In a perfect conductor, the conductivity is infinite, so E = 0 (Eq. 7.3), and any net charge resides on the surface (just as it does for an imperfect conductor, in electrostatics). (a) Show that the...

In Figure a conducting rectangular solid of dimensions dx = 5.00 m, d y = 3.00 m, and dz = 2.00 m moves at constant velocity v = (20.0 m/s) i through a uniform magnetic field B = (30.0mT) j. What is...

Let A = 2xyax + xzay - yaz. Evaluate A dv over: (a) A rectangular region 0 < x < 2, 0 < y < 2, 0 < z < 2 (b) A spherical region r < 4

An astronaut on a strange planet finds that she can jump a maximum horizontal distance of 15.0 m if her initial speed is 3.00 m/s. What is the free-fall acceleration on the planet?

Two smooth coins A and B, each having the same mass, slide on a smooth surface with the motion shown, determine the speed of each coin after collision if they move off along the dashed paths. Hint:...

The filament of an incandescent lamp has a 150-2 resistance and carries a direct current of 1.00 A. The filament is 8.00 cm long and 0.900 mm in radius. (a) Calculate the Poynting vector at the...

A typical laboratory diffraction grating bas 5.00 x 103 lines/cm and these lines are contained in a 3.50-cm width of grating. (a) What is the chromatic resolving power of such a grating in the first...

The distance between a carbon atom (mC = 12 u) and an oxygen atom (mO = 16 u) in the CO molecule is 1.13 X 10-10 m. How far from the carbon atom is the center of mass of the molecule?

A 9.00-kg object starting from rest falls through a viscous medium and experiences a resistive force R = bv, where v is the velocity of the object. If the object reaches one-half its terminal speed...

A 10.0-μF capacitor is charged to 15.0 V. It is next connected in series with an uncharged 5.00-%F capacitor. The series combination is finally connected across a 50.0-V battery, as diagrammed in...

An object's velocity is measured to be vx (t) = a - pt', where a = 4.00 m/s and p = 2.00 m/S3. At t = 0 the object is at x = O. (a) Calculate the object's position and acceleration as functions of...

Chin-Ups while doing a chin-up, a man lifts his body 0.40 m. (a) How much work must the man do per kilogram of body mass? (b) The muscles involved in doing a chin-up can generate about 70 I of work...

How far out on the diving board (Fig 9-42) would a 58-kg diver have to be to exert a torque of 1100 m N on the board, relative to the left (A) support post?

The current in an electromagnet connected to a 240-V line is 17.5 A. At what rate must cooling water pass over the coils if the water temperature is to rise by no more than 7.50Co?

An outfielder throws a baseball with an initial speed of 81.8 mi/h. Just before an infielder catches the ball at the same level, the ball's speed is 110 ft/s. In foot-pounds, by how much is the...

Suppose that the sound level of a conversation is initially at an angry 70 dB and then drops to a soothing 50 dB. Assuming that the frequency of the sound is 500 Hz, determine the (a) Initial and (b)...

Adiabatic wind the normal airflow over the Rocky Mountains is west to east. The air loses much of its moisture content and is chilled as it climbs the western side of the mountains. When it descends...

(a) A brass plug is to be placed in a ring made of iron. At 20oC, the diameter of the plug is 8.753cm and that of the inside of the ring is 8.743cm. They must both be brought to what common...

A 200-m-wide river has a uniform flow speed of 1.1 m/s through a jungle and toward the east. An explorer wishes to leave a small clearing on the south bank and cross the river in a powerboat that...

The motor at C pulls in the cable with an acceleration ac= (3t)2 m/s, where t is in seconds. The motor at D draws in its cable at aD = 5m/s2. If both motors start at the same instant from rest when d...

An airplane is flying with a velocity of 90.0 m/s at an angle of 23.0o above the horizontal. When the plane is 114 m directly above a dog that is standing on level ground, a suitcase drops out of the...

As shown in Fig. 10.46, a string is wrapped several times around the rim of a small hoop with radius 0.0800 m and mass 0.180 kg. The free end of the string is pulled upward in just the right way so...

(a) For the Otto cycle shown in Fig. 20.6, calculate the changes in entropy of the gas in each of the constant-volume processes b c and d a in terms of the temperatures Ta Tb Tc and Td and the number...

A ship, carrying fresh water to a desert island in the Caribbean, has a horizontal cross-sectional area of 2650m2 at the waterline. When unloaded, the ship rises 8.50m higher in the sea. How much...

A highway overpass was observed to resonate as one full loop (½ λ) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of...

A particle of mass m is constrained to move on the surface of a sphere of radius R by ab applied force F (, ). Write the equation of motion.

Spherical mirrors Object O stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance p, (centimeters), the type of mirror, and then the...

In Figure observer S detects two flashes of light. A big flash occurs at x1 = 1200 m and, 5.00s later, a small flash occurs at x2 = 480 m. As detected by observer S', the two flashes occur at a...

Pyramid Builders. Ancient pyramid builders are balancing a uniform rectangular slab of stone tipped at an angle 6 above the horizontal using a rope (Fig. 11.61). The rope is held by five workers who...

An aircraft engine takes in 9000 J of heat and discards 6400 J each cycle. (a) What is the mechanical work output of the engine during one cycle? (b) What is the thermal efficiency of the engine?

A beam of light is emitted in a pool of water from a depth of 62.0cm. Where must it strike that air-water interface, relative to the spot directly above it, in order that the light does not exit the...

Vectors d1 is in the negative direction of a y axis, and vector d2 is in the positive direction of an x axis. What is the direction of? (a) d2/4 and (b) d1/( 4)? What are the magnitudes of products?...

A bola consists of three massive, identical spheres connected to a common point by identical lengths of sturdy string (Figure). To launch this native South American weapon, you hold one of the...

In Figure, three 5.00 kg spheres are located at distances d1 = 0.300 m and d2 = 0.400 m. What are the(a) Magnitude and(b) Direction (relative to the positive direction of the x axis) of the net...

In Figure, light enters a 90? triangular prism at point P with incident angle , and then some of it refracts at point Q with an angle of refraction of 90?. (a) What is the index of refraction of the...

A liquid with a coefficient of volume expansion ' just fills a spherical shell of volume Vi at a temperature of Ti (see Fig. P19.47). The shell is made of a material that has an average coefficient...

Four railroad cars, each of mass 2.50 X 104 kg, are coupled together and coasting along horizontal tracks at speed vi toward the south. A very strong but foolish movie actor, riding on the second...

An electric teakettle has a multiposition switch and two heating coils. When only one of the coils is switched on, the well-insulated kettle brings a full pot of water to a boil over the time...

A steel wire 2.0 mm in diameter stretches by 0.030% when a mass is suspended from it. How large is the mass?

Dry air will break down and generate a spark if the electric field exceeds about 3 X 106N/C. How much charge could be packed onto a green pea (diameter 0.75cm) before the pea spontaneously discharges?

A solar cooker, really a concave mirror pointed at the Sun, focuses the Suns rays 18.0 cm in front of the mirror. What is the radius of the spherical surface from which mirror was made?

A layer of benzene (n = 1.50) 2.60 cm deep floats on water (n = 1.33) that is 6.50 cm deep. What is the apparent distance from the upper benzene surface to the bottom of the water layer when it is...

A small loop of wire (radius a) lies a distance z above the center of a large loop (radius b), as shown in Fig. 7.36. The planes of the two loops are parallel, and perpendicular to the common axis....

(a) What will an object weigh on the Moon's surface if it weights 100 N on Earth's surface? (b) How many Earth radii must this same object be from the center of Earth if it is to weight the same as...

How much work must be done to increase the speed of an electron? (a) From 0.18c to 0.19c and (b) From 0.98c to 0.99c? Note that the speed increase is 0.01c in both cases.

Cancer cells are more vulnerable to x and gamma radiation than are healthy cells. In the past, the standard source for radiation therapy was radioactive 60Co, which decays, with a half-life of 5.27...

To an order of magnitude, how many helium-filled toy balloons would be required to lift you? Because helium is an irreplaceable resource, develop a theoretical answer rather than an experimental...

Consider a point course of light. How would the intensity of light vary with distance from the source according to? (a) Wave theory (b) Particle (photon) theory? Would this help to distinguish the...

A 60.0-kg person is standing at rest on level ground. How fast would she have to run to (a) Double her total energy and (b) Increase her total energy by a factor of 10?

Consider an infinite parallel-plate capacitor, with the lower plate (at z = ?? d/2) carrying the charge density -a, and the upper plate (at z = +d/2) carrying the charge density (a) Determine all...

Certain rifles can fire a bullet with a speed of 965 m/s just as it leaves the muzzle (this speed is called the muzzle velocity). If the muzzle is 70.0 cm long and if the bullet is accelerated...

An inductor used in a dc power supply has an inductance of 12.0 H and a resistance of 180 O. It carries a current of 0.300 A. (a) What is the energy stored in the magnetic field? (b) At what rate is...

A charged parallel-plate capacitor (with uniform electric field E = E z) is placed in a uniform magnetic field B = B x, as shown in Fig. 8.6. 3 (a) Find the electromagnetic momentum in the space...

A projectile is fired horizontally from a gun that is 45.0 m above flat ground, emerging from the gun with a speed of 250 m/s. (a) How long does the projectile remain in the air? (b) At what...

A yo-yo-shaped device mounted on a horizontal frictionless axis is used to lift a 30 kg box as shown in Figure. The outer radius R of the device is 0.50 m, and the radius r of the hub is 0.20 m. When...

The volume of an ideal gas is adiabatically reduced from 200 L to 74.3 L. The initial pressure and temperature are 1.00 atm and 300 K. The final pressure is 4.00 atm. (a) Is the gas monatomic,...

A small circular hole 6.00 nun in diameter is cut in the side of a large water tank, 14.0 m below the water level in the tank. The top of the tank is open to the air. Find (a) The speed of efflux of...

Consider the circuit shown in Fig. The current through the 6.00-Ω resistor is 4.00 A, in the direction shown. What are the currents through the 25.0-Ω and 20.0-Ω resistors? 4.00 A...

A particle of charge + 3.00 x 10-6 C is 12.0 cm distant from a second particle of charge 1.50 x 10-6 g. Calculate the magnitude of the electrostatic force between the particles.

An infinitely long straight wire carrying a current I1 is partially surrounded by a loop as shown in Figure P30.65. The loop has a length L, radius R, and carries a current I2. The axis of the loop...

A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110 m3 of air at a pressure of 3.40 atm. The piston is slowly pulled out...

Inductance of a Solenoid. A long, straight solenoid has N tums, uniform cross-sectional area A, and length I. Show that the inductance of this solenoid is given by the equation L = oAN2/l. Assume...

A dielectric cube of side a, centered at the origin, carries a "frozen-in" polarization P = kr, where k is a constant. Find all the bound charges, and check that they add up to zero.

A block with a weight of 3.0 N is at rest on a horizontal surface. A 1.0 N upward force is applied to the block by means of an attached vertical string. What are the (a) Magnitude and (b) Direction...

The 5-lb ball, attached to the cord, is struck by the boy. Determine the smallest speed he must impart to the ball so that tit will swing around in a vertical circle, without causing the cord to...

The charge per unit length on a long, straight filament is '90.0 %C/m. Find the electric field (a) 10.0 cm, (b) 20.0 cm, and (c) 100 cm from the filament, where distances are measured perpendicular...

Two plastic spheres, each carrying charge uniformly distributed throughout its interior, are initially placed in contact and then released. One sphere is 60.0 cm in diameter, has mass 50.0 g and...

If you stand on a bathroom scale, the spring inside the scale compresses 0.60 mm, and it tells you your weight is 710 N. Now if you jump on the scale from a height of 1.0m, what does the scale read...

A thin uniform donut, carrying charge Q and mass M, rotates about its axis as shown in Fig. 5.64. (a) Find the ratio of its magnetic dipole moment to its angular momentum. This is called the...

The consumption of natural gas by a company satisfies the empirical equation V = 1.50t + 0.008 00t 2, where V is the volume in millions of cubic feet and t the time in months. Express this equation...

Consider a long cylindrical charge distribution of radius R with a uniform charge density 1. Find the electric field at distance r from the axis where r < R.

An FM radio station has a frequency of 107.9 MHz and uses two identical antennas mounted at the same elevation, 12.0 m apart. The antennas radiate in phase. The resulting radiation pattern has a...

The p-V diagram in Figure shows two paths along which a sample of gas can be taken from state a to state 4 where Vb = 3.0V1. Path 1 requires that energy equal to 5.0p1V1 be transferred to the gas as...

Fresh water flows horizontally from pipe section 1 of cross-sectional area Al into pipe section 2 of cross-sectional area A2. Figure gives a plot of the pressure difference p2 ?? p1 versus the...

A thin-walled metal spherical shell has radius 25.0 cm and charge 2.00 x 10-7 g. Find E for a point (a) Inside the shell, (b) Just outside it, and (c) 3.00 m from the center

Hovering over the pit of hell, the devil observes that as a student falls past (with terminal velocity), the frequency of his scream decreases from 842 to 820 Hz. (a) Find the speed of descent of the...

A propped cantilever beam of length 2L with support at B is loaded by a uniformly distributed load with intensity q. Use the method of superposition to solve for all reactions. Also draw shear-force...

Calculate the binding energy per nucleon for a 14/7N nucleus.

A certain force gives an object of mass m1 an acceleration of 12.0 m/s2 and an object of mass wt2 ?rr acceleration of 3.30 m/s2. What acceleration would the force give to an object of mass? (a) m2 ...

In Figure an arrangement known as Helmholtz coils consists of two circular coaxial coils, each of N turns and radius R, separated by distance s. The two coils carry equal currents i in the same...

A helium-neon laser emits red light at wavelength = 633 nm in a beam of diameter 3.5 mm and at an energy-emission rate of 5.0mW. A detector in the beam's path totally absorbs the beam. At what rate...

Fill in the blank with the most reasonable metric unit (m3, L, mL, m2, cm2, ha). 1. Go to the store and buy 4 _____ of root beer for the party. 2. I drank 200 _____ of orange juice for breakfast. 3....

Beam ABC is fixed at support A and rests (at point B) upon the midpoint of beam DE (see the first part of the figure). Thus, beam ABC may be represented as a propped cantilever beam with an overhang...

A ball is tied to one end of a string. The other end of the string is held fixed. The ball is set moving around a vertical circle without friction, and with speed at the top of the circle, as in...

(a) Show that the function y(x, t) = x2 + v2t2 is a solution to the wave equation. (b) Show that the function in part (a) can be written as f (x # vt) # g(x " vt), and determine the functional forms...

One arm of a U-shaped tube (open at both ends) contains water, and the other alcohol. If the two fluids meet at exactly the bottom of the U, and alcohol is at a height of 18.0 cm, at what height will...

A particle of mass m slides down and inclined plane under the influence of gravity. If the motion is resisted by a force ∫ = kmv2, show that the time required to move a distance d after starting...

Observing Planets beyond Our Solar System NASA is considering a project called Planet Imager that would give astronomers the ability to see details on planets orbiting other stars. Using the same...

A ballerina begins a tour jete, (Figure) with angular speed ai and a rotational inertia consisting of two parts: Ileg = 1.44 kg m2 for her leg extended outward at angle = 90.0 to her body and Itrunk...

The Fermi energy of aluminum is 11.6 eV its density and molar mass are 2.70 g/cm3 and 27.0 g/mol, respectively. From these data, determine the number of conduction electrons per atom.

A long, straight wire carries a current that is given by I = Imax sin (wt + 2) and lies in the plane of a rectangular coil of N turns of wire, as shown in Figure P31.9. The quantities Imax, w, and...

The earth does not have a uniform density; it is most dense at its center and least dense at its surface. An approximation of its density is p(r) = A - Br, where A = 12,700kg/rri' and B = 1.50 X 10...

In Fig 12-16, if the frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer together?

Figure is an overhead view of a thin uniform rod of length 0.600 m and mass M rotating horizontally at 80.0 rad/s counterclockwise about an axis through its center. A particle of mass M/3.00 and...

The worlds biggest locomotive is the MK5000C, a behemoth of mass 160 metric tons driven by the most powerful engine ever used for rail transportation, a Caterpillar diesel capable of 5 000 hp. Such a...

A van accelerates down a hill (Fig. P5.69), going from rest to 30.0 m/s in 6.00 s. During the acceleration, a toy (m =0.100 kg) hangs by a string from the vans ceiling. The acceleration is such that...

Combining Standing Waves. A guitar string of length L is plucked in such a way that the total wave produced is the sum of the fundamental and the second harmonic. That is, the standing wave is given...

A charge of 6.00mC is placed at each corner of a square 0.100m on a side. Determine the magnitude and direction of the force on each charge.

Focus of the Eye. The cornea of the eye has a radius of curvature of approximately 0.50 cm, and the aqueous humor behind it has an index of refraction of 1.35. The thickness of the cornea itself is...

An Object at an Angle A 16.0-cm-long pencil is placed at a 45.0? angle, with its center 15.0 cm above the optic axis and 45.0 cm from a lens with a 20.0-cm focal length as shown in Fig. 34.65. (Note...