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college physics reasoning
College Physics Reasoning and Relationships 2nd edition Nicholas Giordano - Solutions
In Chapter 23, we discussed the polarization of light by reflection. Figure P24.87 shows light that is both reflected and refracted as it passes from air into the glass with n = 1.60. The incident light is unpolarized, containing components with the electric field perpendicular to the plane of the
Lens maker’s formula for a double concave lens. Equation 24.32 gives the focal length of a double convex lens (i.e., a lens for which both surfaces are convex) in terms of the radii of curvature of the two surfaces. For a double concave lens (Fig. P24.85), the lens maker’s formula has a
On rare occasions, it is possible to observe a “double” rainbow (Fig. P24.81A). (The secondary rainbow is always present, but is usually too faint to be observed.) The ray diagram in Figure P24.81B shows how the light rays that form the secondary rainbow are refracted and reflected by a water
A rainbow is formed by refraction of light as it passes through a water droplet. In the ray diagram in Figure 24.49B, which of the following statements best explains the origin of a rainbow? Explain your answer.(a) The water droplet must be exactly spherical for a rainbow to occur.(b) Different
Have you ever noticed that as you approach a horse, it appears to raise its head in a way that seems aggressive? In fact, the horse is not usually showing aggression, but rather is raising its head to see you. The lens in the eye of a horse does not have the ability to change shape as in the human
Two converging lenses with f1 = 25 cm and f2 = 35 cm are located 1.50 m apart as shown in Figure P24.70. An object is placed 50 cm in front of the lens on the left.(a) Construct a ray diagram following the steps outlined in the procedures for “Ray Tracing Applied to Lenses.” Find the location
Repeat Problem 62 for an object that is a distance f/3 in front of the lens. Data from problem 62An object is a distance 2f from a converging lens.(a) Following the steps outlined in the procedure for “Ray Tracing Applied to Lenses,” construct a ray diagram showing the location and orientation
A metal spoon acts approximately as a spherical mirror. The spoon in Figure P24.56 produces an upright image of an object.(a) Is the “front” of the spoon (the side that would hold soup) facing toward the object or away from it?(b) If a person holds the spoon at arm’s length and uses it as a
Many stores have “security mirrors” mounted on ceilings or in corners so that employees can keep watch over large parts of the store (Fig. P24.55). Suppose the mirror in Figure P24.55 is spherical with a radius of 0.20 m. If the object is 5.0 m from the mirror, what is the magnification of the
A slab of glass (nglass = 1.75) rests on top of water (nwater = 1.33) as shown in Figure P24.37. Light is incident from the water onto the glass with an angle of incidence θ1 as shown.(a) Is it possible to have total internal reflection when the light reaches the glass–air interface?(b) If total
A flashlight is placed at the bottom of an empty swimming pool a distance L = 1.5 m from a wall of the pool (Fig. P24.36). Light from the flashlight just grazes the corner of the pool and travels along ray 1, which strikes a vertical pole at a height h1 = 2.0 m. The pool is filled with an unknown
When an observer looks into the empty swimming pool in Figure P24.35 and peers over the top edge, she finds that she can just see the far corner of the bottom of the pool. When the pool is filled with water, she can see a much bigger portion of the pool’s bottom; that is, she can now see a point
A rectangular slab of glass has an index of refraction n = 1.80. Light is incident at 45°, striking the upper surface very close to the right edge as shown in Figure P24.33, and is refracted as it enters the glass forming ray 2. When ray 2 strikes the right side of the slab, will any light emerge
The prism in Figure P24.32 is symmetric (i.e., its face forms an isosceles triangle). If the ray showed is perpendicular to the bottom surface of the prism and just barely undergoes total internal reflection at its first reflection (i.e., it strikes the interface at the critical angle) at the left
The prism shown in Figure P24.31 has an index of refraction n = 1.75 for a particular color of light. Four different incident rays are shown in the figure. Construct a ray diagram showing the outgoing rays in all four cases and also calculate the angles these outgoing rays make with a horizontal
Consider again the prism in Figure P24.29. White light is now incident on the prism. Calculate the angular separation of red light and blue light that is refracted by the prism as the rays leave its right edge. Assume the prism is composed of quartz and use the values for the indices of refraction
Monochromatic light (i.e., the light of a single color) is incident on the symmetric triangular prism in Figure P24.29 as shown with θ = 55°. If the index of refraction of the prism is n = 1.60, what angle does the outgoing ray make with the horizontal after leaving the right side of the prism?
Figure 24.28A shows a pencil that penetrates into a body of water. The pencil appears to be bent due to refraction. Explain this effect and find the angle that the pencil appears to be bent at the point it enters the water by calculating the ratio θ'/θ with angles as defined in Figure P24.28B.
A combination of red light and blue light is incident on a flat piece of quartz (Fig. P24.26). The two colors refract at different angles.(a) Which refracted ray in Figure P24.26 is red, and which is blue?(b) What is the angle u between the two rays? Hint: Use the data in Figure 24.20 (page 833).
A thin film of water sits on top of a flat piece of glass, and light is incident from below (Fig. P24.24). If the angle of incidence is 30º, what is the angle of refraction of the final outgoing ray?(Fig. P24.24)
In a typical changing room at a clothing store, you may find two mirrors on opposite walls, a setup that allows you to see how you look from the front and the back (Fig. P24.12). A consequence of this configuration is that you see a seemingly endless number of images of yourself getting farther and
With an ideal corner cube, the reflected ray is precisely parallel to the incident ray. No corner cube will ever be perfect, however. The astronauts who visited the Moon left corner cubes so that scientists can do experiments in which light is reflected from the Moon and back to the Earth. Suppose
A plane mirror made of a very thin piece of glass lies flat on the ground. As shown in Figure P24.10, one end of the mirror is 2.0 m from you and the other end is 30 m from a nearby tree. You are 1.8 m tall, and the mirror has a length L. The mirror is arranged so that you can just see the image of
A marble is placed near a plane mirror as shown in Figure P24.8.(a) Where will the image be located?(b) How does the image location change as the observer moves closer to the mirror?(c) How does the image location change as the marble is moved away from the mirror?
The two plane mirrors in Figure P24.7 come together as shown. Find two images of point A as viewed by an observer at B. Do your analysis graphically and assume the images are made by just a single reflection.
A light ray reflects from a mirror hanging vertically on a wall in your bathroom, and the ray strikes a particular point on the opposite wall (Fig. P24.6). The bottom end of the mirror is then tilted slightly away from the wall so that the mirror makes an angle of 5° with the wall. The spot where
What is the magnification of the pencil in Problem 4 and Figure P24.4? Is the image upright or inverted?
A pencil is placed in front of a plane mirror and is oriented parallel to the plane of the mirror (Fig. P24.4). Construct a careful ray diagram and use it to find the image of the pencil. Be sure to draw several rays from at least two different points on the pencil (not just the tip).
Two plane mirrors meet at a right angle (Fig. P24.3). An incident ray strikes the bottom mirror at point B with an angle of incidence θi; this ray reflects from each mirror once and strikes the screen on top at point A. (The screen is parallel to the bottom mirror.) Given the dimensions in Figure
The light ray in Figure P24.2 emanates from a point on one wall of a room and is incident on a plane mirror that lies flat on the opposite wall. The reflected ray strikes the lefthand wall at point A, which is a distance h = 1.4 m below the light source. What is the angle of incidence θi?
Light from a very tiny lightbulb passes through a hole of diameter 0.15 m in a dark screen that is 2.5 m away (Fig. P24.1). Assume the light travels as ideal rays as it passes from the bulb, through the hole, and onto a second screen on the far right in Figure P24.1. If the light rays illuminate a
A plastic rod becomes invisible when inserted in a container of vegetable oil as shown in Figure Q24.26. What can you conclude about the plastic rod and vegetable oil?
A magnifying glass produces an enlarged image that is upright and virtual as shown in Figure Q24.21. Does it use a converging or a diverging lens? How close must you hold the magnifying glass to the object to view the image in this way?
Funhouse mirrors distort your image so that you look shorter, taller, fatter, or thinner than you actually are. For the three images shown in Figure Q24.20, describe the curvature of the mirror. Figure Q24.20
Figure Q24.18 is a picture of a mirror one might find in a bathroom. The mirror is actually three mirrors with different curvatures so that you can view your image in different ways. The largest of the mirrors produce a normal image, whereas the smaller, two-sided mirror is used to magnify your
Figure Q24.15 shows a water fountain in which many streams of water flow in curved arcs. It appears that light is also flowing along these arcs, along with the water. Explain what is actually happening.
The image formed by a plane mirror appears to be a “reverse” of the object, with left and right interchanged, as illustrated in Figure Q24.13. It is actually more accurate to think of this reversal as front to back.(a) Use a ray diagram to explain why this front-to-back reversal occurs.(b) Use
Imagine a light ray as it passes from one material to another (as in Fig. 24.11) and considers the electric and magnetic fields associated with these rays at the boundary between the materials. At (i.e., very near) the boundary, the component of the electric field directed parallel to the boundary
In the ray diagram in Figure Q24.8, a combination of blue (n 1.60) and red (n 1.50) light strikes the surface of a fl at glass plate. Because of dispersion, there are two different refracted rays inside the glass. Which of the following statements correctly describes this situation? More than
The author’s satellite TV dish receives signals from a satellite in geosynchronous orbit about the Earth. (For this orbit, the period is precisely one day, so the satellite is always “at” the same point in the sky.) The signal is picked up with a receiver located 40 cm from the dish’s
Table 16.2 (after Problem 7) lists the work W associated with several human activities. For walking, the table lists W/t = 50 W, where t is the time spent walking. Use Newton’s laws of motion to estimate the value of W/t for a typical person walking.
Compression ratio and engine efficiency. The Otto cycle shown in Figure P16.61 is the idealized cycle for an internal combustion automobile engine. Corresponding to positions of the piston, the cycle is in four parts (two isochoric and two adiabatic). (a) Show that Equation 16.19 describing the
The Otto cycle shown in Figure P16.61 is the idealized cycle for an internal combustion automobile engine. Consider an engine using the Otto cycle that operates on 0.070 mol of ideal gas between the volumes Vi = V1 = V2 = 0.2 L and Vf = V3 = V4 = 1.6 L. (a) In which parts of the cycle (1 → 2, 2
The Brayton cycle shown in Figure P16.61 is the idealized cycle for a gas turbine or jet engine. Consider an engine using the Brayton cycle that operates on 0.070 mol of ideal gas between the pressures Pi = P1 = P2 = 4.9 atm and Pf = P3 = P4 = 3.5 atm with volumes V1 = 0.50 L, V2 = 1.00 L, V3 =
Figure P16.61 shows the P–V diagrams for idealizations of three important real engines: the Brayton (gas turbine) engine, the Otto (four-stroke) automobile engine, and the diesel engine. For each of these cycles, there is no heat flow for the processes along the curves 2 → 3 and 4 → 1. (a)
The drinking bird. A popular novelty bird toy consists of two semi evacuated glass chambers (the head and the body), which are connected by a glass tube as shown in Figure P16.60 (left). The head is covered with an absorbent coating, and the bottom chamber is partially filled with a liquid that has
Figure P16.57 shows several cyclic processes involving an ideal gas. (a) Which processes might describe a heat engine?(b) Which processes might describe a refrigerator? (c) Which process might be a Carnot cycle?Figure P16.57
(a) For which processes in Figure P16.54 is W positive?(b) For which processes is it negative?Figure P16.54
Suppose process (6) in Figure P16.54 is an isothermal process involving an ideal gas. What is the value of the ratio (Pf / Pi)/(Vi / Vf)?Figure P16.54
Figure P16.54 shows the P–V diagrams for a variety of different processes involving an ideal gas. (a) Which diagrams describe an expansion? (b) Which diagrams describe a compression? (c) Which diagrams might describe an adiabatic process? (d) Which diagrams might describe an isothermal
Firewalking. A man strides across a bed of glowing embers as seen in Figure P14.71, and due to some very specific physical circumstances, he emerges with no physical harm. Assume the glowing charcoal is covered with a thin layer of ash 0.50 mm thick and is at a temperature of 650°C. The thermal
An extreme thermos bottle might use silica aerogel as an insulator. Figure P14.70 demonstrates the insulating properties of the aerogel compound. Aerogel can protect human skin from a blowtorch at nearly point-blank range, made possible by its very low thermal conductivity (only 0.003 W/(m · K))
Mass wasting. Water filling a thin crack in a rock wall and then freezing can put large forces on the rock, making the cracks bigger (Fig. P14.69). (a) Calculate the force exerted by a 10-m2 area of a thin (0.50 mm) sheet of water freezing between two slabs of rock. (b) Take the sheet of water to
The owners of a cabin in the mountains forgot to turn off and purge the water out of the plumbing system before the winter season. One particularly cold night, a pipe near an outside wall freezes. Consider a length of “1/2 -in.” copper plumbing pipe filled with water. Although called 1/2 in.,
A bimetal strip can be used as a thermometer and thermostat, a device that converts small changes in temperature to mechanical motion (Fig. P14.67A). A thermostat can be constructed by joining two pieces of metal, brass and steel, along their length as shown in Figure P14.67B. The brass and steel
Figure P14.66 shows a modern electronic circuit board. It features standard miniature components such as the resistor (R516), which measures 1.6 mm long, 0.80 mm wide, and 0.20 mm high. The ceramic material of the resistor has a Young’s modulus of 1.2 × 1010 Pa. When electricity flows through
One of the brass freeze plugs in Problem 64 is 3.0 cm thick and just fits inside the hole in the steel of the engine block when the block is at room temperature and the brass was brought to the temperature of dry ice. (a) If the bulk modulus of brass is 6.1 × 1010 N/m2, what pressure does the
Freeze plugs. The internal combustion gasoline engines used in automobiles produce much heat, which is mostly a nuisance and must be removed from the engine to prevent deformation and melting. The heat is carried away by a cooling system, typically using a fluid that flows through the walls of the
Phase change hand warmer. Sodium acetate in solution has a freezing point at 58°C and a latent heat of freezing of 210 kJ/kg, but a solution of this compound can remain in liquid form at much lower temperatures. This condition, known as super cooling, occurs in substances that form specific
For the aluminum block in Problem 57, it is likely that at least a little bit of the heat energy will go toward heating the horizontal surface on which the block slides. Will this effect make the final temperature of the block larger or smaller than found in Problem 57?Data From Problem 57.An
When a dog “pants,” it exhausts water vapor through its mouth (Fig. P14.42). This process converts liquid water (inside the dog) into water vapor, removing heat from the dog via the evaporation of water. If 10 g of water evaporates from the dog each minute, how much heat energy does it lose
Energy-efficient windows. Energy-efficient windows are constructed with two panes of glass separated by an air gap (Fig. P14.38). In a typical window of this type, the air gap makes a huge difference in the rate of heat flow. The heat-flow rate is much smaller for an energy-efficient window than
The Eiffel Tower in Paris (Fig. P14.33) is approximately 300 m tall and is composed of iron. How much does its height increase from midnight to noon on a typical summer day?Figure P14.33
You have 5.0 g of an unknown substance. To identify the substance, you decide to measure its specific heat and find that it requires 16 J of heat to increase the temperature of your sample by 25 K. If this substance is one of those listed in Table 14.3, what might it be?
A mass of 3.4 kg is released down a friction less slope from a height of h = 2.0 m. When it reaches the bottom of the slope, it undergoes a completely inelastic collision with a mass of 1.1 kg attached to a spring of spring constant k = 5.0 kN/m as illustrated in Figure P11.66. The combined mass
It is believed that there is a period of time so short that the theory of gravity (or any of the known interactions) cannot make meaningful predictions. Interestingly, there exists an algebraical arrangement of three fundamental constants that gives units of time. The constants are G (Newton’s
Shortly after the discovery of the expansion of space, physicists made many attempts to measure Hubble’s constant. These measurements are difficult, and values of H0 ranging from 12 to 28 (km/s)/Mly were found. (a) Find the age of the universe for this minimum and maximum value of H0. (b) The
The probability for an individual particle to have not yet decayed after a time t since its creation is given by prob(t) = e-t/τ, where t is the mean lifetime of the particle. (a) What is the probability that a π+ at rest will still exist after 0.10 ms? (b) What is the probability that a
A ∑+ particle moving with a kinetic energy of 500 MeV decays to a pion and neutron, ∑+ → n + π+. What is the total kinetic energy of the decay products?
How much energy would be released if a baseball were annihilated with an antibaseball? State your answer in joules and in megatons of TNT. (See Example 30.6, p. 1068.)
A galaxy is found to be 2.0x106 ly away from the Earth. Assume this galaxy does not have any motion relative to us other than that due to the expansion of space. (a) What is the galaxy’s recession speed due to the expansion of space? (b) How much farther away from us will this galaxy be by next
A red shift measurement shows that the speed of a distant galaxy relative to an astronomer on the Earth is v = 0.25c, where c is the speed of light. (a) How far away is the galaxy? (b) If a source of electromagnetic radiation in this galaxy emits blue light with λ = 450 nm (as viewed by an
Complete the following reactions. (a) K0 → π+ + ?(b) p + p̅ → γ + ?(c) ? + n → p + e-
The strong force holds the quarks in a proton together, overcoming the Coulomb’s law repulsion between the positively charged u quarks. For simplicity, ignore the effect of the d quark and estimate the magnitude of the minimum (attractive) strong force between two u quarks needed to keep them
Find the charge on each of these baryons or antibaryons and identify them: (a) uud, (b) u̅u̅d̅, (c) u̅d̅d̅.
The pi mesons π+ and π- are each composed of two quarks. The quark composition of the π+ is ud̅, while the composition of the π- is u̅d. (a) What is the antiparticle of the π+? (b) The π- can decay into a muon and an antimuon neutrino according to π- → μ- + v̅μ What are the final
The following reactions are forbidden because they violate one or more conservation laws. Which conservation law(π+) do they violate? The p particle is a meson. (a) P → e+ + ve(b) P → e+ + γ(c) n → p + e- + vμ(d) P → e- + π+(e) π+→ π+ + n
Determine the quark content of a particle that is composed of 3 or fewer quarks and has a charge of -2e. Is this particle matter or antimatter? A baryon or a meson? There is more than just one answer (but you only need to give one).
Describe the quark content of a particle that has a charge of -e and contains one strange quark. Is this particle a baryon or a meson? There is more than just one answer (but you only need to give one).
A pi meson (π0) that is initially at rest decays into two photons. What is the energy of each photon?
At present, the world's most powerful accelerator is designed to accelerate protons to energies of about 7 TeV. (a) What is the kinetic energy of such a proton, in joules? (b) What is its de Broglie wavelength?
(a) Calculate the energy released when a proton annihilates an antiproton. Express your answer here and in the rest of this problem in MeV. (b) What is the approximate energy released in the fission of one 23592U nucleus? (c) From your answers to parts (a) and (b), calculate the energy per unit
An unknown particle collides with its antiparticle and the two are annihilated, emitting two photons, each with energy 3.0 MeV. Assume the unknown particles are moving very slowly before annihilating. What is the rest mass of the particle, in kilograms?
An electron with speed 0.80c collides head-on with a positron with the same speed, producing two photons. What is the energy of each photon?
An electron–positron pair is produced by a photon with an energy of 11 MeV. (a) Name two quantities this process must conserve. (b) What is the total kinetic energy of the electron and positron combined? (c) What is the total momentum of the electron and positron combined?
A proton and antiproton, both initially at rest, annihilate each other, producing two gamma ray photons. What is the frequency of one of the photons?
At sea level, some hundreds of muons go though your body each second. A muon has a mean lifetime of 2.2 microseconds, so why do we fi nd so many near the Earth’s surface? Consider a muon with a kinetic energy of 150 MeV that is created in the upper atmosphere when a cosmic ray collides with a
A cosmic-ray proton has a de Broglie wavelength of 0.020 fm. What is its kinetic energy? Use the relativistic relations for momentum and energy along with de Broglie’s relation for the wavelength of a particle-wave in Equation 28.9.
The collisions of cosmic-ray particles with the Earth’s atmosphere often produce muons that subsequently decay into an electron and two neutrinos according to the reaction,μ- → e- + nμ + v̅eWhat is the maximum possible kinetic energy of the electron? Assume the muon is at rest just before it
A cosmic-ray proton has a kinetic energy of 1019 eV. What is its speed? You will have to use the relativistic expression for the kinetic energy from Chapter 27.
Due to the cosmological red shift, the photons that make up the cosmic microwave background are, as the name implies, in the microwave region of the electromagnetic spectrum. In what region of the electromagnetic spectrum were these photons when they were first released?
Given the current age of the universe and a telescope powerful enough, how far away is the most distant object we could observe? What kind of object is it?
Consider the science of some hypothetical intelligent life-forms inhabiting a planet in a galaxy many millions of light-years away from the Earth. Would they measure the same Hubble constant as we do?
(a) Where did the Big Bang occur? (b) Does the universe have a center? Does the universe have edges? If not, explain how that could be possible.
Unification of physical laws often leads to new concepts and novel insights. Describe some of the consequences from the unification of the physics of electricity with that of magnetism. How was the concept of light altered?
It has been suggested that Newton’s law of gravity brought about the first unification of physics principles. In what way does his law of gravity unify the motion of heavenly bodies with the motion of earthly objects?
Describe some processes that produce antimatter. Consider radioactive decay processes and interactions involving cosmic rays. How common are anti-electrons (positrons) on the Earth? How common are antimuons on the Earth?
At sea level, a significant number of cosmic-ray particles are muons with relativistic velocities. If the muons have a mean lifetime of only 2.2 microseconds, where do they come from and how are they produced?
Conservation rules rule out certain decays. (a) Which conservation rule explains why a single electron cannot decay into a pair of photons? (b) Which conservation rule explains why a single electron cannot decay into a pair of neutrinos?
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