COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 25, Problem 45QAP
To determine
The half-life of the particles which were at rest in the laboratory.
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In the previous problem, in a race to the moon, by 3/4ths the distance, light is one or ten meters ahead of the particle. We routinely approximate mass as zero, gamma as infinite, and speed as the speed of light. ("Massless particles" -- gamma and m have to be eliminated from the expressions. Light is a true massless particle.)
If a massless particle has momentum 536 MeV/c, calculate its energy in MeV.
I attached the previous problem as well for reference.
A patient’s tumor is being treated with proton-beam therapy. The protons are accelerated through a potential difference of 62 MV. What is the speed of the protons? (Note: The speed is high enough that, in principle, we should use a relativistic calculation—but for this problem you should use the formulas you are already familiar with.)
As seen in the image provided, a double-star system with stars of equal mass rotate in circular orbits around their mutual center of mass that is halfway between them. One of the stars (α) is bright. The other star (β) is its unseen dark companion. Our line of sight passes through the orbital plane such that once in every period, α approaches head-on, and once ever period it recedes directly away. The same is true for β. Suppose light always moves at speed c relative to the source that emits it (i.e., if v is the orbital speed of each star, light travels toward us at speed c + v from α when it is headed toward us, and at speed c - v when it is headed away from us, as depicted).
Find a distance d (in terms of v, c, and the orbital period T) such that α would appear to be simultaneously to the left and right of the center of mass point.
Chapter 25 Solutions
COLLEGE PHYSICS
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- In supei novae, neutrinos are produced in huge amounts. They were detected from the 1987A supernova in the Magellanic Cloud, which is about 120,000 light- years away from Earth (relatively close to our Milky Way Galaxy). If neutrinos have a mass, they cannot travel at the speed of light, but if their mass is small, their velocity would be almost that of light, (a) Suppose a neutrino with a 7eV/c2mass has a kinetic energy of 700 keV. Find the relativistic quantity =11v2/c2for it. (b) If the neutrino leaves the 1987A supernova at the same time as a photon and both travel to Earth, how much sooner does the photon arrive? This is not a large time difference, given that it is impossible to know which neutrino left with which photon and the poor efficiency of the neutrino detectors. Thus, the fact that neutrinos were observed within hours of the brightening of the supernova only places an upper limit on the neutrino’s mass. (Hint: You may need to use a series expansion to find v for the neutrino, since its is so large.)arrow_forwardOur solar system orbits the center of the Milky Way Galaxy. Assuming a circular orbit 30,000 ly in radius and an orbital speed of 250 km/s, how many years does it take for one revolution? Note that this is approximate, assuming constant speed and circular orbit, but it is representative of the time for our system and local stars to make one revolution around the galaxy.arrow_forwardAn interstellar space probe is launched from Earth. After a brief period of acceleration, it moves with a constant velocity, 70.0% of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 15.0 years as measured in a rest frame. (a) How long do the batteries on the space probe last as measured by mission control on Earth? (b) How far is the probe from Earth when its batteries fail as measured by mission control? (c) How far is the probe from Earth as measured by its built-in trip odometer when its batteries fail? (d) For what total time after launch are data received from the probe by mission control? Note dial radio waves travel at the speed of light and fill the space between the probe and Earth at the time the battery fails.arrow_forward
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