At time t = 0, a vessel contains a mixture of 10. kg of water and an unknown mass of ice in equilibrium at 0°C. The temperature of the mixture is measured over a period of an hour, with the following results: During the first 50. min, the mixture remains at 0°C; from 50. min to 60. min, the temperature increases steadily from 0°C to 2.0°C. Neglecting the heat capacity of the vessel, determine the mass of ice that was initially placed in it. Assume a constant power input to the container.
> Suppose the conducting spherical shell of Figure 15.29 carries a charge of 3.00 nC and that a charge of -2.00 nC is at the center of the sphere. If a = 2.00 m and b = 2.40 m, find the electric field at (a) r = 1.50 m, (b) r = 2.20 m, and (c) r = 2.50 m.
> A charge of 1.70 x 102 μC is at the center of a cube of edge 80.0 cm. No other charges are nearby. (a) Find the flux through the whole surface of the cube. (b) Find the flux through each face of the cube. (c) Would your answers to parts (a) or (b) change
> A point charge q is located at the center of a spherical shell of radius a that has a charge -q uniformly distributed on its surface. Find the electric field (a) For all points outside the spherical shell and (b) For a point inside the shell a distance r
> A charge of q = 2.00 x 10-9 C is spread evenly on a thin metal disk of radius 0.200 m. (a) Calculate the charge density on the disk. (b) Find the magnitude of the electric field just above the center of the disk, neglecting edge effects and assuming a un
> The nucleus of 8Be, which consists of 4 protons and 4 neutrons, is very unstable and spontaneously breaks into two alpha particles (helium nuclei, each consisting of 2 protons and 2 neutrons). (a) What is the force between the two alpha particles when th
> A charge q = +5.80 μC is located at the center of a regular tetrahedron (a four - sided surface) as in Figure P15.48. Find (a) The total electric flux through the tetrahedron and (b) The electric flux through one face of the tetrahedron. F
> A 3.00-g copper coin at 25.0°C drops 50.0 m to the ground. (a) Assuming 60.0% of the change in gravitational potential energy of the coin–Earth system goes into increasing the internal energy of the coin, determine the coin’s final temperature. (b) Does
> Four closed surfaces, S1 through S4, together with the charges -2Q , Q , and -Q , are sketched in Figure P15.47. (The colored lines are the intersections of the surfaces with the page.) Find the electric flux through each surface. Figure P15.47:
> The electric field everywhere on the surface of a charged sphere of radius 0.230 m has a magnitude of 575 N/C and points radially outward from the center of the sphere. (a) What is the net charge on the sphere? (b) What can you conclude about the nature
> An electric field of intensity 3.50 kN/C is applied along the x - axis. Calculate the electric flux through a rectangular plane 0.350 m wide and 0.700 m long if (a) The plane is parallel to the yz - plane, (b) The plane is parallel to the xy - plane, and
> A uniform electric field of magnitude E = 435 N/C makes an angle of θ = 65.0° with a plane surface of area A = 3.50 m2 as in Figure P15.44. Find the electric flux through this surface. Figure P15.44:
> A Van de Graaff generator is charged so that a proton at its surface accelerates radially outward at 1.52 x 1012 m/s2. Find (a) The magnitude of the electric force on the proton at that instant and (b) The magnitude and direction of the electric field at
> In the Millikan oil - drop experiment illustrated in Figure 15.21, an atomizer (a sprayer with a fine nozzle) is used to introduce many tiny droplets of oil between two oppositely charged parallel metal plates. Some of the droplets pick up one or more ex
> If the electric field strength in air exceeds 3.0 x 106 N/C, the air becomes a conductor. Using this fact, determine the maximum amount of charge that can be carried by a metal sphere 2.0 m in radius.
> The dome of a Van de Graaff generator receives a charge of 2.0 X 10-4 C. Find the strength of the electric field (a) Inside the dome, (b) At the surface of the dome, assuming it has a radius of 1.0 m, and (c) 4.0 m from the center of the dome.
> A small sphere of mass m = 7.50 g and charge q1 = 32.0 nC is attached to the end of a string and hangs vertically as in Figure P15.4. A second charge of equal mass and charge q2 = -58.0 nC is located below the first charge a distance d = 2.00 cm below th
> Refer to Figure 15.20. The charge lowered into the center of the hollow conductor has a magnitude of 5 μC. Find the magnitude and sign of the charge on the inside and outside of the hollow conductor when the charge is as shown in (a) Figure 15.20a, (b) F
> Convert 3.50 x 103 cal to the equivalent number of (a) Kilocalories (also known as Calories, used to describe the energy content of food) and (b) Joules.
> Three equal positive charges are at the corners of an equilateral triangle of side a as in Figure P15.38. Assume the three charges together create an electric field. (a) Sketch the electric field lines in the plane of the charges. (b) Find the location o
> Two point charges are a small distance apart. (a) Sketch the electric field lines for the two if one has a charge four times that of the other and both charges are positive. (b) Repeat for the case in which both charges are negative.
> (a) Sketch the electric field pattern around two positive point charges of magnitude 1 μC placed close together. (b) Sketch the electric field pattern around two negative point charges of -2 μC, placed close together. (c) Sketch the pattern around two po
> (a) Sketch the electric field lines around an isolated point charge q > 0. (b) Sketch the electric field pattern around an isolated negative point charge of magnitude -2q.
> Figure P15.34 shows the electric field lines for two point charges separated by a small distance. (a) Determine the ratio q1/q2. (b) What are the signs of q1 and q2? Figure P15.34:
> Three identical charges (q = -5.0 μC) lie along a circle of radius 2.0 m at angles of 30°, 150°, and 270°, as shown in Figure P15.33. What is the resultant electric field at the center of the circle? Figure
> Three charges are at the corners of an equilateral triangle, as shown in Figure P15.32. Calculate the electric field at a point midway between the two charges on the x - axis. Figure P15.3:
> In Figure P15.31, determine the point (other than infinity) at which the total electric field is zero. Figure P15.31:
> Three point charges are located on a circular arc as shown in Figure P15.30. (a) What is the total electric field at P, the center of the arc? (b) Find the electric force that would be exerted on a -5.00 - nC charge placed at P. Figure P15.30:
> Rocket observations show that dust particles in Earth’s upper atmosphere are often electrically charged. (a) Find the distance separating two dust particles if each has a charge of +e and the Coulomb force between them has magnitude 1.00 x 10-14 N. (b) C
> An aluminum rod and an iron rod are joined end to end in good thermal contact. The two rods have equal lengths and radii. The free end of the aluminum rod is maintained at a temperature of 100.°C, and the free end of the iron rod is maintained at 0°C. (a
> Two equal positive charges are at opposite corners of a trapezoid as in Figure P15.29. Find symbolic expressions for the components of the electric field at the point P. Figure P15.29:
> A particle of mass 1.00 x 10-9 kg and charge 3.00 pC is moving in a vacuum chamber where the electric field has magnitude 2.00 x 103 N/C and is directed straight upward. Neglecting other forces except gravity, calculate the particle’s (a) Acceleration an
> A charged dust particle at rest in a vacuum is held motionless by an upward - directed 475-N/C electric field. If the dust particle has a mass of 7.50 x 10-10 kg, find (a) The charge on the dust particle and (b) The number of electrons that must be added
> A helium nucleus of mass m = 6.64 x 10-27 kg and charge q = 6.41 x 10-19 C is in a constant electric field of magnitude E = 2.00 x 10-3 N/C pointing in the positive x - direction. Neglecting other forces, calculate (a) The nucleus’ acceleration and (b) I
> Four point charges are located at the corners of a square. Each charge has magnitude 3.20 nC and the square has sides of length 2.00 cm. Find the magnitude of the electric field at the center of the square if (a) All of the charges are positive and (b) T
> (a) Find the magnitude and direction of the electric field at the position of the 2.00 μC charge in Figure P15.13. (b) How would the electric field at that point be affected if the charge there were doubled? Would the magnitude of the elect
> A proton accelerates from rest in a uniform electric field of 640. N/C. At some later time, its speed is 1.20 x 106 m/s. (a) Find the magnitude of the acceleration of the proton. (b) How long does it take the proton to reach this speed? (c) How far has i
> Charge q1 = 1.00 nC is at x1 = 0 and charge q2 = 3.00 nC is at x2 = 2.00 m. At what point between the two charges is the electric field equal to zero?
> An electron is accelerated by a constant electric field of magnitude 300 N/C. (a) Find the acceleration of the electron. (b) Use the equations of motion with constant acceleration to find the electron’s speed after 1.00 x 10-8 s, assuming it starts from
> An ice - cube tray is filled with 75.0 g of water. After the filled tray reaches an equilibrium temperature 20.0°C, it is placed in a freezer set at -8.00°C to make ice cubes. (a) Describe the processes that occur as energy is being removed from the wate
> A charged particle A exerts a force of 2.62 N to the right on charged particle B when the particles are 13.7 mm apart. Particle B moves straight away from A to make the distance between them 17.7 mm. What vector force does particle B then exert on A?
> An electric field of magnitude 5.25 x 105 N/C points due south at a certain location. Find the magnitude and direction of the force on a -6.00 μC charge at this location.
> (a) Determine the electric field strength at a point 1.00 cm to the left of the middle charge shown in Figure P15.10. (b) If a charge of -2.00 μC is placed at this point, what are the magnitude and direction of the force on it? Figure P15.
> A small object of mass 3.80 g and charge -18.0 μC is suspended motionless above the ground when immersed in a uniform electric field perpendicular to the ground. What is the magnitude and direction of the electric field?
> Particle A of charge 3.00 x 10-4 C is at the origin, particle B of charge -6.00 x 10-4 C is at (4.00 m, 0), and particle C of charge 1.00 x 10-4 C is at (0, 3.00 m). (a) What is the x - component of the electric force exerted by A on C? (b) What is the y
> Two small metallic spheres, each of mass m = 0.20 g, are suspended as pendulums by light strings from a common point as shown in Figure P15.15. The spheres are given the same electric charge, and it is found that they come to equilibrium when each string
> Two identical metal blocks resting on a frictionless horizontal surface are connected by a light metal spring having constant k = 100 N/m and un-stretched length Li = 0.400 m as in Figure P15.14a. A charge Q is slowly placed on each block causing the spr
> Three point charges are located at the corners of an equilateral triangle as in Figure P15.13. Find the magnitude and direction of the net electric force on the 2.00 μC charge. Figure P15.13:
> A positive charge q1 = 2.70 μC on a frictionless horizontal surface is attached to a spring of force constant k as in Figure P15.12. When a charge of q2 = -8.60 μC is placed 9.50 cm away from the positive charge, the spring stretches by 5.00 mm, reducing
> Three charges are arranged as shown in Figure P15.11. Find the magnitude and direction of the electrostatic force on the charge at the origin. Figure P15.11:
> Calculate the magnitude and direction of the Coulomb force on each of the three charges shown in Figure P15.10. Figure P15.10:
> A 7.50 - nC charge is located 1.80 m from a 4.20 - nC charge. (a) Find the magnitude of the electrostatic force that one particle exerts on the other. (b) Is the force attractive or repulsive?
> A hammer strikes one end of a thick steel rail of length 8.50 m. A microphone located at the opposite end of the rail detects two pulses of sound, one that travels through the air and a longitudinal wave that travels through the rail. (a) Which pulse rea
> A 0.500 - m - long brass pipe open at both ends has a fundamental frequency of 350. Hz. (a) Determine the temperature of the air in the pipe. (b) If the temperature is increased by 20.0°C, what is the new fundamental frequency of the pipe? Be sure to inc
> By proper excitation, it is possible to produce both longitudinal and transverse waves in a long metal rod. In a particular case, the rod is 1.50 m long and 0.200 cm in radius and has a mass of 50.9 g. Young’s modulus for the material is 6.80 x 1010 Pa.
> A student stands several meters in front of a smooth reflecting wall, holding a board on which a wire is fixed at each end. The wire, vibrating in its third harmonic, is 75.0 cm long, has a mass of 2.25 g, and is under a tension of 400. N. A second stude
> A stone is dropped from rest into a well. The sound of the splash is heard exactly 2.00 s later. Find the depth of the well if the air temperature is 10.0°C.
> A block with a speaker bolted to it is connected to a spring having spring constant k = 20.0 N/m, as shown in Figure P14.79. The total mass of the block and speaker is 5.00 kg, and the amplitude of the unit’s motion is 0.500 m. If the s
> A flute is designed so that it plays a frequency of 261.6 Hz, middle C, when all the holes are covered and the temperature is 20.0°C. (a) Consider the flute to be a pipe open at both ends and find its length, assuming the middle-C frequency is the fundam
> On a workday, the average decibel level of a busy street is 70.0 dB, with 100 cars passing a given point every minute. If the number of cars is reduced to 25 every minute on a weekend, what is the decibel level of the street?
> The evaporation of perspiration is the primary mechanism for cooling the human body. Estimate the amount of water you will lose when you bake in the sun on the beach for an hour. Use a value of 1000 W/m2 for the intensity of sunlight and note that the en
> Two ships are moving along a line due east (Fig. P14.76). The trailing vessel has a speed relative to a land-based observation point of v1 = 64.0 km/h, and the leading ship has a speed of v2 = 45.0 km/h relative to that point. The two ships are in a regi
> A stereo speaker is placed between two observers who are 36.0 m apart, along the line connecting them. If one observer records an intensity level of 60.0 dB, and the other records an intensity level of 80.0 dB, how far is the speaker from each observer?
> A student uses an audio oscillator of adjustable frequency to measure the depth of a water well. He reports hearing two successive resonances at 52.0 Hz and 60.0 Hz. How deep is the well?
> An interstate highway has been built through a neighborhood in a city. In the afternoon, the sound level in an apartment in the neighborhood is 80.0 dB as 100 cars pass outside the window every minute. Late at night, the traffic flow is only five cars pe
> Two small loudspeakers emit sound waves of different frequencies equally in all directions. Speaker A has an output of 1.00 mW, and speaker B has an output of 1.50 mW. Determine the sound level (in decibels) at point C in Figure P14.72 assuming (a) Only
> Assume a 150. - W loudspeaker broadcasts sound equally in all directions and produces sound with a level of 103 dB at a distance of 1.60 m from its center. (a) Find its sound power output. If a salesperson claims the speaker is rated at 150. W, he is ref
> A typical sound level for a buzzing mosquito is 40 dB, and that of a vacuum cleaner is approximately 70 dB. Approximately how many buzzing mosquitoes will produce a sound intensity equal to that of a vacuum cleaner?
> Calculate the reflected percentage of an ultrasound wave passing from human muscle into bone. Muscle has a typical density of 1.06 x 103 kg/m3 and bone has a typical density of 1.90 x 103 kg/m3.
> Some studies suggest that the upper frequency limit of hearing is determined by the diameter of the eardrum. The wavelength of the sound wave and the diameter of the eardrum are approximately equal at this upper limit. If the relationship holds exactly,
> If a human ear canal can be thought of as resembling an organ pipe, closed at one end, that resonates at a fundamental frequency of 3.0 x 103 Hz, what is the length of the canal? Use a normal body temperature of 37.0°C for your determination of the speed
> The surface of the Sun has a temperature of about 5800 K. The radius of the Sun is 6.96 x 108 m. Calculate the total energy radiated by the Sun each second. Assume the emissivity of the Sun is 0.986.
> A student holds a tuning fork oscillating at 256 Hz. He walks toward a wall at a constant speed of 1.33 m/s. (a) What beat frequency does he observe between the tuning fork and its echo? (b) How fast must he walk away from the wall to observe a beat freq
> Two pipes of equal length are each open at one end. Each has a fundamental frequency of 480. Hz at 300. K. In one pipe the air temperature is increased to 305 K. If the two pipes are sounded together, what beat frequency results?
> Two train whistles have identical frequencies of 1.80 x 102 Hz. When one train is at rest in the station and the other is moving nearby, a commuter standing on the station platform hears beats with a frequency of 2.00 beats/s when the whistles operate to
> The G string on a violin has a fundamental frequency of 196 Hz. It is 30.0 cm long and has a mass of 0.500 g. While this string is sounding, a nearby violinist effectively shortens the G string on her identical violin (by sliding her finger down the stri
> In certain ranges of a piano keyboard, more than one string is tuned to the same note to provide extra loudness. For example, the note at 1.10 x 102 Hz has two strings at this frequency. If one string slips from its normal tension of 6.00 x 102 N to 5.40
> Two nearby trumpets are sounded together and a beat frequency of 2 Hz is heard. If one of the trumpets sounds at a frequency of 525 Hz, what are the two possible frequencies of the other trumpet?
> A guitarist sounds a tuner at 196 Hz while his guitar sounds a frequency of 199 Hz. Find the beat frequency.
> Two adjacent natural frequencies of an organ pipe are found to be 550. Hz and 650. Hz. (a) Calculate the fundamental frequency of the pipe. (b) Is the pipe open at both ends or open at only one end? (c) What is the length of the pipe?
> The range of human hearing extends from approximately 20 Hz to 20000 Hz. Find the wavelengths of these extremes at a temperature of 27°C.
> A pipe open at both ends has a fundamental frequency of 3.00 x 102 Hz when the temperature is 0°C. (a) What is the length of the pipe? (b) What is the fundamental frequency at a temperature of 30.0°C?
> For bacteriological testing of water supplies and in medical clinics, samples must routinely be incubated for 24 h at 37°C. A standard constant - temperature bath with electric heating and thermostatic control is not suitable in developing nations withou
> A tunnel under a river is 2.00 km long. (a) At what frequencies can the air in the tunnel resonate? (b) Explain whether it would be good to make a rule against blowing your car horn when you are in the tunnel.
> The human ear canal is about 2.8 cm long. If it is regarded as a tube that is open at one end and closed at the eardrum, what is the fundamental frequency around which we would expect hearing to be most sensitive?
> The overall length of a piccolo is 32.0 cm. The resonating air column vibrates as in a pipe that is open at both ends. (a) Find the frequency of the lowest note a piccolo can play. (b) Opening holes in the side effectively shortens the length of the reso
> The windpipe of a typical whooping crane is about 5.0 ft. long. What is the lowest resonant frequency of this pipe, assuming it is closed at one end? Assume a temperature of 37°C.
> A pipe has a length of 0.750 m and is open at both ends. (a) Calculate the two lowest harmonics of the pipe. (b) Calculate the two lowest harmonics after one end of the pipe is closed.
> A car’s 30.0 - kg front tire is suspended by a spring with spring constant k = 1.00 × 105 N/m. At what speed is the car moving if washboard bumps on the road every 0.750 m drive the tire into a resonant oscillation?
> Standing - wave vibrations are set up in a crystal goblet with four nodes and four antinodes equally spaced around the 20.0 - cm circumference of its rim. If transverse waves move around the glass at 900. m/s, an opera singer would have to produce a high
> A 60.00 - cm guitar string under a tension of 50.000 N has a mass per unit length of 0.10000 g/cm. What is the highest resonant frequency that can be heard by a person capable of hearing frequencies up to 20000 Hz?
> In the arrangement shown in Figure P14.50, an object of mass m = 5.0 kg hangs from a cord around a light pulley. The length of the cord between point P and the pulley is L = 2.0 m. (a) When the vibrator is set to a frequency of 150 Hz, a standing wave wi
> A group of hikers hears an echo 3.00 s after shouting. How far away is the mountain that reflected the sound wave?
> A “solar cooker” consists of a curved reflecting mirror that focuses sunlight onto the object to be heated (Fig. P11.69). The solar power per unit area reaching the Earth at the location of a 0.50 - m - diameter solar
> An electron is released from rest in a uniform electric field. Determine whether the following quantities increase, decrease, or remain unchanged as the electron moves. Indicate your answers with I (increase), D (decrease), or U (unchanged), respectively
> A 12.0 - kg object hangs in equilibrium from a string with total length of L = 5.00 m and linear mass density of μ = 0.00100 kg/m. The string is wrapped around two light, frictionless pulleys that are separated by the distance d = 2.00 m (F
> A standing wave is set up in a string of variable length and tension by a vibrator of variable frequency. Both ends of the string are fixed. When the vibrator has a frequency fA, in a string of length LA and under tension TA, nA antinodes are set up in t
> A steel wire with mass 25.0 g and length 1.35 m is strung on a bass so that the distance from the nut to the bridge is 1.10 m. (a) Compute the linear density of the string. (b) What velocity wave on the string will produce the desired fundamental frequen
> A distance of 5.00 cm is measured between two adjacent nodes of a standing wave on a 20.0 - cm - long string. (a) In which harmonic number n is the string vibrating? (b) Find the frequency of this harmonic if the string has a mass of 1.75 x 10–2 kg and a
> A stretched string of length L is observed to vibrate in five equal segments when driven by a 630.-Hz oscillator. What oscillator frequency will set up a standing wave so that the string vibrates in three segments?
> How far, and in what direction, should a cellist move her finger to adjust a string’s tone from an out - of - tune 449 Hz to an in - tune 440 Hz? The string is 68.0 cm long, and the finger is 20.0 cm from the nut for the 449-Hz tone.
