16 - Special Relativity

# 16 - Special Relativity - Physics 8B 16 Special Relativity...

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Physics 8B 16 – Special Relativity rev 4.0 16 – Special Relativity 1. Q: The principle of relativity says that the laws of physics agree the same in all reference frames. Since different kinds of “clocks” agree about the time in our earth frame, they must agree in all frames. We used a light clock to derive the equations for time dilation and length contraction. Name four other things that can act as clocks and therefore see time dilation. 2. P: In physics, we have redefined our system of standards to have the speed of light be exact c = 299,792,458 m/s (= 3.00 x 10 8 m/s to three figures). We can use this to establish a “conversion” between units of time and distance. Let’s see how to go back and forth between them. a) Class is 2 hours long. Express this in meters (i.e. the distance light would travel). b) The distance to Proxima Centauri is 4.3 light-years. What is the distance in meters? c) The half-life of I 237 is 24.5 seconds. Express this in meters. d) The diameter of a hydrogen atom is 1.06 x 10 -10 meters. Express this in seconds.

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Physics 8B 16 – Special Relativity rev 4.0 3. P: To get a feel for how big the factor " = 1 1 # v 2 c 2 can be, calculate γ in the following situations. Note when v 2 /c 2 is small, your calculator may not have the precision to distinguish between 1 and 1-v 2 /c 2 . In those cases you can use the Taylor expansion # 1 + 1 2 v 2 c 2 a) An object at rest. b) A sprinter running at 10 m/s. (Use approx.) c) A jet flying at 600 m/s. (Use approx.) d) The earth traveling around the sun at 3 x 10 4 m/s e) An electron traveling at speed 0.1 c. f) A proton traveling at speed 0.6 c. g) A muon traveling at speed 0.999 c
Physics 8B 16 – Special Relativity rev 4.0 4. P: You see a muon traveling at speed 0.99c and measure its lifetime to be 15.6 μ sec. If the muon were at rest in your lab, what would its lifetime be? 5. P: A friend carries a meter stick past you at very high speed. How fast must he be moving if you measure the length to be 30 cm? 6.

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16 - Special Relativity - Physics 8B 16 Special Relativity...

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