronaut has an initial velocity with respect to his spaceship which points away from the center of the Earth, his new orbit around the Earth will be elliptical with almost the same period, but the radius will oscillate outwards and inwards and back again. But even a small change in the period of the astronaut's orbit will take him far away from his spaceship.

Forces arising from the different strengths of gravity from one place to another are called "tidal" forces, because it is the variation of the sun's…