For the vectors shown in Fig. 3-32, determine (a) B 2A, (b) 2A 3B + 2C

When high-energy charged particles move through a transparent medium with a speed greater than the speed of light in that medium, a shock wave, or bow wave, of light is produced. This phenomenon is...

Equation (5.10) applies to the case where the initial velocity is zero. (a) Derive the corresponding equation for v,(t) when the falling object has an initial downward velocity with magnitude vo. (b)...

(a)A deuteron, 2/1H1 is the nucleus of a hydrogen isotope and consists of one proton and one neutron. The plasma of deuterons in a nuclear fusion reactor must be heated to about 300 million K. What...

The speed, v of an object is given by the equation v = At3 Bt, where t refers to time. What are the dimensions of A and B?

Monochromatic light falls on two very narrow slits 0.048mm apart. Successive fringes on a screen 5.00m away are 6.5cm apart near the center of the pattern. Determine the wavelength and frequency of...

In Figure the pulley has negligible mass, and both it and the inclined plane are frictionless. Block A has a mass of 1.0 kg, block B has a mass of 2.0 kg, and angle ? is 30o. If the blocks are...

An astronaut on the surface of the Moon fires a cannon to launch an experiment package, which leaves the barrel moving horizontally. (a) What must be the muzzle speed of the package so that it...

A resistor is constructed of a carbon rod that has a uniform cross-sectional area of 5.00 mm2. When a potential difference of 15.0 V is applied across the ends of the rod, the rod carries a current...

In mechanics, mass less strings are often assumed. Why is this not a good assumption when discussing waves on strings?

A point source emits 30.0 W of sound isotropically. A small microphone intercepts the sound in an area of 0.750 cm2, 200 m from the source. Calculate (a) The sound intensity there and (b) The power...

A laser beam with vacuum wavelength 632.8 nm is incident from air onto a block of Lucite as shown in Figure 35.10b. The line of sight of the photograph is perpendicular to the plane in which the...

Figure shows a uniform square plate of edge length 6d = 6.0 m from which a square piece of edge length 2d has been removed. What are? (a) The x coordinate and (b) The y coordinates of the center of...

In Figure sound with a 40.0 cm wavelength travels rightward from a source and through a tube that consists of a straight portion and a half-circle. Part of the sound wave travels through the...

A rocket that is in deep space and initially at rest relative to an inertial reference frame has a mass of 2.55 x 105 kg, of which 1.81 x 105 kg is fuel. The rocket engine is then fired for 250 s...

Light of wavelength 624 nm is incident perpendicularly on a soap film (n = 1.33) suspended in air. What ate the (a) Least and (b) Second least thicknesses of the film for which the reflections from...

Long flights at mid latitudes in the Northern Hemisphere encounter the jet stream, &r eastward airflow that can affect a plane's speed relative to Earth's surface, if a pilot maintains a certain...

Lightning strikes a dielectric sphere of radius 20 mm for which r = 2.5, = 5 X 106 mhos/m and deposits uniformly a charge of 10C. Determine the initial charge density and the charge density 2s later.

The determined coyote is out once more in pursuit of the elusive roadrunner. The coyote wears a pair of Acme jet powered roller skates, which provide a constant horizontal acceleration of 15.0 m/s2...

A projectile is thrown from a point P. It moves in such a way that its distance from P is always increasing. Find the maximum angle above the horizontal with which the projectile could have been...

An automobile engine slows down from 45000 rpm to 1200 rpm in 2.5s. Calculate (a) Its angular acceleration, assumed constant, and (b) The total number of revolutions the engine makes in this time.

An l0-km-long underground cable extends east to west and consists of two parallel wires each of which has resistance 13?/km. An electrical short develops at distance x from the west end when a...

An electron is accelerated rest through potential difference V and then enters a region of uniform magnetic field where it undergoes uniform circular motion. Figure gives the radius r of that motion...

A box with a total surface area of 1.20 m2 and a wall thickness of 4.00 cm is made of an insulating material. A 10.0-W electric heater inside the box maintains the inside temperature at 15.0C above...

On a cold winter day you buy roasted chestnuts from a street vendor. Into the pocket of your down parka you put the change he gives youcoins constituting 9.00 g of copper at -12.0C. Your pocket...

A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along the rope in 10.0 s. What is the...

Calculate the power delivered to each resistor shown in Figure P28.30. 2.0 50 V 4.0 4.0 2.0

Using Gauss's Law for Magnetism In a certain region of space, the magnetic field B is not uniform. The magnetic field has both a z component and a component that points radially away from or toward...

Your auditory system can accommodate a huge range of sound levels. What is the ratio of highest to lowest intensity at? (a) 100 Hz, (b) 5000 Hz (See Fig. 12-6)

Consider a wave packet with a Gaussian amplitude distribution A (k) = B exp [ σ (k k0)2] where 2/√σ is equal to the 1/e width* of the packet. Using this function for A (k), show...

A 0.70 kg ball moving horizontally at 5.0 m/s strikes a vertical wall and rebounds with speed 2.0 m/s. What is the magnitude of the change in its linear momentum?

A certain loudspeaker system emits sound isotropically with a frequency of 2000 Hz and an intensity of 0.960mW/m2 at a distance of 6.10 m. Assume that there are no reflections. (a) What is the...

In Figure two light pulses are sent through layers of plastic with thicknesses of either L or 2L as shown and indexes of refraction n1 = 1.55, n2 = 1.70, n3 = 1.60, n4 = 1.45, ns = 7.59, /t6 : I.65,...

Four uniform spheres, with masses mA = 40 kg, mB = 35 kg, mC = 200 kg, and mD = 50 kg, have (x, y) coordinates of (0, 50 cm), (0, 0), (-80 cm, 0), and (40 cm, 0), respectively. In unit-vector...

A conducting sphere of radius a, at potential V0, is surrounded by a thin concentric spherical shell of radius b, over which someone has glued a surface charge () = k cos, where k is a constant, and ...

A 4.00-kg counterweight is attached to a light cord, which is wound around a spool (refer to Fig. 10.20). The spool is a uniform solid cylinder of radius 8.00 cm and mass 2.00 kg. (a) What is the net...

A roller-coaster car is released from rest at the top of the first rise and then moves freely with negligible friction. The roller coaster shown in Figure P8.73 has a circular loop of radius R in a...

Jan first uses a Michelson interferaneter with the 606-nm light from a krypton-86 lamp. He displaces the movable mirror away from him, counting 818 fringes moving across a line in his field of view....

The potential at the surface of a sphere (radius R) is given by V0 = k cos 3, where k is a constant. Find the potential inside and outside the sphere, as well as the surface charge density () on the...

A magnetic dipole with a dipole moment of magnitude 0.020 J/T is released from rest in a uniform magnetic field of magnitude 52mT. The rotation of the dipole due to the magnetic force on it is...

Bicyclists in the Tour de France do enormous amounts of work during a race. For example, the average power per kilogram generated by seven-time-winner Lance Armstrong (m = 75.0 kg) is 6.50 W per...

As some molten metal splashes, one droplet flies off to the east with initial velocity vi at angle 'i above the horizontal, and another droplet to the west with the same speed at the same angle above...

Consider the arrangement shown in Figure P31.20. Assume that R = 6.00 Ω, = 1.20 m, and a uniform 2.50-T magnetic field is directed into the page. At what speed should the bar be moved to...

Fill in the missing particles or nuclei; (a) n + 137/56Ba ? + y; (b) n + 137/56Ba 137/55Cs + ?; (c) d + 2/1H 4/2 He + ?; (d) + 197/79Au ? + d where d stands for deuterium.

A pendulum consists of a 2.0 kg stone swinging on a 4.0 m string of negligible mass. The stone has a speed of 8.0 m/s when it passes its lowest point. (a) What is the speed when the string is at 60"...

In a long jump, an athlete leaves the ground with an initial angular momentum that tends to rotate her body forward, threatening to ruin her landing. To counter this tendency, she rotates her...

In Figure, four particles are fixed along an x axis, separated by distances d = 2.00cm. The charges are q1 = + 2e, q1 = ?? e, q3 = + e, and q4 = + 4e, with e = 1.60 x 10??19C, in unit-vector...

1. A quantity of liquid weighs 4.65 lb with a weight density of 39.8 lb/ft3. What is its volume? 2. The density of a metal is 694 kg/m3. Find its specific gravity. 3. A solid displaces 4.30 gal of...

In gravity-free interstellar space, a spaceship fires its rockets to speed up. The rockets are programmed to increase thrust from zero to 1.00 x 104 N with a linear increase over the course of 18.0...

A uniform rod of mass 100 g and length 50.0 cm rotates in a horizontal plane about a fixed, vertical, frictionless pin through its center. Two small beads, each of mass 30.0 g, are mounted on the rod...

A platinum wire (density 21.4 g/cm3) is 225 m in diameter and 0.450 m long. One end of the wire is attached to the ceiling, while a 420-g mass is attached to the other end so that the wire hangs...

The flywheel of a gasoline engine is required to give up 500 J of kinetic energy while its angular velocity decreases from 650 rev/min to 520 rev/min. What moment of inertia is required?

A mouse is initially at rest on a horizontal turntable mounted on a frictionless vertical axle. If the mouse begins to walk clockwise around the perimeter, what happens to the turntable? Explain.

How would you shield an electronic circuit or laboratory from stray electric fields? Why does this work?

A 3.00-μF and a 4.00-μF capacitor are connected in series, and this combination is connected in parallel with a 2.00-μF capacitor (see Fig. 19-52). What is the net capacitance? 3.00 F 4.00 F...

A particle of mass m is constrained to move on a circle of radius R. The circle rotates in space about one point on the circle, which is fixed. The rotation takes place in the plane of the circle and...

What should be the index of refraction of a transparent sphere in order for paraxial rays from an infinitely distant object to be brought to a focus at the vertex of the surface opposite the point of...

An observer in frame S' is moving to the right (+ x-direction) at speed u = 0.600c away from a stationary observer in frame S. The observer in S' measures the speed v' of a particle moving to the...

Consider a particle in a box with rigid walls at x = 0 and x = L. Let the particle be in the ground level. Calculate the probability | |2 dx that the particle will be found in the interval x to x +...

A 10-kg block rests on a 5-kg bracket like the one in figure. The 5-kg bracket sits on a frictionless surface. The coefficients of friction between the 10-kg block and the bracket on which it rests...

A telephone line has the following parameters: R = 40 /m, G = 400S/m, L = 0.2H/m, C = 0.5nF/m (a) If the line operates at 10 MHz, calculate the characteristic impedance Zo and velocity u. (b) After...

A steel bar 8.0 ft long has a circular cross section of diameter d1 = 0.75 in. over one-half of its length and diameter d2 = 0.5 in. over the other half (see figure). The modulus of elasticity E = 30...

Assume that the Earths atmosphere has a uniform temperature of 20C and uniform composition, with an effective molar mass of 28.9 g/mol. (a) Show that the number density of molecules depends on height...

A race car starts from rest on a circular track. The car increases its speed at a constant ate at as it goes once around the track. Find the angle that the total acceleration of the car makeswith the...

In a darkened room, a burning candle is placed 1.50 m from a white wall. A lens is placed between candle and wall at a location that causes a larger, inverted image to form on the wall. When the lens...

Three moles of an ideal gas are taken around the cycle abc shown in Fig. 19.31. For this gas, Cp = 29.l J/mol· K Process ac is at constant pressure, process ba is at constant volume, and...

Rocket a passes earth at a speed of 0.75c. At the same time, rocket B passes earth moving 0.95c relative to earth in the same direction. How fast is B moving relative to A when it passes A?

In Problem 8, what are the magnitudes of (a) The horizontal component and (b) The vertical component of the net force acting on the block at point Q? (c) At what height h should the block be released...

The temperature of 0.150 mol of an ideal gas is held constant at 77.0oC while its volume is reduced to 25.0% of its initial volume. The initial pressure of the gas is 1.25 atm. (a) Determine the work...

Three equal 1.20-C point charges are placed at the comers of an equilateral triangle whose sides are 0.500 m long. What is the potential energy of the system? (Take as zero the potential energy of...

Two resistors and two uncharged capacitors are arranged as shown in Fig. 19-58. Then a potential difference of 24 V is applied across the combination as shown. (a) What is the potential at point a...

A grandfather clock has a pendulum length of 0.7m and mass bob of 0.4kg. A mass of 2kg falls 0.8m in seven days to keep the amplitude (from equilibrium) of the pendulum oscillation steady at 0.03...

A force in the negative direction of an x axis is applied for 27 ms to a 0.40 kg ball initially moving at 14 m/s in the positive direction of the axis. The force varies in magnitude, and the impulse...

Figure shows a ball with mass m = 0.341 kg attached to the end of a thin rod with length L = 0.452 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical...

Juggling Act a juggler performs in a room whose ceiling is 3.0 m above the level of his hands. He throws a ball upward so that it just reaches the ceiling. (a) What is the initial velocity of the...

The eyepiece of a compound microscope has a focal length of 2.70 cm, and the objective lens has f =0.740 cm, if an object is placed 0.790 cm from the objective lens, calculate (a) The distance...

Calculate the ratio of the resistance of 10.0m of aluminum wire 2.0 mm in diameter, to 20.0m of copper wire 2.5 mm in diameter.

On a compact disc (CD), music is coded in a pattern of tiny pits arranged in a track that spirals outward toward the rim of the disc. As the disc spins inside a CD player, the track is scanned at a...

The (United States) National Electric Code, which sets maximum safe currents for insulated copper wires of various diameters, is given (in part) in the table. Plot the safe current density as a...

In Figure two curved plastic rods, one of charge + q and the other of charge ? q, form a circle of radius R = 8.50 cm in an xy plane. The x axis asses through both of the connecting points, and the...

A material having an index of refraction n is surrounded by a vacuum and is in the shape of a quarter circle of radius R (Fig. P35.66). A light ray parallel to the base of the material is incident...

In Section 8.6, we considered a rocket fired in outer space where there is no air resistance and where gravity is negligible. Suppose instead that the rocket is accelerating vertically upward from...

You drill a small hole in the side of a vertical cylindrical water tank that is standing on the ground with its top open to the air. (a) If the water level has a height H, at what height above the...

1. A gasoline service station owner receives a truckload of 34,000 L of gasoline at 32C. It cools to 15C in the underground tank. At 75 cents/L, how much money is lost as a result of the contraction...

A 1 500-kg car is moving at 20.0 m/s. The driver brakes to a stop. The brakes cool off to the temperature of the surrounding air, which is nearly constant at 20.0C. What is the total entropy change?

What is the maximum KE of the emitted particle during the decay of 60/27Co?

A golfer takes three putts to get the ball into the hole. The first putt displaces the ball 3.66 m north, the second 1.83 m southeast, and the third 0.91 m southwest. What are? (a) The magnitude and...

A transverse wave on a string is described by the wave function y = (0.120 m) sin [(x/8) + 4t] (a) Determine the transverse speed and acceleration at t = 0.200 s for the point on the string located...

For a person with normal hearing, the faintest sound that can be heard at a frequency of 400 Hz has a pressure amplitude of about 6.0 X 10-5 Pa. Calculate the (a) Intensity; (b) Sound intensity...

In Figure an electron is shot at an initial speed of v0 = 2.00 x 106 m/s, at angle ?0 = 40.0o from an x axis. It moves through a uniform electric field E = (5.00 N/C)j. A screen for detecting...

A thick-walled spherical shell of charge Q and uniform volume charge density p is bounded by radii r1 and r2 > r1. With V = 0 at infinity, find the electric potential V as a function of distance r...

The figure shows two displacement vectors and . Vector points at an angle of 22 o above has an x component B x = 35.0 m and has an unknown y component B y . These two vectors are equal. Concepts: (i)...

An archer shoots an arrow with a velocity of 45.0 m/s at an angle of 50.0 with the horizontal. An assistant standing on the level ground 150 m downrange from the launch point throws an apple straight...

The Wheatstone Bridge The circuit shown in Fig called a Wheatstone bridge. is used to determine !he value of an unknown resistor X by comparison with three resistors M, N, and P whose resistances can...

A heat pump is used to keep a house warm at 22oC. How much work is required of the pump to deliver 2800 J of heat into the house if the outdoor temperature is? (a) 0oC, (b) 15oC? Assume ideal...

The angular position of a point on a rotating wheel is given by = 2.0 + 4.0t2 + 4.0t3, where is in radians and t is in seconds. At t = 0, what are? (a) The point's angular position and (b) Its...

An Earth satellite used in the global positioning system moves in a circular orbit with period 11 h 58 min. (a) Determine the radius of its orbit. (b) Determine its speed. (c) The satellite contains...

You can think of the workkinetic energy theorem as a second theory of motion, parallel to Newtons laws in describing how outside influences affect the motion of an object. In this problem, solve...

You are given a sample of metal and asked to determine its specific heat. You weigh the sample and find that its weight is 28.4 N. You carefully add 1.25 X 104 J of heat energy to the sample and find...

A child slides a block of mass 2 kg along a slick kitchen floor. If the initial speed is 4m/s and the block hits a spring with spring constant 6 N/m, what is the maximum compression of the spring?...