Question: A nonuniform, but spherically symmetric,

> A 15.0-kg block of ice at 0.00C melts to liquid water at 0.00C inside a large room at 20.00C. Treat the ice and the room as an isolated system, and assume that the room is large enough for its temperature change to be ignored. (a). Is the melting of the

> You decide to take a nice hot bath but discover that your thoughtless roommate has used up most of the hot water. You fill the tub with 195 kg of 30.00C water and attempt to warm it further by pouring in 5.00 kg of boiling water from the stove. (a). Is t

> A 4.50-kg block of ice at 0.00°C falls into the ocean and melts. The average temperature of the ocean is 3.50°C, including all the deep water. By how much does the change of this ice to water at 3.50°C alter the entropy of the world? Does the entropy inc

> A Carnot refrigerator is operated between two heat reservoirs at temperatures of 320 K and 270 K. (a). If in each cycle the refrigerator receives 415 J of heat energy from the reservoir at 270 K, how many joules of heat energy does it deliver to the res

> A certain brand of freezer is advertised to use 730 kW ∙ h of energy per year. (a). Assuming the freezer operates for 5 hours each day, how much power does it require while operating? (b). If the freezer keeps its interior at -5.00C in a 20.00C room, w

> A Carnot engine has an efficiency of 66% and performs 2.5 × 104 J of work in each cycle. (a). How much heat does the engine extract from its heat source in each cycle? (b). Suppose the engine exhausts heat at room temperature (20.00C). What is the temp

> (a).In a certain region of space, the volume charge density

> An ice-making machine operates in a Carnot cycle. It takes heat from water at 0.00C and rejects heat to a room at 24.00C. Suppose that 85.0 kg of water at 0.00C are converted to ice at 0.00C. (a). How much heat is discharged into the room? (b). How muc

> A refrigerator has a coefficient of performance of 2.25, runs on an input of 135 W of electrical power, and keeps its inside compartment at 5°C. If you put a dozen 1.0-L plastic bottles of water at 31°C into this refrigerator, how long will it take for t

> A freezer has a coefficient of performance of 2.40. The freezer is to convert 1.80 kg of water at 25.00C to 1.80 kg of ice at -5.00C in one hour. (a). What amount of heat must be removed from the water at 25.00C to convert it to ice at -5.00C? (b). How

> A refrigerator has a coefficient of performance of 2.10. In each cycle it absorbs 3.10 × 104 J of heat from the cold reservoir. (a). How much mechanical energy is required each cycle to operate the refrigerator? (b). During each cycle, how much heat is

> The coefficient of performance K = H/P is a dimensionless quantity. Its value is independent of the units used for H and P, as long as the same units, such as watts, are used for both quantities. However, it is common practice to express H in Btu/h and P

> The Otto-cycle engine in a Mercedes-Benz SLK230 has a compression ratio of 8.8. (a). What is the ideal efficiency of the engine? Use γ = 1.40. (b). The engine in a Dodge Viper GT2 has a slightly higher compression ratio of 9.6. How much increase in the

> (a). Calculate the theoretical efficiency for an Otto-cycle engine with γ = 1.40 and r = 9.50. (b). If this engine takes in 10,000 J of heat from burning its fuel, how much heat does it discard to the outside air?

> A solid conducting sphere with radius R that carries positive charge Q is concentric with a very thin insulating shell of radius 2R that also carries charge Q. The charge Q is distributed uniformly over the insulating shell. (a). Find the electric field

> A solid conducting sphere carrying charge q has radius a. It is inside a concentric hollow conducting sphere with inner radius b and outer radius c. The hollow sphere has no net charge. (a). Derive expressions for the electric field magnitude in terms o

> A very long, solid cylinder with radius R has positive charge uniformly distributed throughout it, with charge per unit volume

> When two point charges of equal mass and charge are released on a frictionless table, each has an initial acceleration (magnitude) a0. If instead you keep one fixed and release the other one, what will be its initial acceleration: a0, 2a0, or a0/2? Expla

> A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It carries charge per unit length +

> A long coaxial cable consists of an inner cylindrical conductor with radius a and an outer coaxial cylinder with inner radius b and outer radius c. The outer cylinder is mounted on insulating supports and has no net charge. The inner cylinder has a unifo

> A long line carrying a uniform linear charge density +50.0 µC/m runs parallel to and 10.0 cm from the surface of a large, flat plastic sheet that has a uniform surface charge density of -100 µC/m2 on one side. Find the location of all points where an a p

> The electric field

> Two particles having charges q1 = 0.500 nC and q2 = 8.00 nC are separated by a distance of 1.20 m. At what point along the line connecting the two charges is the total electric field due to the two charges equal to zero?

> Point charge q1 = -6.00 × 10-6 C is on the x-axis at x = -0.200 m. Point charge q2 is on the x-axis at x = +0.400 m. Point charge q3 = +3.00 × 10-6 C is at the origin. What is q2 (magnitude and sign) (a). if the net force on q3 is 6.00 N in the +x-direc

> A small 12.3-g plastic ball is tied to a very light 28.6-cm string that is attached to the vertical wall of a room (Fig. P21.65). A uniform horizontal electric field exists in this room. When the ball has been given an excess charge of -1.11 Â&micr

> Two identical spheres are each attached to silk threads of length L = 0.500 m and hung from a common point (Fig. P21.62). Each sphere has mass m = 8.00 g. The radius of each sphere is very small compared to the distance between the spheres, so they may b

> Two small spheres with mass m = 15.0 g are hung by silk threads of length L = 1.20 m from a common point (Fig. P21.62). When the spheres are given equal quantities of negative charge, so that q1 = q2 = q, each thread hangs at

> The electric field

> Explain this statement: “In a static situation, the electric field at the surface of a conductor can have no component parallel to the surface because this would violate the condition that the charges on the surface are at rest.” Would this statement be

> A very small object with mass 8.20 × 10-9 kg and positive charge 6.50 × 10-9 C is projected directly toward a very large insulating sheet of positive charge that has uniform surface charge density 5.90 × 10-8 C/m2. The object is initially 0.400 m from th

> Two charges are placed on the x-axis: one, of 2.50 µC, at the origin and the other, of -3.50 µC, at x = 0.600 m (Fig. P21.60). Find the position on the x-axis where the net force on a small charge +q would be zero. Fig. P21.60:

> A person who has skin of surface area 1.85 m2 and temperature 30.0°C is resting in an insulated room where the ambient air temperature is 20.0°C. In this state, a person gets rid of excess heat by radiation. By how much does the person change the entropy

> A heat engine operates using the cycle shown in Fig. P20.41. The working substance is 2.00 mol of helium gas, which reaches a maximum temperature of 3270C. Assume the helium can be treated as an ideal gas. Process bc is isothermal. Fig. P20.41: The pr

> As a budding mechanical engineer, you are called upon to design a Carnot engine that has 2.00 mol of a monatomic ideal gas as its working substance and operates from a high temperature reservoir at 5000C. The engine is to lift a 15.0-kg weight 2.00 m per

> You build a heat engine that takes 1.00 mol of an ideal diatomic gas through the cycle shown in Fig. P20.39. Fig. P20.39: (a). Show that process ab is an isothermal compression. (b). During which process(es) of the cycle is heat absorbed by the gas?

> What is the thermal efficiency of an engine that operates by taking n moles of diatomic ideal gas through the cycle 1→ 2→ 3→ 4→ 1 shown in Fig. P20.38? Fig. P20.38: P 2 3 2po P

> Digesting fat produces 9.3 food calories per gram of fat, and typically 80% of this energy goes to heat when metabolized. (One food calorie is 1000 calories and therefore equals 4186 J.) The body then moves all this heat to the surface by a combination o

> A heat engine takes 0.350 mol of a diatomic ideal gas around the cycle shown in the pV-diagram of Fig. P20.36. Process 1→ 2 is at constant volume, process 2→ 3 is adiabatic, and process 3→ 1 is at a c

> A certain heat engine operating on a Carnot cycle absorbs 410 J of heat per cycle at its hot reservoir at 135°C and has a thermal efficiency of 22.0%. (a). How much work does this engine do per cycle? (b). How much heat does the engine waste each cycle

> A solid conductor has a cavity in its interior. Would the presence of a point charge inside the cavity affect the electric field outside the conductor? Why or why not? Would the presence of a point charge outside the conductor affect the electric field i

> An average sleeping person metabolizes at a rate of about 80 W by digesting food or burning fat. Typically, 20% of this energy goes into bodily functions, such as cell repair, pumping blood, and other uses of mechanical energy, while the rest goes to hea

> A small sphere with mass 4.00 × 10-6 kg and charge 5.00 × 10-8 C hangs from a thread near a very large, charged insulating sheet (Fig. P22.33). The charge density on the surface of the sheet is uniform and equal to -2.50 &Atilde

> You are designing a Carnot engine that has 2 mol of CO2 as its working substance; the gas may be treated as ideal. The gas is to have a maximum temperature of 527sC and a maximum pressure of 5.00 atm. With a heat input of 400 J per cycle, you want 300 J

> At time t = 0 a proton is a distance of 0.360 m from a very large insulating sheet of charge and is moving parallel to the sheet with speed 9.70 × 102 m/s. The sheet has uniform surface charge density 2.34 × 10-9 C/m2. What is the speed of the proton at

> In one experiment the electric field is measured for points at distances r from a uniform line of charge that has charge per unit length λ and length l, where l >> r. In a second experiment the electric field is measured for points at distances r from th

> (a). An insulating sphere with radius a has a uniform charge density

> A nonuniform, but spherically symmetric, distribution of charge has a charge density

> Repeat Problem 22.54, but now let the charge density of the slab be given by

> A slab of insulating material has thickness 2d and is oriented so that its faces are parallel to the yz-plane and given by the planes x = d and x = -d. The y- and z-dimensions of the slab are very large compared to d; treat them as essentially infinite.

> Because the charges on the electron and proton have the same absolute value, atoms are electrically neutral. Suppose that this is not precisely true, and the absolute value of the charge of the electron is less than the charge of the proton by 0.00100%.

> (a). How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere 30.0 cm in diameter to produce an electric field of magnitude 1390 N/C just outside the surface of the sphere? (b). What is the electric field a

> Using Thomson’s (outdated) model of the atom described in Problem 22.50, consider an atom consisting of two electrons, each of charge -e, embedded in a sphere of charge +2e and radius R. In equilibrium, each electron is a distance d fro

> Early in the 20th century, a leading model of the structure of the atom was that of English physicist J. J. Thomson (the discoverer of the electron). In Thomson’s model, an atom consisted of a sphere of positively charged material in wh

> An insulating hollow sphere has inner radius a and outer radius b. Within the insulating material the volume charge density is given by

> A solid conducting sphere with radius R carries a positive total charge Q. The sphere is surrounded by an insulating shell with inner radius R and outer radius 2R. The insulating shell has a uniform charge density

> Repeat Problem 22.45, but now let the outer shell have charge -2q. The inner shell still has charge +2q. Problem 22.45: A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell wit

> A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d (Fig. P22.45). The inner shell has total charge +2q, and the outer shell has charge +4

> A conducting spherical shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is -3Q, and it is insulated from its surroundings (Fig. P22.44). Fig. P22.44: (a). Derive expressio

> In a follow-up experiment, a charge of +40 pC was placed at the center of an artificial flower at the end of a 30-cmlong stem. Bees were observed to approach no closer than 15 cm from the center of this flower before they flew away. This observation sugg

> After one bee left a flower with a positive charge, that bee flew away and another bee with the same amount of positive charge flew close to the plant. Which diagram in Fig. P21.100 best represents the electric field lines between the bee and the flower?

> Two identical metal objects are mounted on insulating stands. Describe how you could place charges of opposite sign but exactly equal magnitude on the two objects.

> If you peel two strips of transparent tape off the same roll and immediately let them hang near each other, they will repel each other. If you then stick the sticky side of one to the shiny side of the other and rip them apart, they will attract each oth

> After a long day of driving you take a late-night swim in a motel swimming pool. When you go to your room, you realize that you have lost your room key in the pool. You borrow a powerful flashlight and walk around the pool, shining the light into it. The

> A series circuit has an impedance of 60.0 Ω and a power factor of 0.720 at 50.0 Hz. The source voltage lags the current. a. What circuit element, an inductor or a capacitor, should be placed in series with the circuit to raise its power factor? b. What

> A circular wire loop has a radius of 7.50 cm. A sinusoidal electromagnetic plane wave traveling in air passes through the loop, with the direction of the magnetic field of the wave perpendicular to the plane of the loop. The intensity of the wave at the

> A ray of light traveling in a block of glass (n = 1.52) is incident on the top surface at an angle of 57.2° with respect to the normal in the glass. If a layer of oil is placed on the top surface of the glass, the ray is totally reflected. What is the ma

> A source of sinusoidal electromagnetic waves radiates uniformly in all directions. At a distance of 10.0 m from this source, the amplitude of the electric field is measured to be 3.50 N/C. What is the electric-field amplitude 20.0 cm from the source?

> Two square reflectors, each 1.50 cm on a side and of mass 4.00 g, are located at opposite ends of a thin, extremely light, 1.00-m rod that can rotate without friction and in vacuum about an axle perpendicular to it through its center (Fig. P32.39). These

> When a solenoid is connected to a 48.0-V dc battery that has negligible internal resistance, the current in the solenoid is 5.50 A. When this solenoid is connected to an ac source that has voltage amplitude 48.0 V and angular frequency 20.0 rad/s, the cu

> A coworker of yours was making measurements of a large solenoid that is connected to an ac voltage source. Unfortunately, she left for vacation before she completed the analysis, and your boss has asked you to finish it. You are given a graph of 1/I2 ver

> A ray of light traveling in air is incident at angle θa on one face of a 90.0° prism made of glass. Part of the light refracts into the prism and strikes the opposite face at point A (Fig. P33.42). If the ray at A is at the critic

> A light ray in air strikes the right angle prism shown in Fig. P33.40. The prism angle at B is 30.0°. This ray consists of two different wavelengths. When it emerges at face AB, it has been split into two different rays that diverge from each

> The sun emits energy in the form of electromagnetic waves at a rate of 3.9 * 1026 W. This energy is produced by nuclear reactions deep in the sun’s interior. a. Find the intensity of electromagnetic radiation and the radiation pressure on an absorbing o

> A ray of light is incident in air on a block of a transparent solid whose index of refraction is n. If n = 1.38, what is the largest angle of incidence θa for which total internal reflection will occur at the vertical face (point A shown in

> A 400-Ω resistor and a 6.00-µF capacitor are connected in parallel to an ac generator that supplies an rms voltage of 180 V at an angular frequency of 360 rad/s. Use the results of Problem 31.54. Note that since there is no inductor in this circuit, the

> An L-R-C series circuit has R = 500 Ω, L = 2.00 H, C = 0.500 µF, and V = 100 V. a. For ω = 800 rad/s, calculate VR, VL, VC, and ɸ. Using a single set of axes, graph v, vR, vL, and vC as functions of time. Include two cycles of v on your graph. b. Repea

> A horizontal cylindrical tank 2.20 m in diameter is half full of water. The space above the water is filled with a pressurized gas of unknown refractive index. A small laser can move along the curved bottom of the water and aims a light beam toward the c

> When the sun is either rising or setting and appears to be just on the horizon, it is in fact below the horizon. The explanation for this seeming paradox is that light from the sun bends slightly when entering the earth’s atmosphere, as shown in

> Figure P31.48 shows a low-pass filter (see Problem 31.47); the output voltage is taken across the capacitor in an L-R-C series circuit. Derive an expression for Vout /Vs, the ratio of the output and source voltage amplitudes, as a function of the angular

> A thin layer of ice (n = 1.309) floats on the surface of water (n = 1.333) in a bucket. A ray of light from the bottom of the bucket travels upward through the water. a. What is the largest angle with respect to the normal that the ray can make at the i

> A laser beam shines along the surface of a block of transparent material (see Fig. E33.8). Half of the beam goes straight to a detector, while the other half travels through the block and then hits the detector. The time delay between the arrival of the

> NASA is giving serious consideration to the concept of solar sailing. A solar sail craft uses a large, low mass sail and the energy and momentum of sunlight for propulsion. a. Should the sail be absorbing or reflective? Why? b. The total power output o

> The GPS network consists of 24 satellites, each of which makes two orbits around the earth per day. Each satellite transmits a 50.0-W (or even less) sinusoidal electromagnetic signal at two frequencies, one of which is 1575.42 MHz. Assume that a satellit

> a. Compute the reactance of a 0.450-H inductor at frequencies of 60.0 Hz and 600 Hz. b. Compute the reactance of a 2.50-µF capacitor at the same frequencies. c. At what frequency is the reactance of a 0.450-H inductor equal to that of a 2.50-µF capacit

> A light beam is directed parallel to the axis of a hollow cylindrical tube. When the tube contains only air, the light takes 8.72 ns to travel the length of the tube, but when the tube is filled with a transparent jelly, the light takes 1.82 ns longer to

> Very short pulses of high-intensity laser beams are used to repair detached portions of the retina of the eye. The brief pulses of energy absorbed by the retina weld the detached portions back into place. In one such procedure, a laser beam has a wavelen

> As a physics lab instructor, you conduct an experiment on standing waves of microwaves, similar to the standing waves produced in a microwave oven. A transmitter emits microwaves of frequency f. The waves are reflected by a flat metal reflector, and a re

> The company where you work has obtained and stored five lasers in a supply room. You have been asked to determine the intensity of the electromagnetic radiation produced by each laser. The lasers are marked with specifications, but unfortunately differen

> In a certain experiment, a radio transmitter emits sinusoidal electromagnetic waves of frequency 110.0 MHz in opposite directions inside a narrow cavity with reflectors at both ends, causing a standing-wave pattern to occur. a. How far apart are the nod

> A thin beam of white light is directed at a flat sheet of silicate flint glass at an angle of 20.0° to the surface of the sheet. Due to dispersion in the glass, the beam is spread out in a spectrum as shown in Fig. P33.56. The refractive index

> A beam of unpolarized sunlight strikes the vertical plastic wall of a water tank at an unknown angle. Some of the light reflects from the wall and enters the water (Fig. P33.55). The refractive index of the plastic wall is 1.61. If the light that has bee

> Light is incident in air at an angle θa (Fig. P33.54) on the upper surface of a transparent plate, the surfaces of the plate being plane and parallel to each other. a. Prove that θa = θ′ a. b. S

> The incident angle θa shown in Fig. P33.53 is chosen so that the light passes symmetrically through the prism, which has refractive index n and apex angle A. a. Show that the angle of deviation δ (the angle between the initial

> Light is incident normally on the short face of a 30°-60°-90° prism (Fig. P33.50). A drop of liquid is placed on the hypotenuse of the prism. If the index of refraction of the prism is 1.56, find the maximum index that th

> A parallel beam of light in air makes an angle of 47.5° with the surface of a glass plate having a refractive index of 1.66. a. What is the angle between the reflected part of the beam and the surface of the glass? b. What is the angle between the refr

> The prism shown in Fig. P33.49 has a refractive index of 1.66, and the angles A are 25.0°. Two light rays m and n are parallel as they enter the prism. What is the angle between them after they emerge? Figure P33.49 m A A n

> a. At what angular frequency is the voltage amplitude across the resistor in an L-R-C series circuit at maximum value? b. At what angular frequency is the voltage amplitude across the inductor at maximum value? c. At what angular frequency is the volta

> In an L-R-C series circuit the current is given by i = I cos ωt. The voltage amplitudes for the resistor, inductor, and capacitor are VR, VL, and VC. a. Show that the instantaneous power into the resistor is PR = VRIcos2ωt = 1/2VRI(1+cos2ωt). What does

> You are given this table of data recorded for a circuit that has a resistor, an inductor with negligible resistance, and a capacitor, all in series with an ac voltage source: Here f is the frequency of the voltage source, Z is the impedance of the circ

> You sight along the rim of a glass with vertical sides so that the top rim is lined up with the opposite edge of the bottom (Fig. P33.45a). The glass is a thin-walled, hollow cylinder 16.0 cm high. The diameter of the top and bottom of the glass is 8.0 c