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1. A conclusion from special relativity is that events that are simultaneous in one inertial frame
are simultaneous in all inertial reference frames.
are simultaneous in all inertial frames moving at the same speed.
may not be simultaneous in another inertial reference frame.
are simultaneous in inertial reference frames moving in the same direction.
are simultaneous in inertial reference frames moving in the opposite direction.
2. A spaceship is observed from the Earth to be moving toward a star at a speed of 0.80 c. If the distance from the spaceship to the star is 1.6 light-years as measured from earth, how long does an observer on Earth find that it takes for the space ship to reach the star?
No relativity involved in the calculations, since everything is measured with respect to a single frame namely earth.
t = d/v = 1.6 c /0.8 c = 2 years
3. A spaceship is observed from the Earth to be moving toward a star at a speed of 0.80 c. If the distance from the spaceship to the star is 1.6 ly as measured from earth, how much time passes on the space ship while traveling to the star?
As observed from space ship, distance = 1.6 ly/¦Ã
where ¦Ã = 1/ sqrt(1-v^2/c^2) = 1.666.
As observed from space ship, distance = 1.6 ly/¦Ã = 0.96 ly
Time as measured from space ship = distance/velocity = 0.96 c /0.8 y = 1.2 y
4. How fast is a particle moving if its kinetic energy is equal to its rest energy?
Relativistic K.E = ¦Ã mc^2 ¨C mc^2
Rest energy = mc^2
Equating these two and solving for v, one get v = 0.87 c
Note that ¦Ã = 1/ sqrt(1-v^2/c^2)
5. If the momentum of an electron is 1.53 MeV/c, what is its kinetic energy?
K.E = [sqrt(p^2c^2 ¨C mc^2)] ¨C mc^2
For electron mc^2 = 0.511 Mev
Plugging in the given value for p, we get K.E = 1.10 Mev
6. The rest energy of a proton is 938.3 MeV. What is the kinetic energy of a proton moving at 0.80 c?
¦Ã = 1/ sqrt(1-v^2/c^2) = 1.666.
K.E = ¦Ã mc^2 ¨C mc^2 = 938.3 * (¦Ã-1) = 626 Mev
7. A star like the sun has a luminosity of 3.9E+26 W. How much mass must be turned into energy each second to produce this power?
I have provided step-by-step solutions to a total of 32 physics questions. Note that the answers to conceptual questions does not have steps.
1. The wavelength spectrum of the radiation energy emitted from a system in thermal equilibrium is observes to have a maximum value which decreases with increasing temperature. Outline briefly the significance of this observation for quantum physics.
2. The “stopping potential” in a photoelectric cell depends only on the frequency v of the incident electromagnetic radiation and not on its intensity. Explain how the assumption that each photoelectron is emitted following the absorption of a single quantum of energy hv is consistent with this observation.
3. Write down the de Broglie equations relating the momentum and energy of free particle to, respectively, the wave number k and angular frequency w of the wave-function which describes the particle.
4. Write down the Heisenberg uncertainty Principle as it applies to the position x and momentum p of a particle moving in one dimension.
5. Estimate the minimum range of the momentum of a quark confined inside a proton size 10 ^ -15 m.
6. Explain briefly how the concept of wave-particle duality and the introduction of a wave packet for a particle satisfies the Uncertainty Principle.