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physics
college physics 2nd
College Physics 2nd Edition OpenStax - Solutions
Explain why it only appears that we are at the center of expansion of the universe and why an observer in another galaxy would see the same relative motion of all but the closest galaxies away from her.
Find the approximate mass of the dark and luminous matter in the Milky Way galaxy. Assume the luminous matter is due to approximately 1011 stars of average mass 1.5 times that of our Sun, and take the dark matter to be 10 times as massive as the luminous matter.
If there is no observable edge to the universe, can we determine where its center of expansion is? Explain.
(a) Estimate the mass of the luminous matter in the known universe, given there are 1011 galaxies, each containing 1011 stars of average mass 1.5 times that of our Sun.(b) How many protons (the most abundant nuclide) are there in this mass?(c) Estimate the total number of particles in the
If the universe is infinite, does it have a center? Discuss.
If a galaxy is 500 Mly away from us, how fast do we expect it to be moving and in what direction?
Another known cause of red shift in light is the source being in a high gravitational field. Discuss how this can be eliminated as the source of galactic red shifts, given that the shifts are proportional to distance and not to the size of the galaxy.
On average, how far away are galaxies that are moving away from us at 2.0% of the speed of light?
If some unknown cause of red shift—such as light becoming “tired” from traveling long distances through empty space—is discovered, what effect would there be on cosmology?
Our 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
Olbers’s paradox poses an interesting question: If the universe is infinite, then any line of sight should eventually fall on a star’s surface. Why then is the sky dark at night? Discuss the commonly accepted evolution of the universe as a solution to this paradox.
(a) What is the approximate speed relative to us of a galaxy near the edge of the known universe, some 10 Gly away? (b) What fraction of the speed of light is this? Note that we have observed galaxies moving away from us at greater than 0.9c.
If the cosmic microwave background radiation (CMBR) is the remnant of the Big Bang’s fireball, we expect to see hot and cold regions in it. What are two causes of these wrinkles in the CMBR? Are the observed temperature variations greater or less than originally expected?
(a) Calculate the approximate age of the universe from the average value of the Hubble constant, H0 = 20 km/s · Mly. To do this, calculate the time it would take to travel 1 Mly at a constant expansion rate of 20 km/s.(b) If deceleration is taken into account, would the actual age of the universe
The decay of one type of K- meson is cited as evidence that nature favors matter over antimatter. Since mesons are composed of a quark and an antiquark, is it surprising that they would preferentially decay to one type over another? Is this an asymmetry in nature? Is the predominance of matter over
Assuming a circular orbit for the Sun about the center of the Milky Way galaxy, calculate its orbital speed using the following information: The mass of the galaxy is equivalent to a single mass 1.5 x 1011 times that of the Sun (or 3 x 1041 kg), located 30,000 ly away.
Distances to local galaxies are determined by measuring the brightness of stars, called Cepheid variables, that can be observed individually and that have absolute brightnesses at a standard distance that are well known. Explain how the measured brightness would vary with distance as compared with
If the smallest meaningful time interval is greater than zero, will the lines in Figure 34.9 ever meet?Data from figure 34.9 Leptons, hadrons, photons Leptons, quarks, W. zº. photons Light nuclei Atoms Stars, protogalaxies, galaxies 100 GeV 1 GeV Complete identical particles symmetry. Spontaneous
(a) What is the approximate force of gravity on a 70-kg person due to the Andromeda galaxy, assuming its total mass is 1013 that of our Sun and acts like a single mass 2 Mly away? (b) What is the ratio of this force to the person's weight? Note that Andromeda is the closest large galaxy.
Distances to very remote galaxies are estimated based on their apparent type, which indicate the number of stars in the galaxy, and their measured brightness. Explain how the measured brightness would vary with distance. Would there be any correction necessary to compensate for the red shift of the
(a) A particle and its antiparticle are at rest relative to an observer and annihilate (completely destroying both masses), creating two rays of equal energy. What is the characteristic -ray energy you would look for if searching for evidence of proton-antiproton annihilation? (The fact that such
Quantum gravity, if developed, would be an improvement on both general relativity and quantum mechanics, but more mathematically difficult. Under what circumstances would it be necessary to use quantum gravity? Similarly, under what circumstances could general relativity be used? When could special
The average particle energy needed to observe unification of forces is estimated to be 10 GeV.(a) What is the rest mass in kilograms of a particle that has a rest mass of 1019 GeV/c2? (b) How many times the mass of a hydrogen atom is this?
Does observed gravitational lensing correspond to a converging or diverging lens? Explain briefly.
Suppose you measure the red shifts of all the images produced by gravitational lensing, such as in Figure 34.12.You find that the central image has a red shift less than the outer images, and those all have the same red shift. Discuss how this not only shows that the images are of the same object,
The peak intensity of the CMBR occurs at a wavelength of 1.1 mm.(a) What is the energy in eV of a 1.1-mm photon?(b) There are approximately 109 photons for each massive particle in deep space. Calculate the energy of 109 such photons. (c) If the average massive particle in space has a mass half
What are gravitational waves, and have they yet been observed either directly or indirectly?
Is the event horizon of a black hole the actual physical surface of the object?
The core of a star collapses during a supernova, forming a neutron star. Angular momentum of the core is conserved, and so the neutron star spins rapidly. If the initial core radius is 5.0 x 105 km. and it collapses to 10.0 km, find the neutron star's angular velocity in revolutions per second,
Distances to the nearest stars (up to 500 ly away) can be measured by a technique called parallax, as shown in Figure 34.26. What are the angles θ1 and θ2 relative to the plane of the Earth's orbit for a star 4.0 ly directly above the Sun?Data from figure 34.26 Star 4 ly Sun - Diameter of
Suppose black holes radiate their mass away and the lifetime of a black hole created by a supernova is about 1067 years. How does this lifetime compare with the accepted age of the universe? Is it surprising that we do not observe the predicted characteristic radiation?
Using data from the previous problem, find the increase in rotational kinetic energy, given the core’s mass is 1.3 times that of our Sun. Where does this increase in kinetic energy come from?Data from Previous problemThe core of a star collapses during a supernova, forming a neutron star. Angular
Discuss the possibility that star velocities at the edges of galaxies being greater than expected is due to unknown properties of gravity rather than to the existence of dark matter. Would this mean, for example, that gravity is greater or smaller than expected at large distances? Are there other
How does relativistic time dilation prohibit neutrino oscillations if they are massless?
If neutrino oscillations do occur, will they violate conservation of the various lepton family numbers (Le, Lμ, and Lr)? Will neutrino oscillations violate conservation of the total number of leptons?
(a) Use the Heisenberg uncertainty principle to calculate the uncertainty in energy for a corresponding time interval of 10-43 s.(b) Compare this energy with the 1019 GeV unification-of-forces energy and discuss why they are similar.
Lacking direct evidence of WIMPs as dark matter, why must we eliminate all other possible explanations based on the known forms of matter before we invoke their existence?
Consider a star moving in a circular orbit at the edge of a galaxy. Construct a problem in which you calculate the mass of that galaxy in kg and in multiples of the solar mass based on the velocity of the star and its distance from the center of the galaxy.
Must a complex system be adaptive to be of interest in the field of complexity? Give an example to support your answer.
What is the Schwarzschild radius of a black hole that has a mass eight times that of our Sun? Note that stars must be more massive than the Sun to form black holes as a result of a supernova.
State a necessary condition for a system to be chaotic.
Black holes with masses smaller than those formed in supernovas may have been created in the Big Bang. Calculate the radius of one that has a mass equal to the Earth’s.
What is critical temperature Tc ? Do all materials have a critical temperature? Explain why or why not.
Supermassive black holes are thought to exist at the center of many galaxies.(a) What is the radius of such an object if it has a mass of 109 Suns?(b) What is this radius in light years?
Explain how good thermal contact with liquid nitrogen can keep objects at a temperature of 77 K (liquid nitrogen’s boiling point at atmospheric pressure).
Consider a supermassive black hole near the center of a galaxy. Calculate the radius of such an object based on its mass. You must consider how much mass is reasonable for these large objects, and which is now nearly directly observed.
Not only is liquid nitrogen a cheaper coolant than liquid helium, its boiling point is higher (77 K vs. 4.2 K). How does higher temperature help lower the cost of cooling a material? Explain in terms of the rate of heat transfer being related to the temperature difference between the sample and its
The characteristic length of entities in Superstring theory is approximately 10-35 m.(a) Find the energy in GeV of a photon of this wavelength. (b) Compare this with the average particle energy of 1019 GeV needed for unification of forces.
For experimental evidence, particularly of previously unobserved phenomena, to be taken seriously it must be reproducible or of sufficiently high quality that a single observation is meaningful. Supernova 1987A is not reproducible. How do we know observations of it were valid? The fifth force is
If the dark matter in the Milky Way were composed entirely of MACHOS (evidence shows it is not), approximately how many would there have to be? Assume the average mass of a MACHO is 1/ 1000 that of the Sun, and that dark matter has a mass 10 times that of the luminous Milky Way galaxy with its 1011
Discuss whether you think there are limits to what humans can understand about the laws of physics. Support your arguments.
The critical mass density needed to just halt the expansion of the universe is approximately 10-26 kg/m3.(a) Convert this to eV/c2 · m3.(b) Find the number of neutrinos per cubic meter needed to close the universe if their average mass is 7 eV/c2 and they have negligible kinetic energies.
Assume the average density of the universe is 0.1 of the critical density needed for closure. What is the average number of protons per cubic meter, assuming the universe is composed mostly of hydrogen?
To get an idea of how empty deep space is on the average, perform the following calculations:(a) Find the volume our Sun would occupy if it had an average density equal to the critical density of 10-26 kg/m3 thought necessary to halt the expansion of the universe.(b) Find the radius of a sphere of
A section of superconducting wire carries a current of 100 A and requires 1.00 L of liquid nitrogen per hour to keep it below its critical temperature. For it to be economically advantageous to use a superconducting wire, the cost of cooling the wire must be less than the cost of energy lost to
Assume two galaxies are 2.00 x 102 Mly apart.(a) How fast are they separating due to space expansion?(b) Now suppose a third galaxy is located 2.00 x 102 Mly along a line that is a perpendicular bisector of the line segment between the first two galaxies. How fast is this galaxy separating from
An amateur astronomer wants to build a telescope with a diffraction limit that will allow him to see if there are people on the moons of Jupiter. (a) What diameter mirror is needed to be able to see 1.00 m detail on a Jovian Moon at a distance of 7.50 x 108 km from Earth? The wavelength of light
For an electron having a de Broglie wavelength of 0.167 nm (appropriate for interacting with crystal lattice structures that are about this size):(a) Calculate the electron’s velocity, assuming it is nonrelativistic. (b) Calculate the electron’s kinetic energy in eV.StrategyFor part (a), since
What is the wavelength of EM radiation that ejects 2.00-eV electrons from calcium metal, given that the binding energy is 2.71 eV? What type of EM radiation is this?
What is the distance between the slits of a grating that produces a first-order maximum for the second Balmer line at an angle of 15°?Strategy and ConceptFor an Integrated Concept problem, we must first identify the physical principles involved. In this example, we need to know (a) the wavelength
What are the approximate energies of the Kα and Kβ× rays for copper?
Write the complete decay equation for the given nuclide in the complete Z. B+ decay of 50Mn-. 4XN notation. Refer to the periodic table for values of
Write the complete decay equation for the given nuclide in the complete Z. B+ decay of 52Fe. 4XN notation. Refer to the periodic table for values of
Write the complete decay equation for the given nuclide in the complete Z. Electron capture by 7Be. 4XN notation. Refer to the periodic table for values of
Write the complete decay equation for the given nuclide in the complete Z. Electron capture by 106In. 4XN notation. Refer to the periodic table for values of
Write the complete decay equation for the given nuclide in the complete Z. α decay of 210Po, the isotope of polonium in the decay series of 238U that was discovered by the Curies. A favorite isotope in physics labs, since it has a short half-life and decays to a stable nuclide. 4XN notation.
In the following four problems, identify the parent nuclide and write the complete decay equation in the notation. Refer to the periodic table for values of Z.α decay producing 228Ra. The parent nuclide is nearly 100% of the natural element and is found in gas lantern mantles and in metal alloys
Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for a decay given in the equation To do this, identify the values of each before and after the decay. AXNYN-2 + 2He2.
(a) Write the complete α decay equation for 226Ra.(b) Find the energy released in the decay.
A 1.00-MT bomb exploded a few kilometers above the ground deposits 25.0% of its energy into radiant heat.(a) Find the calories per cm2 at a distance of 10.0 km by assuming a uniform distribution over a spherical surface of that radius. (b) If this heat falls on a person's body, what temperature
One scheme to put nuclear weapons to nonmilitary use is to explode them underground in a geologically stable region and extract the geothermal energy for electricity production.There was a total yield of about 4,000 MT in the combined arsenals in 2006. If 1.00 MT per day could be converted to
A spherical target in a body is being targeted with β+ radiation. The target is centered at (0.00, 2.00, 3.00) on a grid that is in centimeters. The target has a radius of 0.500 centimeters.(a) What two points on the x-axis are at the extremes of where the positrons annihilate the electrons? (b)
What type of experimental evidence indicates that light is a wave?
Suppose you pass light from a He-Ne laser through two slits separated by 0.0100 mm and find that the third bright line on a screen is formed at an angle of 10.95° relative to the incident beam. What is the wavelength of the light?StrategyThe third bright line is due to third-order constructive
Give an example of a wave characteristic of light that is easily observed outside the laboratory.
Find the range of visible wavelengths of light in crown glass.
Interference patterns do not have an infinite number of lines, since there is a limit to how big m can be. What is the highest-order constructive interference possible with the system described in the preceding example?Strategy and ConceptThe equation d sin θ= mλ (for m = 0, 1, -1, 2, -2, ...)
How do wave effects depend on the size of the object with which the wave interacts? For example, why does sound bend around the corner of a building while light does not?
Diffraction gratings with 10,000 lines per centimeter are readily available. Suppose you have one, and you send a beam of white light through it to a screen 2.00 m away.(a) Find the angles for the first-order diffraction of the shortest and longest wavelengths of visible light (380 and 760
The primary mirror of the orbiting Hubble Space Telescope has a diameter of 2.40 m. Being in orbit, this telescope avoids the degrading effects of atmospheric distortion on its resolution.(a) What is the angle between two justresolvable point light sources (perhaps two stars)? Assume an average
A non-reflective coating like the one described in Example 27.6 works ideally for a single wavelength and for perpendicular incidence. What happens for other wavelengths and other incident directions? Be specific.Data from Example 27.6Sophisticated cameras use a series of several lenses. Light can
Consider a spectrometer based on a diffraction grating. Construct a problem in which you calculate the distance between two wavelengths of electromagnetic radiation in your spectrometer. Among the things to be considered are the wavelengths you wish to be able to distinguish, the number of lines
(a) At what angle is the first minimum for 550-nm light falling on a single slit of width 1.00 μm? (b) Will there be a second minimum?
(a) Calculate the angle at which a 2.00-μm-wide slit produces its first minimum for 410-nm violet light. (b) Where is the first minimum for 700-nm red light?
(a) How wide is a single slit that produces its first minimum for 633-nm light at an angle of 28.0°?(b) At what angle will the second minimum be?
(a) What is the width of a single slit that produces its first minimum at 60.0° for 600-nm light? (b) Find the wavelength of light that has its first minimum at 62.0°.
Find the wavelength of light that has its third minimum at an angle of 48.6° when it falls on a single slit of width 3.00 μm.
(a) Sodium vapor light averaging 589 nm in wavelength falls on a single slit of width 7.50 μm. At what angle does it produces its second minimum? (b) What is the highest-order minimum produced?
(a) Find the angle of the third diffraction minimum for 633-nm light falling on a slit of width 20.0 μm.(b) What slit width would place this minimum at 85.0°? Explicitly show how you follow the steps in Problem-Solving Strategies for Wave Optics.
(a) Find the angle between the first minima for the two sodium vapor lines, which have wavelengths of 589.1 and 589.6 nm, when they fall upon a single slit of width 2.00 μm.(b) What is the distance between these minima if the diffraction pattern falls on a screen 1.00 m from the slit? (c) Discuss
(a) What is the minimum width of a single slit (in multiples of λ) that will produce a first minimum for a wavelength ? (b) What is its minimum width if it produces 50 minima? (c) 1000 minima?
(a) If a single slit produces a first minimum at 14.5°, at what angle is the second-order minimum? (b) What is the angle of the third-order minimum? (c) Is there a fourth-order minimum? (d) Use your answers to illustrate how the angular width of the central maximum is about twice the angular
An aircraft maintenance technician walks past a tall hangar door that acts like a single slit for sound entering the hangar. Outside the door, on a line perpendicular to the opening in the door, a jet engine makes a 600-Hz sound. At what angle with the door will the technician observe the first
The 300-m-diameter Arecibo radio telescope pictured in Figure 27.28 detects radio waves with a 4.00 cm average wavelength.(a) What is the angle between two just-resolvable point sources for this telescope?(b) How close together could these point sources be at the 2 million light year distance of
Assuming the angular resolution found for the Hubble Telescope in Example 27.5, what is the smallest detail that could be observed on the Moon?Data from Example 27.5The primary mirror of the orbiting Hubble Space Telescope has a diameter of 2.40 m. Being in orbit, this telescope avoids the
Diffraction spreading for a flashlight is insignificant compared with other limitations in its optics, such as spherical aberrations in its mirror. To show this, calculate the minimum angular spreading of a flashlight beam that is originally 5.00 cm in diameter with an average wavelength of 600 nm.
(a) What is the minimum angular spread of a 633-nm wavelength He-Ne laser beam that is originally 1.00 mm in diameter?(b) If this laser is aimed at a mountain cliff 15.0 km away, how big will the illuminated spot be?(c) How big a spot would be illuminated on the Moon, neglecting atmospheric
A telescope can be used to enlarge the diameter of a laser beam and limit diffraction spreading.The laser beam is sent through the telescope in opposite the normal direction and can then be projected onto a satellite or the Moon.(a) If this is done with the Mount Wilson telescope, producing a
What is the minimum diameter mirror on a telescope that would allow you to see details as small as 5.00 km on the Moon some 384,000 km away? Assume an average wavelength of 550 nm for the light received.
You are told not to shoot until you see the whites of their eyes. If the eyes are separated by 6.5 cm and the diameter of your pupil is 5.0 mm, at what distance can you resolve the two eyes using light of wavelength 555 nm?
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