Physics 142 chapter 26 and 27 PDF

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Chapter 26 and 27 notes from college physics textbook...

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Chapter 26: To describe a physical event, a frame of reference is needed - The laws of mechanics must be the same in all of the inertial frames of reference - An inertial frame of reference is a frame in which newton’s laws are obeyed Motion is relative to reference frame, physics is not relative Inertial reference frame = a frame of reference (coordinate system) that is NOT accelerating ALL INTERTIAL REFERENCE FRAMES ARE EQUAL Galilean relativity: motion in a stationary frame is related to the motion in the moving frame Two observers can be in 2 different reference frames and measure 2 different motions - While the objects wll not necessarily agree on the same path… they WILL agree that the object obeys the same laws of Newtonian physics

The speed of light is ALWAYS the same  regardless of relative velocity to an object i.e. Waves need a medium to travel through: - Thought there was a “luminiferous ether” that supported light propagation - The reference frame would then be the ABSOLUTE frame Michelson-Morley Experiment: - Series of experiments to measure speed difference through ether - Michelson inferometer used reflections from mirrors to create measurable fringe pattern that would change if inferometer was rotated with respect to ether - No shift pattern was ever measured meaning light requires NO medium to travel and NO absolute frame - Light is understood to be an electromagnetic wave that requires no medium for it’s propagation Special Theory of Relativity: 1) The principle of relativity: all the laws of physics are the same in all inertial frames 2) The speed of light in a vacuum is constant in all inertial reference frames, regardless of the velocity of the observer or the velocity of the resource There is no way to measure the speed of your frame since light always travels at C so everything is always RELATIVE - There is no such thing as absolute length or absolute time - Events at different locations are observed to occur simultaneously in one frame and are not observed to be simultaneous in another frame moving uniformly past the first

Principal of relativity states that there is no preferred inertial frame of reference – although they reach different conclusions both observations are correct in terms of their Time dilation: even time is relative - Observers at different locations (stationary vs in motion) will see light pulse in a different motion o That said they still measure the speed of light as C Proper time: the time interval measured in the same inertial reference frame as the clock - If you synchronize 2 clocks and then send one out into space at high velocity… when it returns to earth it will be BEHIND the earth-based clock o This is due to the difference required to travel for time change Heart rate concept: - The measured heart rate would be slower since the clock is within the moving reference frame accelerating and the observer on earth see’s their time pass slower - Moving frame speeds time along so to the observer its moving slower Length contraction: - An object will appear shorter as it moves faster and faster - Length contraction only occurs in the direction of motion o A meter stick moving parallel to a longer dimension will appear shorter BUT its width will appear the same The Twin Paradox: In physics, the twin paradox is a thought experiment in special relativity involving identical twins: - one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more - This result appears puzzling because each twin sees the other twin as moving, and so, according to an incorrect[and naive[ application of time dilation and the principle of relativity each should paradoxically find the other to have aged less - However, this scenario can be resolved within the standard framework of special relativity: the travelling twin's trajectory involves two different inertial frames, one for the outbound journey and one for the inbound journey o so there is no symmetry between the space-time paths of the twins o given the different path lengths, the result is different aging constructs Relativistic Energy: - the kinetic energy of a particle can change - if the velocity is much smaller than the speed of light, than the expression reduces to KE= ½ mv^2 - if conservation of energy I true, you have to use the relativistic formula - it takes an infinite amount of energy to accelerate to the speed of light Rest Energy = the energy of a particle when it is NOT moving The constant term (mc^2) is the rest energy

Consequences of equivalence between mass and energy: - A system with MORE KE is HARDER to accelerate - so it seems like it has more mass than it does - a HOT object = MORE molecular KE = higher mass than colder - the apparent mass of a compressed spring will be larger than the spring at equilibrium o the energy released during fusion depends on how tightly bound the nucleus is  during fission and fusion atoms break apart but mass is NOT conserved  mass lost is converted into energy Different materials have different energy storage potential - the more calories the more energy it creates if we combine the expressions for energy and momentum we find a relation: - if a particle has NO momentum, then E= mc^2 = rest energy - if the particle has no mass, E=pc , travels at speed of light Inertial mass and gravitational mass don’t necessarily have to be the same but Einstein posited than they are - this results in the tenet that NO mechanical experiment could distinguish between the 2 scenarios: o being accelerated in an elevator o being at rest and feeling the pull of gravity Thus, if acceleration can affect the path of light SO CAN GRAVITY: 1. all the laws of physics have the same form for ALL observers in any frame of reference, accelerated or not 2. at a given point in space, a gravitational field is equivalent to an accelerated frame without a gravitational field

Chapter 27: The quantum World - light can behave as a particle and particles can also behave as waves - Heat from a campfire is due to infrared radiation generated from the fire which is felt by the face Blackbody Radiation - An ideal blackbody absorbs all impingent radiation and radiates a broad spectrum - Relative objects, like mirrors, are NOT ideal blackbodies - Any photons coming in and out of a blackbody container are in thermal equilibrium with the walls of the container - The ultraviolet catastrophe was a result of experimental data not correlating with the original classical theory

If you take the area under the curve for intensity/wavelength you can calculate the total power emitted by a hot object Light as a particle - Photons are corpuscles of discrete energy - Photons were proportional to their frequency where proportionality constant is Planck’s constant h -

Photoelectric effect: - When light impinges on a metal, a current is produced - When light strikes the emitted, electrons are liberated and then accelerated towards the collector - The resulting current is measured with an ammeter - For all intensities of light: o Voltage required to stop the flow of current (stopping potential) was the same o Somehow the energy given to electrons is independent of the brightness of light - If the stopping potential (deltaVs) is enough to stop an electron which has been emitted, the maximum kinetic energy of a photon when released can be related to the potential - Scientists also found that if the frequency of light was too low, no current gets emitted at all o A photon must have enough energy to overcome the work function of the metal Electrons don’t just jump off of materials, it takes a certain amount of energy to liberate them from the metal  A photon with energy greater than the work function can accomplish this Compton Scattering: - The X-rays that are scattered have a LONGER wavelength than the original - Photon transfers energy and momentum to an electron so its wavelength increases and energy lowers - For Compton scattering to hold there must be RELATIVITY AND QUANTIUM MECHANICS (since the electron is moving so fast) De Broigle: - Matter behaves as waves - Double slit particle experiment - Electron microscopes accelerate electrons to high energies so they have a very short wavelength and can resolve small structures Wave Function: - Think of an electron as a traveling wave packet - The wavelength is just the de broigle wavelength - The wave function is the electric field in light o Intensity is proportional to the E^2 o Probability of finding the electron at a given location is proportional to the wave function squared Heisenberg Uncertainty Principle:

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You can only know the values of wavelength of momentum of a particle to a certain extent There is a fundamental limit on how well the quantities can be known...