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mathematics
calculus early transcendentals 9th

Physics For Scientists And Engineers A Strategic Approach With Modern Physics 3rd Edition Randall D. Knight - Solutions

Charges q1 = –4Q and q2 = +2Q are located at x = –a and x = +a, respectively. What is the net electric flux through a sphere of radius 2a centered(a) At the origin(b) At x = 2a?
A 2.0 cm × 3.0 cm rectangle lies in the xz-plane. What is the electric flux through the rectangle ifa. E(vector) = (100î + 50k̂) N/C?b. E(vector) = (100î + 50ĵ) N/C?
A 2.0 cm × 3.0 cm rectangle lies in the xy-plane. What is the electric flux through the rectangle ifa. E(vector) = (100î + 50k̂) N/C?b. E(vector) = (100î + 50ĵ) N/C?
Three 10-cm-long rods form an equilateral triangle in a plane. Two of the rods are charged to +10 nC, the third to -10 nC. What is the electric field strength at the center of the triangle?
Two infinite lines of charge, each with linear charge density λ, lie along the x- and y-axes, crossing at the origin. What is the electric field strength at position (x, y)?
Three charges are on the y-axis. Charges -q are at y = ±d and charge ±2q is at y = 0.a. Find an expression for the electric field E(vector) at a point on the x-axis.b. Verify that your answer to part a has the expected behavior as x becomes very small and very large.
Derive Equation 26.12 for the field E(vector)dipole in the plane that bisects an electric dipole. 1 dipole 4TE, r3
Two positive charges q are on the y-axis at y = ±1/2 s.a. Find an expression for the electric field strength at distance x on the axis that bisects the two charges.b. For q = 1.0 nC and s = 6.0 mm, evaluate E at x = 0, 2, 4, 6, and 10 mm.
A 0.10 g glass bead is charged by the removal of 1.0 × 1010 electrons. What electric field E(vector) (strength and direction) will cause the bead to hang suspended in the air?
The electric field strength 2.0 cm from a 10-cm-diameter metal ball is 50,000 N/C. What is the charge (in nC) on the ball?
A 2.0-mm-diameter copper ball is charged to +50 nC. What fraction of its electrons have been removed?
As a science project, you’ve invented an “electron pump” that moves electrons from one object to another. To demonstrate your invention, you bolt a small metal plate to the ceiling, connect the pump between the metal plate and yourself, and start pumping electrons from the metal plate to you.
Charge q2 in Figure P25.44 is in static equilibrium. What is q1? 92 5.0 nC 10 cm 10 cm
What are the strength and direction of the electric field 1.0 mm from(a) A proton(b) An electron?
The electric field strength at one point near a point charge is 1000 N/C. What is the field strength if(a) The distance from the point charge is doubled(b) The distance from the point charge is halved?
What is the total charge of all the protons in 1.0 mol of He gas?
Can a conductor be charged? If so, how would you charge a conductor? If not, why not?
You’ve been asked to build a 12× microscope from a 2.0× magnifying lens and a 4.0× magnifying lens.a. Which lens should be used as the objective?b. What will be the tube length of your microscope?
You use your 8× binoculars to focus on a 14-cm-long bird in a tree 18 m away from you. What angle (in degrees) does the image of the warbler subtend on your retina?
The rays leaving the two-component optical system of Figure P24.25 produce two distinct images of the 1.0-cm-tall object.a. What are the position (relative to the lens), orientation, and height of each image?b. Draw two ray diagrams, one for each image, showing how the images are formed. f = 10 cm
In Figure P24.24, are parallel rays from the left focused to a point? If so, on which side of the lens and at what distance? fi = -10 cm f = 10 cm 20 cm
A 1.0-cm-tall object is located 4.0 cm to the left of a converging lens with a focal length of 5.0 cm. A diverging lens, of focal length -8.0 cm, is 12 cm to the right of the first lens. Find the position, size, and orientation of the final image.
A 12-mm-focal-length lens has a 4.0-mm-diameter aperture. What is the aperture diameter of an 18-mm-focal-length lens with the same f-number?
A sports photographer has a 150-mm-focal-length lens on his camera. The photographer wants to photograph a sprinter running straight away from him at 5.0 m/s. What is the speed (in mm/s ) of the sprinter’s image at the instant the sprinter is 10 m in front of the lens?
a. Estimate the diameter of your eyeball.b. Bring this page up to the closest distance at which the text is sharp—not the closest at which you can still read it, but the closest at which the letters remain sharp. If you wear glasses or contact lenses, leave them on. This distance is called the
A 6.0-cm-diameter cubic zirconia sphere has an air bubble exactly in the center. As you look into the sphere, how far beneath the surface does the bubble appear to be?
Your supervisor asks you to measure the index of refraction of a piece of plastic. You notice that, because of scattering of the light, you can see the path of a laser beam through the plastic. You decide to shoot a laser beam toward the plastic at several different incident angles and measure the
A laser beam with a wavelength of 524 nm is exactly perpendicular to a screen having two narrow slits spaced 0.150 mm apart. Interference fringes, including a central maximum, are observed on a viewing screen 1.00 m away. The direction of the laser beam is then slowly rotated by 1.0° around an
Light of 600 nm wavelength illuminates a single slit. The intensity pattern shown in Figure EX 22.18 is seen on a screen 2.0 m behind the slits. What is the width (in mm) of the slit? Intensity x (cm) 3
A fish is 20 m from the shore of a lake. A bonfire is burning on the edge of the lake nearest the fish.a. Does the fish need to be shallow (just below the surface) or very deep to see the light from the bonfire? Explain.b. What is the deepest or shallowest, depending on your answer to part a, that
You’re helping with an experiment in which a vertical cylinder will rotate about its axis by a very small angle. You need to devise a way to measure this angle. You decide to use what is called an optical lever. You begin by mounting a small mirror on top of the cylinder. A laser 5.0 m away
Find the focal length of the glass lens in Figure EX23.28. 24 cm 40 cm
Figure Q23.10 shows an object near a lens. The focal points are marked. Is there an image? If so, is the image real or virtual? Is it upright or inverted? If not, why not? Explain.
The laser beam in Figure EX23.7 is aimed at the center of a rotating hexagonal mirror. How long is the streak of laser light as the reflected laser beam sweeps across the wall behind the laser? Wall 40 cm Laser 50 cm 2.0 m
If you turn on your car headlights during the day, the road ahead of you doesn’t appear to get brighter. Why not?
The diffraction grating analysis in this chapter assumed that the incident light is normal to the grating. Figure CP 22.73 shows a plane wave approaching a diffraction grating at angle Φ.a. Show that the angles θm for constructive interference are given by the grating equationwhere m = 0, ±1, $Grating Incident wave Diffraction at angle o at angle 0$
Light consisting of two nearly equal wavelengths λ + Δλ and λ, where Δλ << λ, is incident on a diffraction grating. The slit separation of the grating is d.a. Show that the angular separation of these two wavelengths in the mth order isb. Sodium atoms emit light at 589.0 nm and 589.6
A 0.10-mm-thick piece of glass is inserted into one arm of a Michelson interferometer that is using light of wavelength 500 nm. This causes the fringe pattern to shift by 200 fringes. What is the index of refraction of this piece of glass?
You’ve set up a Michelson interferometer with a helium-neon laser (λ = 632.8 nm). After adjusting mirror M2 to produce a bright spot at the center of the pattern, you carefully move M2 away from the beam splitter while counting 1200 new bright spots at the center. Then you put the laser away.
Figure P 22.30 shows the light intensity on a screen 2.5 m behind an aperture. The aperture is illuminated with light of wavelength 600 nm.a. Is the aperture a single slit or a double slit? Explain.b. If the aperture is a single slit, what is its width? If it is a double slit, what is the spacing
A Michelson interferometer uses light whose wavelength is known to be 602.446 nm. Mirror M2 is slowly moved while exactly 33,198 bright-dark bright fringe shifts are observed. What distance has M2 moved? Be sure to give your answer to an appropriate number of significant figures.
The opening to a cave is a tall, 30-cm-wide crack. A bat that is preparing to leave the cave emits a 30 kHz ultrasonic chirp. How wide is the “sound beam” 100 m outside the cave opening? Use vsound = 340 m/s.
The central maximum of a single slit has width 4000λ when viewed on a screen 1.0 m behind the slit. How wide (in mm) is the slit?
Light of wavelength 600 nm illuminates a diffraction grating. The second-order maximum is at angle 39.5°. How many lines per millimeter does this grating have?
A double-slit interference pattern is created by two narrow slits spaced 0.20 mm apart. The distance between the first and the fifth minimum on a screen 60 cm behind the slits is 6.0 mm. What is the wavelength (in nm) of the light used in this experiment?
Light of 600 nm wavelength illuminates a double slit. The intensity pattern shown in Figure EX 22.5 is seen on a screen 2.0 m behind the slits. What is the spacing (in mm) between the slits? Intensity - x (cm) 2 1
A double-slit experiment is performed with light of wavelength 600 nm. The bright interference fringes are spaced 1.8 mm apart on the viewing screen. What will the fringe spacing be if the light is changed to a wavelength of 400 nm?
Light of wavelength 500 nm illuminates a double slit, and the interference pattern is observed on a screen. At the position of the m = 2 bright fringe, how much farther is it to the more distant slit than to the nearer slit?
A double slit is illuminated simultaneously with orange light of wavelength 600 nm and light of an unknown wavelength. The m = 4 bright fringe of the unknown wavelength overlaps the m = 3 bright orange fringe. What is the unknown wavelength?
Two narrow slits 80 μm apart are illuminated with light of wavelength 600 nm. What is the angle of the m = 3 bright fringe in radians? In degrees?
The broadcast antenna of an AM radio station is located at the edge of town. The station owners would like to beam all of the energy into town and none into the countryside, but a single antenna radiates energy equally in all directions. Figure CP21.80 shows two parallel antennas separated by
Two loudspeakers face each other from opposite walls of a room. Both are playing exactly the same frequency, thus setting up a standing wave with distance λ/2 between antinodes. Assume that λ is much less than the room width, so there are many antinodes.a. Yvette starts at one speaker and runs
Two radio antennas are 100 m apart along a north-south line. They broadcast identical radio waves at a frequency of 3.0 MHz. Your job is to monitor the signal strength with a handheld receiver. To get to your first measuring point, you walk 800 m east from the midpoint between the antennas, then
Two in-phase loudspeakers are located at (x, y) coordinates (–3.0 m, +2.0 m) and (–3.0 m, –2.0 m). They emit identical sound waves with a 2.0 m wavelength and amplitude a. Determine the amplitude of the sound at the five positions on the y-axis (x = 0) with y = 0.0 m, 0.5 m, 1.0 m, 1.5 m, and
A narrow column of 20°C air is found to have standing waves at frequencies of 390 Hz, 520 Hz, and 650 Hz and at no frequencies in between these. The behavior of the tube at frequencies less than 390 Hz or greater than 650 Hz is not known.a. Is this an open-open tube or an open-closed tube?
The two strings in Figure P 21.45 are of equal length and are being driven at equal frequencies. The linear density of the left string is μ0. What is the linear density of the right string? www Stretched spring
Two sinusoidal waves with equal wavelengths travel along a string in opposite directions at 3.0 m/s. The time between two successive instants when the antinodes are at maximum height is 0.25 s. What is the wavelength?
A string of length L vibrates at its fundamental frequency. The amplitude at a point 1/4L from one end is 2.0 cm. What is the amplitude of each of the traveling waves that form this standing wave?
Two waves on a string travel in opposite directions at 100 m/s. Figure P21.30 shows a snapshot graph of the string at t = 0 s, when the two waves are overlapped, and a snapshot graph of the left-traveling wave at t = 0.050 s. Draw a snapshot graph of the right-traveling wave at t = 0.050 s. D (cm)
Figure EX 21.3 is a snapshot graph at t = 0 s of two waves approaching each other at 1.0 m/s. Draw four snapshot graphs, stacked vertically, showing the string at t = 2, 4, 6, and 8 s. D (cm) at t = 0 s 1- 1.0 m/s 2 4 6 TX (m) 8 10 12 14 16 18 1.0 m/s -14
An important characteristic of the heart, one used to diagnose heart disease, is the pressure difference between the blood pressure inside the heart and the blood pressure in the aorta, the large artery leading away from the heart. The blood inside the heart is essentially at rest, but it speeds up
A mad doctor believes that baldness can be cured by warming the scalp with sound waves. His patients sit underneath the Bald-o-Matic loudspeakers, where their heads are bathed with 93 dB of soothing 800 Hz sound waves. Suppose we model a bald head as a 16-cm-diameter hemisphere. If 0.10 J of sound
Two loudspeakers on elevated platforms are at opposite ends of a field. Each broadcasts equally in all directions. The sound intensity level at a point halfway between the loudspeakers is 75.0 dB. What is the sound intensity level at a point one-quarter of the way from one speaker to the other
a. A 100 W lightbulb produces 5.0 W of visible light. (The other 95 W are dissipated as heat and infrared radiation.) What is the light intensity on a wall 2.0 m away from the lightbulb?b. A krypton laser produces a cylindrical red laser beam 2.0 mm in diameter with 5.0 W of power. What is the
A string with linear density 2.0 g/m is stretched along the positive x-axis with tension 20 N. One end of the string, at x = 0 m, is tied to a hook that oscillates up and down at a frequency of 100 Hz with a maximum displacement of 1.0 mm. At t = 0 s, the hook is at its lowest point.a. What are the
Write the displacement equation for a sinusoidal wave that is traveling in the positive x-direction with frequency 200 Hz, speed 400 m/s, amplitude 0.010 mm, and phase constant π/2 rad.
Write the displacement equation for a sinusoidal wave that is traveling in the negative y-direction with wavelength 50 cm, speed 4.0 m/s, and amplitude 5.0 cm. Assume Φ = 0.
Ships measure the distance to the ocean bottom with sonar. A pulse of sound waves is aimed at the ocean bottom, then sensitive microphones listen for the echo. Figure P20.45 shows the delay time as a function of the ship’s position as it crosses 60 km of ocean. Draw a graph of the ocean bottom.
A wave travels along a string at speed v0. What will be the speed if the string is replaced by one made of the same material and under the same tension but having twice the radius?
The displacement of a traveling wave iswhere x is in m and t in s.a. Draw displacement-versus-position graphs from x = -2 m to x = 12 m at 1 s intervals from t = 0 s to t = 3 s.b. Determine the wave speed from the graphs. Explain.c. Determine the wave speed from the equation for D(x, t). Does it
What are the intensities of sound waves with sound intensity levels(a) 46 dB(b) 103 dB?
Draw the snapshot graph D(x, t = 0 s) at t = 0 s for the wave shown in Figure EX 20.6. D (cm) 14 (s) 2 3 4 5 6 -2-1 -14
Draw the history graph D(x = 5.0 m, t) at x = 5.0 m for the wave shown in Figure EX 20.5. D (cm) 14 1.0 m/s -x (m) 1 2 3 4 5 6 7 -11 -1
Draw the history graph D(x = 0 m, t) at x = 0 m for the wave shown in Figure EX 20.4. D (cm) 14 x (m) 1 2 34 5 6 7 -11 Snapshot graph of a wave at t = 2 s -1 1.0 m/s
a. A large nuclear power plant has a power output of 1000 MW. In other words, it generates electric energy at the rate 1000 MJ/s. How much energy does this power plant supply in one day?b. The oceans are vast. How much energy could be extracted from 1 km3 of water if its temperature were decreased
Three engineering students submit their solutions to a design problem in which they were asked to design an engine that operates between temperatures 300 K and 500 K. The heat input/output and work done by their designs are shown in the following table:Critique their designs. Are they acceptable or
You and your roommates need a new refrigerator. At the appliance store, the salesman shows you the DreamFridge. According to its sticker, the DreamFridge uses a mere 100 W of power to remove 100 kJ of heat per minute from the 2°C interior. According to the fine print on the sticker, this claim is
A Carnot refrigerator operates between reservoirs at 55°C and –20°C. If the engine exhausts 250 J of energy to the hot reservoir per cycle, how many cycles will it take to cool a 500 mL soda from 25°C to 5°C?
The hot-reservoir temperature of a Carnot engine with 25% efficiency is 80°C higher than the cold-reservoir temperature. What are the reservoir temperatures, in °C?
An inventor wants you to invest money with his company, offering you 10% of all future profits. He reminds you that the brakes on cars get extremely hot when they stop and that there is a large quantity of thermal energy in the brakes. He has invented a device, he tells you, that converts that
Equal masses of hydrogen gas and oxygen gas are mixed together in a container and held at constant temperature. What is the hydrogen/oxygen ratio of(a) vrms(b) Pavg(c) Eth?
How many degrees of freedom does a system have if ϒ = 1.29?
A gas at p = 50 kPa and T = 300 K has a mass density of 0.0802 kg/m3.a. Identify the gas.b. What is the rms speed of the atoms in this gas?c. What is the mean free path of the atoms in the gas?
At what temperature (in °C) is the rms speed of helium atoms(a) Half(b) Twice its value at STP?
a. What compression ratio Vmax/Vmin will raise the air temperature from 20° C to 1000° C in an adiabatic process?b. What pressure ratio pmax/pmin does this process have?
0.10 mol of a monatomic gas follow the process shown in Figure P 17.60.a. How much heat energy is transferred to or from the gas during process 1 → 2?b. How much heat energy is transferred to or from the gas during process 2 → 3?c. What is the total change in thermal energy of the gas? р (atm)
Figure P17.57 shows two processes that take a gas from state i to state f. Show that QA – QB = piVi. 2p Pi- 0+ V, 2V,
What is oxygen’s specific heat at constant volume in J/kg K?
A 100 g ice cube at -10°C is placed in an aluminum bucket whose initial temperature is 70°C. The system comes to an equilibrium temperature of 20°C. What is the mass of the bucket?
Reptiles don’t use enough metabolic energy to keep their body temperature constant. They cool off at night and must warm up in the morning sun. Suppose a 2.9-m-long, 60-cm-wide, 350 kg alligator is basking in the sun. If the sun’s intensity on the back of the alligator is 500 W/m2, and if
An 11 kg bowling ball at 0°C is dropped into a tub containing a mixture of ice and water. A short time later, when a new equilibrium has been established, there are 5.0 g less ice. From what height was the ball dropped? Assume no water or ice splashes out.
A rigid cylinder contains 7.0 g of nitrogen at 20°C. What is the minimum amount of heat energy that must be removed to liquify the nitrogen?
How much heat energy must be added to a 6.0 cm × 6.0 cm × 6.0 cm block of aluminum to raise its temperature from - 50°C to 50°C?
Describe a series of steps in which you use the cylinder of Figure 17.13 to implement the ideal-gas process shown in Figure Q 17.10. Then show the process as a first-law bar chart.Figure Q 17.10Figure 17.13 Pz Isotherm Pi = P3- V, = V3 V V,
Describe a series of steps in which you use the cylinder of Figure 17.13 to implement the ideal-gas process shown in Figure Q 17.9. Then show the process as a first-law bar chart.Figure Q 17.9Figure Q 17.13 P1= P2 V V2
A compressed-air cylinder is known to fail if the pressure exceeds 110 atm. A cylinder that was filled to 25 atm at 20°C is stored in a warehouse. Unfortunately, the warehouse catches fire and the temperature reaches 950°C. Does the cylinder blow?
Estimate the number density of gas molecules in the earth’s atmosphere at sea level.
Figure Q14.8 shows a velocity-versus-time graph for a particle in SHM.a. What is the phase constant Φ? Explain.b. What is the phase of the particle at each of the three numbered points on the graph? max 3 -v. max 2.
Equation 14.25 states that 1/2kA2 = 1/2m(vmax)2. What does this mean? Write a couple of sentences explaining how to interpret this equation.
Figure CP 12.85 shows a triangular block of Swiss cheese sitting on a cheese board. You and your friends start to wonder what will happen if you slowly tilt the board, increasing angle θ. Emily thinks the cheese will start to slide before it topples over. Fred thinks it will topple before starting

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