Concept explainers
The classical Doppler shift for light. A light source recedes from an observer with a speed v that is small compared with c. (a) Show that in this case, Equation 1.15 reduces to
(b) Also show that in this case
(Hint: Differentiate λf = c to show that Δλ/λ = –Δf/f) (c) Spectroscopic measurements of an absorption line normally found at λ = 397 nm reveal a redshift of 20 nm for light coming from a galaxy in Ursa Major. What is the recessional speed of this galaxy?
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Chapter 1 Solutions
Modern Physics
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- According to special relativity, a particle of rest mass m0 accelerated in one dimension by a force F obeys the equation of motion dp/dt = F. Here p = m0v/(1 –v2/c2)1/2 is the relativistic momentum, which reduces to m0v for v2/c2 << 1. (a) For the case of constant F and initial conditions x(0) = 0 = v(0), find x(t) and v(t). (b) Sketch your result for v(t). (c) Suppose that F/m0 = 10 m/s2 ( ≈ g on Earth). How much time is required for the particle to reach half the speed of light and of 99% the speed of light?arrow_forwardSpacecraft I, containing students taking a physics exam, approaches the Earth with a speed of 0.600c (relative to the Earth), while spacecraft II, containing professors proctoring the exam, moves at 0.280c (relative to the Earth) directly toward the students. If the professors stop the exam after 50.0 min have passed on their clock, for what time interval does the exam last as measured by (a) the students and (b) an observer on the Earth?arrow_forwardTwo powerless rockets are on a collision course. The rockets are moving with speeds of 0.800c and 0.600c and are initially 2.52 × 1012 m apart as measured by Liz, an Earth observer, as shown in Figure P1.34. Both rockets are 50.0 m in length as measured by Liz. (a) What are their respective proper lengths? (b) What is the length of each rocket as measured by an observer in the other rocket? (c) According to Liz, how long before the rockets collide? (d) According to rocket 1, how long before they collide? (e) According to rocket 2, how long before they collide? (f) If both rocket crews are capable of total evacuation within 90 min (their own time), will there be any casualties? Figure P1.34arrow_forward
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