Modern Physics class
Posted 29 October 2008
on:15/15 and 8/8 on two different questions. These are the questions and their answers.
<!– @page { size: 8.5in 11in; margin: 0.79in } P { marginbottom: 0.08in } –>

What are the two postulates of Special Relativity and what do they mean?
The two postulates of Special Relativity are
A. The laws of physics are the same in all inertial frames of reference.
B. The speed of light is the same constant in all inertial frames of reference.
Postulate A can mean that there is no possible experiment to determine if you are in a stationary frame or a nonaccelerating moving frame, because the laws of physics do not change between the two.
Postulate B causes the inconsistency that the speed of light is always the same. As a result of high linear motion requiring that the speed of light is the same constant in the directions against and towards travel, time and space must be bent in order to retain the constants. Examples fall out of this in the form of Lorentz equations, which support the relationship between increasing speed and modifications to the environment as regards to space and time.
Simultaneity becomes an issue, due to directional issues related to time dilation and length contraction. A person moving left to right may see events differently from a person moving right to left. If they are simultaneous to all observers, according to Lorentz equations, all the events must be occurring also in the same location.
As the speed of light is the same constant, and spacetime distorts itself for the purposes of keeping this postulate according to the Lorentz transformations, the speed of light becomes the ultimate speed limit, in that no information can travel faster than it.
Comments: None
==
<!– @page { size: 8.5in 11in; margin: 0.79in } P { marginbottom: 0.08in } –>

How much mass gets converted into energy in the explosion of a 10megaton H bomb? (hint: 1 megaton = 4.20 10^{15 }J). How much mass would be needed for an 8kiloton bomb? Find an object at home or in school that has a similar mass. What is the object and what is the mass?
For this example, I am using the American Mark 17 nuclear bomb as my explosive, which has a mass of 21 U.S. tons, or 19,000 kilograms. A perfect conversion of mass into energy for such a device would have a yield of 89.9 x 10^{12} J per gram, which we use to divide the yield of the device (42 x 10^{15} J) in order to attain a weight in grams, which turns out to be 467.186. Dividing the amount of mass converted to energy by the weight of the bomb, we receive a negligible percentage of 0.000025%. My guess is that this high discrepancy of masstoenergy conversion being excessively low is due to the fact that the Mark 17 was a very, very old nuclear device, and probably had a lot of extra weight for nonnuclear mechanisms.
For an 8 kiloton bomb with the same masstoenergy conversion as the Mark 17, then, we proportionally lower the yield in joules to 1 kt = 4.2 x 10^{12} J. Afterwards, we perform the same equations to bring the total device yield to 33.6 x 10^{12} J. Dividing the yield of the device again by the yield of perfect mass to energy conversion, we receive the value of 0.373 grams. An object that weighs about 0.373 grams is something along the lines of an average fragment of a paper clip, or half of a monetary bill.
Comments: This actually works but just use E = mc^2 (creative solution)
Leave a Reply