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Physics for Scientists and Engineers A Strategic Approach with Modern Physics 4th edition Randall D. Knight - Solutions

Astronauts visiting Planet X have a 250-cm-long string whose mass is 5.00 g. They tie the string to a support, stretch it horizontally over a pulley 2.00 m away, and hang a 4.00 kg mass on the free end. Then the astronauts begin to excite standing waves on the horizontal portion of the string.
A 75 g bungee cord has an equilibrium length of 1.20 m. The cord is stretched to a length of 1.80 m, then vibrated at 20 Hz. This produces a standing wave with two antinodes. What is the spring constant of the bungee cord?
A metal wire under tension T0 vibrates at its fundamental frequency. For what tension will the second-harmonic frequency be the same as the fundamental frequency at tension T0?
In a laboratory experiment, one end of a horizontal string is tied to a support while the other end passes over a frictionless pulley and is tied to a 1.5 kg sphere. Students determine the frequencies of standing waves on the horizontal segment of the string, then they raise a beaker of water until
A vibrating standing wave on a string radiates a sound wave with intensity proportional to the square of the standing-wave amplitude. When a piano key is struck and held down, so that the string continues to vibrate, the sound level decreases by 8.0 dB in 1.0 s. What is the string’s damping time
What is the fundamental frequency of the steel wire in FIGURE P17.48? 75 g steel wire 4.0 kg bar 45° 2.0 m 8.0 kg FIGURE P17.48
The two strings in FIGURE P17.49 are of equal length and are being driven at equal frequencies. The linear density of the left string is 5.0 g/m. What is the linear density of the right string? www- Stretched spring FIGURE P17.49
An open-open organ pipe is 78.0 cm long. An open-closed pipe has a fundamental frequency equal to the third harmonic of the open-open pipe. How long is the open-closed pipe?
In 1866, the German scientist Adolph Kundt developed a technique for accurately measuring the speed of sound in various gases. A long glass tube, known today as a Kundt€™s tube, has a vibrating piston at one end and is closed at the other. Very finely ground particles of cork are
A 1.0-m-tall vertical tube is filled with 20°C water. A tuning fork vibrating at 580 Hz is held just over the top of the tube as the water is slowly drained from the bottom. At what water heights, measured from the bottom of the tube, will there be a standing wave in the tube above the water?
A 25-cm-long wire with a linear density of 20 g/m passes across the open end of an 85-cm-long open-closed tube of air. If the wire, which is fixed at both ends, vibrates at its fundamental frequency, the sound wave it generates excites the second vibrational mode of the tube of air. What is the
An old mining tunnel disappears into a hillside. You would like to know how long the tunnel is, but it’s too dangerous to go inside.Recalling your recent physics class, you decide to try setting up standing-wave resonances inside the tunnel. Using your subsonic amplifier and loudspeaker, you find
Engineers are testing a new thin-film coating whose index of refraction is less than that of glass. They deposit a 560-nm thick layer on glass, then shine lasers on it. A red laser with a wavelength of 640 nm has no reflection at all, but a violet laser with a wavelength of 400 nm has a maximum
Two in-phase loudspeakers emit identical 1000 Hz sound waves along the x-axis. What distance should one speaker be placed behind the other for the sound to have an amplitude 1.5 times that of each speaker alone?
Analyze the standing sound waves in an open-closed tube to show that the possible wavelengths and frequencies are given by Equation 17.18. 4L m= 1, 3, 5, 7,... (open-closed tube) т (17.18) fm = m mf 4L
Two loudspeakers emit sound waves of the same frequency along the x-axis. The amplitude of each wave is a. The sound intensity is minimum when speaker 2 is 10 cm behind speaker 1. The intensity increases as speaker 2 is moved forward and first reaches maximum, with amplitude
Two loudspeakers emit sound waves along the x-axis. A listener in front of both speakers hears a maximum sound intensity when speaker 2 is at the origin and speaker 1 is at x = 0.50 m. If speaker 1 is slowly moved forward, the sound intensity decreases and then increases,
A sheet of glass is coated with a 500-nm-thick layer of oil (n = 1.42).a. For what visible wavelengths of light do the reflected waves interfere constructively?b. For what visible wavelengths of light do the reflected waves interfere destructively?c. What is the color of reflected light? What is
A soap bubble is essentially a very thin film of water (n = 1.33) surrounded by air. The colors that you see in soap bubbles are produced by interference.a. Derive an expression for the wavelengths λC for which constructive interference causes a strong reflection from a soap bubble of thickness
A manufacturing firm has hired your company, Acoustical Consulting, to help with a problem. Their employees are complaining about the annoying hum from a piece of machinery. Using a frequency meter, you quickly determine that the machine emits a rather loud sound at 1200 Hz. After investigating,
Scientists are testing a transparent material whose index of refraction for visible light varies with wavelength as n = 30.0 nm1/2/λ1/2, where λ is in nm. If a 295-nm-thick coating is placed on glass (n = 1.50) for what visible wavelengths will the reflected light have maximum constructive
You are standing 2.5 m directly in front of one of the two loudspeakers shown in FIGURE P17.68. They are 3.0 m apart and both are playing a 686 Hz tone in phase. As you begin to walk directly away from the speaker, at what distances from the speaker do you hear a minimum sound intensity?The room
Two loudspeakers in a plane, 5.0 m apart, are playing the same frequency. If you stand 12.0 m in front of the plane of the speakers, centered between them, you hear a sound of maximum intensity.As you walk parallel to the plane of the speakers, staying 12.0 m in front of them, you first hear a
Two identical loudspeakers separated by distance Δx each emit sound waves of wavelength λ and amplitude a along the x-axis. What is the minimum value of the ratio Δx/λ for which the amplitude of their superposition is also a?
Piano tuners tune pianos by listening to the beats between the harmonics of two different strings. When properly tuned, the note A should have a frequency of 440 Hz and the note E should be at 659 Hz.a. What is the frequency difference between the third harmonic of the A and the second harmonic of
A flutist assembles her flute in a room where the speed of sound is 342 m/s. When she plays the note A, it is in perfect tune with a 440 Hz tuning fork. After a few minutes, the air inside her flute has warmed to where the speed of sound is 346 m/s.a. How many beats per second will she hear if she
You have two small, identical boxes that generate 440 Hz notes. While holding one, you drop the other from a 20-m-high balcony. How many beats will you hear before the falling box hits the ground? You can ignore air resistance.
Two loudspeakers emit 400 Hz notes. One speaker sits on the ground. The other speaker is in the back of a pickup truck. You hear eight beats per second as the truck drives away from you. What is the truck’s speed?
Two radio antennas are separated by 2.0 m. Both broadcast identical 750 MHz waves. If you walk around the antennas in a circle of radius 10 m, how many maxima will you detect?
A 280 Hz sound wave is directed into one end of the trombone slide seen in FIGURE CP17.77. A microphone is placed at the other end to record the intensity of sound waves that are transmitted through the tube. The straight sides of the slide are 80 cm in length and 10 cm apart with a semicircular
As the captain of the scientific team sent to Planet Physics, one of your tasks is to measure g. You have a long, thin wire labeled 1.00 g/m and a 1.25 kg weight. You have your accurate space cadet chronometer but, unfortunately, you seem to have forgotten a meter stick. Undeterred, you first find
When mass M is tied to the bottom of a long, thin wire suspended from the ceiling, the wire’s second-harmonic frequency is 200 Hz. Adding an additional 1.0 kg to the hanging mass increases the second-harmonic frequency to 245 Hz. What is M?
Ultrasound has many medical applications, one of which is to monitor fetal heartbeats by reflecting ultrasound off a fetus in the womb.a. Consider an object moving at speed votoward an at-rest source that is emitting sound waves of frequency f0. Show that the reflected wave (i.e., the echo) that
A water wave is called a deep-water wave if the water’s depth is more than one-quarter of the wavelength. Unlike the waves we’ve considered in this chapter, the speed of a deep-water wave depends on its wavelength:v = √gλ/2πLonger wavelengths travel faster. Let’s apply this to standing
A long horizontal tube has a square cross section with sides of width L. A fluid moves through the tube with speed v0. The tube then changes to a circular cross section with diameter L. What is the fluid’s speed in the circular part of the tube?
a. In FIGURE P14.38, how much force does the fluid exert on the end of the cylinder at A?b. How much force does the fluid exert on the end of the cylinder at B? - 10 kg floating piston 4.0 cm 100 cm 20 cm A 60 cm Oil B FIGURE P14.38
A hurricane wind blows across a 6.0 m × 15.0 m flat roof at a speed of 130 km/h.a. Is the air pressure above the roof higher or lower than the pressure inside the house? Explain.b. What is the pressure difference?c. How much force is exerted on the roof? If the roof cannot withstand this much
Air flows through the tube shown in FIGURE P14.66 at a rate of 1200 cm3/s. Assume that air is an ideal fluid. What is the height h of mercury in the right side of the U-tube? 4.0 mm 2.0 cm 1200 cm/s |h Hg FIGURE P14.66
Air flows through the tube shown in FIGURE P14.67. Assume that air is an ideal fluid.a. What are the air speeds v1and v2at points 1 and 2?b. What is the volume flow rate? 2.0 mm 2. 1.0 cm Air 10 cm Hg FIGURE P14.67
A water tank of height h has a small hole at height y. The water is replenished to keep h from changing. The water squirting from the hole has range x. The range approaches zero as y → 0 because the water squirts right onto the ground. The range also approaches zero as y → h because the
a. A cylindrical tank of radius R, filled to the top with a liquid, has a small hole in the side, of radius r, at distance d below the surface. Find an expression for the volume flow rate through the hole.b. A 4.0-mm-diameter hole is 1.0 m below the surface of a 2.0-m-diameter tank of water. What
There is a disk of cartilage between each pair of vertebrae in your spine. Young’s modulus for cartilage is 1.0 × 106 N/m2.Suppose a relaxed disk is 4.0 cm in diameter and 5.0 mm thick. If a disk in the lower spine supports half the weight of a 66 kg person, by how many mm does the disk compress?
The bottom of a steel “boat” is a 5.0 m × 10 m × 2.0 cm piece of steel (ρsteel = 7900 kg/m3). The sides are made of 0.50-cm thick steel. What minimum height must the sides have for this boat to float in perfectly calm water?
The tank shown in FIGURE CP14.72 is completely filled with a liquid of density Ï. The right face is not permanently attached to the tank but, instead, is held against a rubber seal by the tension in a spring. To prevent leakage, the spring must both pull with sufficient strength and
In FIGURE CP14.73, a cone of density Ïoand total height l floats in a liquid of density Ïf. The height of the cone above the liquid is h. What is the ratio h/l of the exposed height to the total height? FIGURE CP14.73
Disk brakes, such as those in your car, operate by using pressurized oil to push outward on a piston. The piston, in turn, presses brake pads against a spinning rotor or wheel, as seen in FIGURE CP14.74. Consider a 15 kg industrial grinding wheel, 26 cm in diameter, spinning at 900 rpm. The brake
In addition to the buoyant force, an object moving in a liquid experiences a linear drag force Fdrag = (bv, direction opposite the motion), where b is a constant. For a sphere of radius R, the drag constant can be shown to be b = 6πηR, where η is the viscosity of the liquid. Consider a sphere of
A sphere completely submerged in water is tethered to the bottom with a string. The tension in the string is one-third the weight of the sphere. What is the density of the sphere?
Astronauts visiting a new planet find a lake filled with an unknown liquid. They have with them a plastic cube, 6.0 cm on each side, with a density of 840 kg/m3. First they weigh the cube with a spring scale, measuring a weight of 21 N. Then they float the cube in the lake and find that two-thirds
A 2.0 cm × 2.0 cm × 6.0 cm block floats in water with its long axis vertical. The length of the block above water is 2.0 cm. What is the block’s mass density?
A 6.00-cm-diameter sphere with a mass of 89.3 g is neutrally buoyant in a liquid. Identify the liquid.
How far must a 2.0-cm-diameter piston be pushed down into one cylinder of a hydraulic lift to raise an 8.0-cm-diameter piston by 20 cm?
What is the minimum hose diameter of an ideal vacuum cleaner that could lift a 10 kg (22 lb) dog off the floor?
What is the height of a water barometer at atmospheric pressure?
A wire is stretched right to the breaking point by a 5000 N force. A longer wire made of the same material has the same diameter.Is the force that will stretch it right to the breaking point larger than, smaller than, or equal to 5000 N? Explain.
The container shown in FIGURE EX14.12 is filled with oil. It is open to the atmosphere on the left.a. What is the pressure at point A?b. What is the pressure difference between points A and B? Between points A and C? У (ст) 100- 75- 50- 25 B
A 2000 N force stretches a wire by 1 mm. A second wire of the same material is twice as long and has twice the diameter. How much force is needed to stretch it by 1 mm? Explain.
A 20-cm-diameter circular cover is placed over a 10-cm diameter hole that leads into an evacuated chamber. The pressure in the chamber is 20 kPa. How much force is required to pull the cover off?
Wind blows over the house in FIGURE Q14.11. A window on the ground floor is open. Is there an airflow through the house?If so, does the air flow in the window and out the chimney, or in the chimney and out the window? Explain. Wind FIGURE Q14.11
A research submarine has a 20-cm-diameter window 8.0 cm thick. The manufacturer says the window can withstand forces up to 1.0 × 106 N. What is the submarine’s maximum safe depth? The pressure inside the submarine is maintained at 1.0 atm.
Gas flows through the pipe of FIGURE Q14.10. You can€™t see into the pipe to know how the inner diameter changes. Rank in order, from largest to smallest, the gas speeds va, vb, and vcat points a, b, and c. Explain. b Liquid - FIGURE Q14.10
A 50-cm-thick layer of oil floats on a 120-cm-thick layer of water. What is the pressure at the bottom of the water layer?
The two identical beakers in FIGURE Q14.9 are filled to the same height with water. Beaker B has a plastic sphere floating in it.Which beaker, with all its contents, weighs more? Or are they equal? Explain. A B FIGURE Q14.9
a. What volume of water has the same mass as 8.0 m3 of ethyl alcohol?b. If this volume of water is in a cubic tank, what is the pressure at the bottom?
Blocks a, b, and c in FIGURE Q14.7 have the same density. Rank in order, from largest to smallest, the sizes of the buoyant forces Fa, Fb, and Fcon a, b, and c. Explain. 50 g 40 g 50 g
A 3.0-cm-diameter tube is held upright and filled to the top with mercury. The mercury pressure at the bottom of the tube— the pressure in excess of atmospheric pressure—is 50 kPa. How tall is the tube?
Blocks a, b, and c in FIGURE Q14.7 have the same volume. Rank in order, from largest to smallest, the sizes of the buoyant forces Fa, Fb, and Fcon a, b, and c. Explain. 50 g 40 g 50 g
The deepest point in the ocean is 11 km below sea level, deeper than Mt. Everest is tall. What is the pressure in atmospheres at this depth?
A 1.0-m-diameter vat of liquid is 2.0 m deep. The pressure at the bottom of the vat is 1.3 atm. What is the mass of the liquid in the vat?
Rank in order, from largest to smallest, the densities of blocks a, b, and c in FIGURE Q14.6. Explain. FIGURE Q14.6
In FIGURE Q14.5, is pAlarger than, smaller than, or equal to pB? Explain. A B FIGURE Q14.5
A 6.0 m × 12.0 m swimming pool slopes linearly from a 1.0 m depth at one end to a 3.0 m depth at the other. What is the mass of water in the pool?
FIGURE Q14.4 shows two rectangular tanks, A and B, full of water. They have equal depths and equal thicknesses (the dimension into the page) but different widths.a. Compare the forces the water exerts on the bottoms of the tanks. Is FAlarger than, smaller than, or equal to FB? Explain.b. Compare
a. 50 g of gasoline are mixed with 50 g of water. What is the average density of the mixture?b. 50 cm3 of gasoline are mixed with 50 cm3 of water. What is the average density of the mixture
Cylinders A and B have equal heights. Cylinder A is filled with helium gas at 1.0 atm pressure and 0°C. The diameter of cylinder B is half that of cylinder A, and cylinder B is filled with glycerin. What is the ratio of the fluid mass in cylinder B to that in cylinder A?
Rank in order, from largest to smallest, the pressures at a, b, and c in FIGURE Q14.2. Explain. f b
What is the volume in mL of 55 g of a liquid with density 1100 kg/m3?
An object has density ρ.a. Suppose each of the object’s three dimensions is increased by a factor of 2 without changing the material of which the object is made. Will the density change? If so, by what factor? Explain.b. Suppose each of the object’s three dimensions is increased by a factor of
A motorcycle daredevil plans to ride up a 2.0-m-high, 20° ramp, sail across a 10-m-wide pool filled with hungry crocodiles, and land at ground level on the other side. He has done this stunt many times and approaches it with confidence. Unfortunately, the motorcycle engine dies just as he starts
In uniform circular motion, which of the following are constant: speed, velocity, angular velocity, centripetal acceleration, magnitude of the net force?
As a science fair project, you want to launch an 800 g model rocket straight up and hit a horizontally moving target as it passes 30 m above the launch point. The rocket engine provides a constant thrust of 15.0 N. The target is approaching at a speed of 15 m/s. At what horizontal distance between
A car runs out of gas while driving down a hill. It rolls through the valley and starts up the other side. At the very bottom of the valley, which of the free-body diagrams in FIGURE Q8.2 is correct?The car is moving to the right, and drag and rolling friction are negligible. (f) (e) (d) (c) (b)
A 500 g model rocket is on a cart that is rolling to the right at a speed of 3.0 m/s. The rocket engine, when it is fired, exerts an 8.0 N vertical thrust on the rocket. Your goal is to have the rocket pass through a small horizontal hoop that is 20 m above the ground. At what horizontal distance
FIGURE Q8.3 is a bird€™s-eye view of particles on strings moving in horizontal circles on a tabletop. All are moving at the same speed. Rank in order, from largest to smallest, the tensions Tato Td. Give your answer in the form a > b = c > d and explain your ranking. 2m т 2m т 2r
A 4.0 × 1010 kg asteroid is heading directly toward the center of the earth at a steady 20 km/s. To save the planet, astronauts strap a giant rocket to the asteroid perpendicular to its direction of travel. The rocket generates 5.0 × 109 N of thrust. The rocket is fired when the asteroid is 4.0
Tarzan swings through the jungle on a massless vine. At the lowest point of his swing, is the tension in the vine greater than, less than, or equal to the gravitational force on Tarzan? Explain.
A 55 kg astronaut who weighs 180 N on a distant planet is pondering whether she can leap over a 3.5-m-wide chasm without falling in. If she leaps at a 15° angle, what initial speed does she need to clear the chasm?
FIGURE Q8.5 shows two balls of equal mass moving in vertical circles. Is the tension in string A greater than, less than, or equal to the tension in string B if the balls travel over the top of the circle(a) With equal speed(b) With equal angular velocity? т т 2r A B FIGURE Q8.5
A 1500 kg car drives around a flat 200-m-diameter circular track at 25 m/s. What are the magnitude and direction of the net force on the car? What causes this force?
Ramon and Sally are observing a toy car speed up as it goes around a circular track. Ramon says, “The car’s speeding up, so there must be a net force parallel to the track.” “I don’t think so,” replies Sally. “It’s moving in a circle, and that requires centripetal acceleration. The
A 1500 kg car takes a 50-m-radius unbanked curve at 15 m/s. What is the size of the friction force on the car?
A jet plane is flying on a level course at constant speed. The engines are at full throttle.(a) What is the net force on the plane? Explain.(b) Draw a free-body diagram of the plane as seen from the side with the plane flying to the right. Name (don’t just label) any and all forces shown on your
A 200 g block on a 50-cm-long string swings in a circle on a horizontal, frictionless table at 75 rpm.a. What is the speed of the block?b. What is the tension in the string?
A small projectile is launched parallel to the ground at height h = 1 m with sufficient speed to orbit a completely smooth, airless planet. A bug rides inside a small hole inside the projectile. Is the bug weightless? Explain.
In the Bohr model of the hydrogen atom, an electron (mass m = 9.1 × 10-31 kg) orbits a proton at a distance of 5.3 × 10-11 m. The proton pulls on the electron with an electric force of 8.2 × 10-8 N. How many revolutions per second does the electron make?
You can swing a ball on a string in a vertical circle if you swing it fast enough. But if you swing too slowly, the string goes slack as the ball nears the top. Explain why there’s a minimum speed to keep the ball moving in a circle.
Suppose the moon were held in its orbit not by gravity but by a massless cable attached to the center of the earth. What would be the tension in the cable? Use the table of astronomical data inside the back cover of the book.
A golfer starts with the club over her head and swings it to reach maximum speed as it contacts the ball. Halfway through her swing, when the golf club is parallel to the ground, does the acceleration vector of the club head point (a) Straight down,(b) Parallel to the ground, approximately
A highway curve of radius 500 m is designed for traffic moving at a speed of 90 km/h. What is the correct banking angle of the road?
It is proposed that future space stations create an artificial gravity by rotating. Suppose a space station is constructed as a 1000-m-diameter cylinder that rotates about its axis. The inside surface is the deck of the space station. What rotation period will provide “normal” gravity?

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