AS404- Day 2 – Gavity, Light & Failure of Classical Physics

Mass and Weight

The mass of an object is a fundamental property of the object; a numerical measure of its inertia; a fundamental measure of the amount of matter in the object. Definitions of mass often seem circular because it is such a fundamental quantity that it is hard to define in terms of something else. All mechanical quantities can be defined in terms of mass, length, and time. The usual symbol for mass is m and its SI unit is the kilogram. While the mass is normally considered to be an unchanging property of an object, at speeds approaching the speed of light one must consider the increase in the relativistic mass.

The weight of an object is the force of gravity on the object and may be defined as the mass times the acceleration of gravity, w = mg. Since the weight is a force, its SI unit is the newton. Density is mass/volume.

Weight

The weight of an object is defined as the force of gravity on the object and may be calculated as the mass times the acceleration of gravity, w = mg. Since the weight is a force, its SI unit is the newton.

For an object in free fall, so that gravity is the only force acting on it, then the expression for weight follows from Newton's second law.

You might well ask, as many do, "Why do you multiply the mass times the freefall acceleration of gravity when the mass is sitting at rest on the table?". The value of g allows you to determine the net gravity force if it were in freefall, and that net gravity force is the weight. Another approach is to consider "g" to be the measure of the intensity of the gravity field in Newtons/kg at your location. You can view the weight as a measure of the mass in kg times the intensity of the gravity field, 9.8 Newtons/kg under standard conditions.

Weightlessness

While the actual weight of a person is determined by his mass and the acceleration of gravity, one's "perceived weight" or "effective weight" comes from the fact that he is supported by floor, chair, etc. If all support is removed suddenly and the person begins to fall freely, he feels suddenly "weightless" - so weightlessness refers to a state of being in free fall in which there is no perceived support. The state of weightlessness can be achieved in several ways, all of which involve significant physical principles.

c as Speed Limit

The speed of light c is said to be the speed limit of the universe because nothing can be accelerated to the speed of light with respect to you. A common way of describing this situation is to say that as an object approaches the speed of light, its mass increases and more force must be exerted to produce a given acceleration. There are difficulties with the "changing mass" perspective, and it is generally preferable to say that the relativistic momentum and relativistic energy approach infinity at the speed of light. Since the net applied force is equal to the rate of change of momentum and the work done is equal to the change in energy, it would take an infinite time and an infinite amount of work to accelerate an object to the speed of light. (Sorry, Captain Kirk. We can't give you warp speed!)

A common resistance to the speed limit is to suggest that you just accelerate two different objects to more than half of the speed of light and point them toward each other, giving a relative speed greater than c. But that doesn't work! Time and space are interwoven in such a way that no one observer ever sees another object moving toward them at greater than c. The Einstein velocity addition deals with the transformation of velocities, always yielding a relative velocity less than c. It doesn't agree with your common sense, but it appears to be the way the universe works.

Wave-Particle Duality

Publicized early in the debate about whether light was composed of particles or waves, a wave-particle dual nature soon was found to be characteristic of electrons as well. The evidence for the description of light as waves was well established at the turn of the century when the photoelectric effect introduced firm evidence of a particle nature as well. On the other hand, the particle properties of electrons was well documented when the DeBroglie hypothesis and the subsequent experiments by Davisson and Germer established the wave nature of the electron.

The Photoelectric Effect

The details of the photoelectric effect were in direct contradiction to the expectations of very well developed classical physics. The explanation marked one of the major steps toward quantum theory.

The remarkable aspects of the photoelectric effect when it was first observed were: 1. The electrons were emitted immediately - no time lag! 2. Increasing the intensity of the light increased the number of photoelectrons, but not their maximum kinetic energy! 3. Red light will not cause the ejection of electrons, no matter what the intensity! 4. A weak violet light will eject only a few electrons, but their maximum kinetic energies are greater than those for intense light of longer wavelengths!

Experiment

Analysis of data from the photoelectric experiment showed that the energy of the ejected electrons was proportional to the frequency of the illuminating light. This showed that whatever was knocking the electrons out had an energy proportional to light frequency. The remarkable fact that the ejection energy was independent of the total energy of illumination showed that the interaction must be like that of a particle which gave all of its energy to the electron! This fit in well with Planck's hypothesis that light in the blackbody radiation experiment could exist only in discrete bundles with energy

E = hν

This equation says that the energy of a particle of light (E), called a photon, is proportional to its frequency (v), by the Plank constant (h). This means that photons with low frequencies, like radio waves, have lower energies than photons with high frequencies, like x-rays.

Wave-Particle Duality: Light

Does light consist of particles or waves? When one focuses upon the different types of phenomena observed with light, a strong case can be built for a wave picture:

Interference

Diffraction

Polarization

By the turn of the 20th century, most physicists were convinced by phenomena lke the above that light could be fully described by a wave, with no necessity for invoking a particle nature. But the story was not over.

Phenomenon	Can be explained in terms of waves.	Can be explained in terms of particles.
Reflection (mirror)
Refraction (glass)
Interference(soap bubbles & oil on pavement)
Diffraction (image is circle with dark band then a light band)
Polarization (planar & circular) sunglasses
Photoelectric effect

Most commonly observed phenomena with light can be explained by waves. But the photoelectric effect suggested a particle nature for light. Then electrons too were found to exhibit dual natures.

3-6: The Hypothesis of Light Quanta and the Photoelectric Effect

Look up this link Richardson

Average Mean Median and Mode: http://mathforum.org/library/drmath/view/57602.html

Day 2 - Gavity, Light & Failure of Classical Physics-Homework

1. Discuss the wave/particle theory of Quantum Mechanics.

2. What is electromagnetism?

3. What were J.J. Thompson’s contributions? Why did he get the Nobel Prize?

4. George Thompson won a Nobel Prize in Physics? Why? What ramifications did his work have?

5. Discuss Earnest Rutherford’s contributions and the physicists he inspired or taught. Why are his students important?

6. How did Plank’s constant (ħ) help with understanding the Photoelectric effect?

7. You weigh 72 kilograms on earth, how many pounds do you weigh on the Jupiter? (Jupiter’s gravity is 2.5 times greater than earth).

8. Tie your ankles together with a rope or yarn that is five feet long. Without removing the rope, drop your pants and put them back on inside out. Describe your reactions and understanding throughout this process.

Lecture Notes, Day 3: Gravity, Weight and Thermodynamics

Dealing with Euclidean Space

Vector addition in Euclidean space. Dealing with the combination of motions and a parallelogram of force.

One essential property with Euclidean space is flatness. As soon as the space is NOT flat the geometry goes non-Euclidean. For example, the surface of a sphere is non-Euclidean; a triangle on a sphere (suitably defined) will have angles that sum to something greater than 180 degrees. In fact, there is essentially only one Euclidean space of each dimension, while there are many non-Euclidean spaces of each dimension.

p.19 of the handout…when dealing with equations on the page that are written out in English, use symbols in the margins to work out the details. Get used to making sentences into equations when forces, matter, energy and distances are being discussed. Example: the surface area of a sphere is directly proportional to the square of its radius. Make sure to write this out on the side of the paragraph as: A α r²

Perihelion precession of Mercury (footnote on page 19 of handout) The exceptions to Newton’s laws are few. However, when we have them, they take new mathematics to solve the differences in gravitational effects and space-time warping. One such problem child was Mercury’s orbit. Some of the theories used to explain Mercury’s curious perturbation was that there was another planet closer to the Sun and it was even given a name, Vulcan. Thanks to the discoverer of Neptune (French mathematician Urbain Le Verrier). He thought the same method could be used for explaining the weird movements of Mercury. No such luck!

In Newtonian physics, a lone object orbiting a spherical mass would trace out an ellipse with the spherical mass at a focus. The point of closest approach, called the perihelion in the solar system, is fixed. There are a number of solar system effects that cause the perihelion of a planet to precess, or rotate around the sun. These are mainly because of the presence of other planets, which perturb orbits. Another effect is solar oblateness, which produces only a minor contribution.

The precession of the perihelion of Mercury was a longstanding problem in celestial mechanics. Careful observations of Mercury showed that the actual value of the precession disagreed with that calculated from Newton's theory by 43 seconds of arc per century, which was much larger than the experimental error at the time. However, the problem was resolved by Einstein's theory, which predicted exactly the observed amount of perihelion shift. This was a powerful factor motivating the adoption of Einstein's theory.

p. 21 of the handout explains stresses, strain and elasticity of matter. Can anyone find a few videos on the web that demonstrate the elasticity of matter as forces of stress are in operation? I’ve seen them used on PBS documentaries where you actually see a spherical baseball flatten itself against the bat and then “snap back” into its original form after it is hit by the bat. It totally rocks!

How to measure Gravitational Forces to assist Newton with his gravitational constant.
Robert Hooke created Hooke’s Law to explain: The strain is proportional to the stress. And this principle can be applied to twisting forces by means of a torsion balance. Thanks to Henry Cavendish for his delicate torsion balance that gave us a number to use! We now use an even more exact figure than Cavendish was able to measure; G=6.67 x 10^-11m³/kg-sec²

How Much Do You Weigh?

Centripetal Force - The force directed inward to a rotating body

Centrifugal Force – The force directed outward from a rotating body

These two forces acting together on the earth as it spins on its axis give it an oblate spherical shape.

This causes the measurement of weight to be different if one is located at the poles or at the equator. If you want to weigh less, move to Alaska! The way scientists have managed to negate the differences in gravitational effects is by calibrating double-pan balances with known weights.

Thermodynamics

The study of heat requires us to understand the three different scales of temperature that have been created. Fahrenheit, Celsius and Kelvin.

F = 9/5C + 32

C = 5/9(F-32)

K = C + 273 more commonly written as T = t + 273

When building the St. Louis Arch the builders had a dilemma putting in the last block due to temperature changes and steel expansion at mid-day.

This is the coefficient of linear expansion at work.

To get a handle on the coefficient of cubic expansion one can look at the Chernobyl accident of 1986 to determine what happens when huge amounts of liquid are instantaneously turned to steam due to high levels of heat.

The First Law of Thermodynamics:

Whenever heat is added to a system, it transforms to an equal amount of some other form of energy. Or in any process, the total energy of the universe remains constant.

Parallelepiped - is a three-dimensional figure formed by six rectangles.

The Second Law of Thermodynamics:

Heat will never itself flow from a cold object to a hot object. Or it can be stated, Natural systems tend to proceed toward a state of greater disorder.

The Third Law of Thermodynamics:

As temperature approaches absolute zero, the entropy of a system approaches a constant.

Entropy – the measure of the amount of disorder

Here is the diagram I used in class to discuss supercritical fluid