The French physicist Armand Fizeau was the first to measure the speed of light accurately. He also found experimentally that the speed, relative to the lab frame, of light traveling in a tank of water that is itself moving at a speed V relative to the lab frame is v = c/n + kV where n = 1.333 is the index of refraction of water. Fizeau called k the dragging coefficient and obtained an experimental value of k = 0.44. What value of k do you calculate from relativistic transformations?
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- Galaxies are moving apart due to the expansion of the universe. Suppose another galaxy-approximated as a sphere-is moving away from us at 3.00 x 106 m/s. How will an Earth-bound observer with access to extremely high resolution equipment perceive the other galaxy's shape? It will appear as a sphere to the Earth-bound observer with its dimensions unchanged. a It will appear as a sphere to the Earth-bound observer, with all dimensions stretched b proportionally to the relativistic factor. It will be stretched in the direction of travel away from Earth proportionally to the relativistic factor. It will be compressed in the direction of travel away from Earth proportionally to the d relativistic factor.Starting from rest, two skaters "push off" against each other on smooth level ice, where friction is negligible. One is a woman and one is a man. The woman moves away with a velocity of +2.0 m/s relative to the ice. The mass of the woman is 57 kg, and the mass of the man is 76 kg. Assuming that the speed of light is 3.5 m/s, so that the relativistic momentum must be used, find the recoil velocity of the man relative to the ice. (Hint: This problem is similar to Example 6 in Chapter 7.) Number i UnitsStarting from rest, two skaters "push off" against each other on smooth level ice, where friction is negligible. One is a woman and one is a man. The woman moves away with a velocity of +2.2 m/s relative to the ice. The mass of the woman is 57 kg, and the mass of the man is 88 kg. Assuming that the speed of light is 2.8 m/s, so that the relativistic momentum must be used, find the recoil velocity of the man relative to the ice. (Hint: This problem is similar to Example 6 in Chapter 7.) Number i Units
- One of the wavelengths of light emitted by hydrogen atoms under normal laboratory conditions is l = 656.3 nm, in the red portion of the electromagnetic spectrum. In the light emitted from a distant galaxy this same spectral line is observed to be Doppler-shifted to l = 953.4 nm, in the infrared portion of the spectrum. How fast are the emitting atoms moving relative to the earth? Are they approaching the earth or receding from it?One of the many fundamental particles in nature is the muon μ. This particle acts very much like a "heavy electron." It has a mass of 106 MeV/c2, compared to the electron's mass of just 0.511 MeV/c2. (We are using E=mc2 to obtain the mass in units of energy and the speed of light c). Unlike the electron, though, the muon has a finite lifetime, after which it decays into an electron and two very light particles called neutrinos (ν). We'll ignore the neutrinos throughout this problem. If the muon is at rest, the characteristic time that it takes it to decay is about 2.2μs (τμ=2.2×10−6s). Most of the time, though, particles such as muons are not at rest and, if they are moving relativistically, their lifetimes are increased by time dilation. In this problem we will explore some of these relativistic effects. Part A: If a muon is traveling at 70% of the speed of light, how long does it take to decay in the observer's rest frame (i.e., what is the observed lifetime τμ of the muon)? Express…The Juno spacecraft arrived at Jupiter on July 4, 2016. Assuming the distance between the Earth and Jupiter is approximately 6.30 × 1011 m, determine the time, in minutes, for a signal traveling at the speed of light to reach Earth from Juno.
- A laser pointer is placed on a platform that rotates at a rate of 19 revolutions per minute. The beam hits a wall 8 m away, producing a dot of light that moves horizontally along the wall. Let 0 be the angle between the beam and the line through the searchlight perpendicular to the wall. How fast is this dot moving when 0 = Wall π ? 6 8 m Laser (Use decimal notation. Give your answer to one decimal place.) velocity of the dot: m/minYour video analysis of the motion of a marble gives it position in frame 23 as (x23 , Y23) = (0.134 m, 0.120 m) and its position in frame 24 as (x24, Y24) = (0.102 m, 0.112 m). You estimate that you can measure the x and y positions with uncertainty +0.003 m. The frame rate of the video is 30 frames/s, which means the time interval between frames is At = 0.033333 s. The uncertainty of the frame rate of a video camera is VERY small. For the sake of this problem, use 8(At) = 1 x 10- s. The mass of the marble is (2.031 +0.001) × 10 kg.Consider the case of two kids, Sam and Peter, riding a train and playing catch in an empty car. The train is moving to the right at 10 m/s. The kids can throw the ball at a speed of 5 m/s. The side of the car is transparent and a poodle named Max can see the boys playing inside. What is the speed and direction of Sam’s throw to Peter, according to Max? Explain.
- One of the many fundamental particles in nature is the muon μ. This particle acts very much like a "heavy electron." It has a mass of 106 MeV/c².compared to the electron's mass of just 0.511 MeV/c². (We are using E=mc² to obtain the mass in units of energy and the speed of light c). Unlike the electron, though, the muon has a finite lifetime, after which it decays into an electron and two very light particles called neutrinos (V). We'll ignore the neutrinos throughout this problem. If the muon is at rest, the characteristic time that it takes it to decay is about 2.2 μs (Tμ = 2.2 × 10 s). Most of the time, though, particles such as muons are not at rest and, if they are moving relativistically, their lifetimes are increased by time dilation. In this problem we will explore some of these relativistic effects. Figure Earth μ 27 Proton A stream of particles, often called cosmic rays, is constantly raining down on the earth from outer space. (Figure 1) Most cosmic-ray particles are…Your video analysis of the motion of a marble gives it position in frame 23 as (x23, Y23) = (0.134 m, 0.120 m) and its position in frame 24 as (x24, 324) = (0.122 m, 0.112 m). You esti- mate that you can measure the r and y positions with uncertainty +0.003 m. The frame rate of the video is 30 frames/s, which means the time interval between frames is At = 0.033 333 s. The uncertainty of the frame rate of a video camera is VERY small. For the sake of this prob- lem, use 8(At) = 1 x 10-6 s. The mass of the marble is (2.031 +0.001) x 10-2 kg. Calculate the following quantities: 4. The value of the momentum component p = mv, and its uncertainty, 5. The value of the momentum component py = muy and its uncertainty, and 6. The value of the kinetic energy K = mv² = m(v² + v²) and its uncertainty.A driver is sentenced in court for crossing an intersection in red light. For his defense, the driver claims that due to the relativistic Doppler effect he saw the traffic light as green color. Color of light depends on the light wavelength (wavelength of a wave is equal to the speed of the wave times the period). The wavelength of red light is 700 nm and the wavelength of green light is 500 nm. How fast the driver should have travelled to see red color as green color? Give answer in units of speed of light. 0.32 X