The formula for length contraction gives the length of an interval on a ruler moving with velocity v relative to an observer as L' = L 1 - where L is the length of the same interval on a ruler at rest with respect to the observer. By what fraction is the length of a meter stick reduced if its velocity relative to you is measured to be 67 percent of the speed of light? L- L'
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- a) Find the value of y for the following situation. An astronaut measures the length of his spaceship to be 100 m, while an earthbound observer measures it to be 25 m. b) What is the speed of the spaceship relative to Earth?The speed of light relative to still water is 2.25 * 10^8 m/s. If the water is moving past us, the speed of light we measure depends on the speed of the water. Do these facts violate Einstein’s second postulate? Explain.If ever the human race would need to leave Earth, the Trappist-1 system might make a good destination – the star there has seven temperate terrestrial planets, a few of which are close to Earth’s size and mass. It’s 39.6 light years away, though, so it could take a long time to get there. (a) If the spaceship had a speed of 0.95c, how long would the journey take from the Earth’s reference frame? (b) How long would the journey be for the passengers on the spaceship?
- Determine an expression for the total travel time of the light pulse, as measured by the following: A) an observer in the S frame (Use the following as necessary: c, d, and v.) B) an observer on the spacecraft (Use the following as necessary: c, d, and v.) What If? If the transmitted light beam has a wavelength λT, determine an expression for the shift in the wavelength of the light beam, as measured by the following C) an observer in the S frame (Use the following as necessary: c, v, and λT.) D) an observer on the spacecraft (Use the following as necessary: c, v, and λT.)The distance between two light pulses moving along the x-axis of the frame S is 2km. What is the distance between them from the point of view of an observer moving at a speed of 0.2c along the x-axis relative to S?An alarm clock is set to sound in 10.0 = h. Att 0, the clock is placed in a spaceship moving with a speed of 0.736 c (relative to Earth). What distance, as determined by an Earth observer, does the spaceship travel before the alarm clock sounds? (Hint: Keep track of your units!) answer in m
- The "muon" is an unstable particle with rest mass m = 106 MeV/c^2. The mean lifetime of a muon at rest is 2.2 microseconds. (micro= 10^-6) Now consider a muon moving in a laboratory, with total relativistic energy E = 2.5 GeV. (G= giga = 10^9). What is the mean distance that the muon would travel relative to the lab, before decaying? (in m) OA: 5.098x103 OB: 7.392x103 OC: OD: OE: 1.072x104 1.554x104 2.254x104 OF: 3.268x104 OG: 4.738x104 OH: 6.870x104dp" qF" u' (v summation implied), dr Verify that the relativistic force law where E, E, cB. -cB, E. E, %3D Е, -сВ. Е. сВ, -сВ, cBx yields the relativistic Lorentz force equation d(ymv) =q(E+v×B) q(È +vx. dt when evaluated on the space components a = 1,2,3.I am currently working through a physics book (Spacetime Physics by Edwin Taylor) and I have come across this question and I don't know how to solve it: "Take the differential of this equation for g to obtain an approximate algebraic expression for Δg, the change in g, for a small change Δr in height." How do I sovle this question?