The electric field of an electric dipole along the dipole axis is approximated by Eqs 22-8 and 22-9. If a binomial expansion is made of Eq. 22-7, what is the next term in the expression for the...

As shown in Figure P18.42, water is pumped into a tall vertical cylinder at a volume flow rate R. The radius of the cylinder is r, and at the open top of the cylinder a tuning fork is vibrating with...

Two infinitely long solenoids (seen in cross section) pass through a circuit as shown in Figure P31.49. The magnitude of B inside each is the same and is increasing at the rate of 100 T/s. What is...

Assume that crude oil from a supertanker has density 750 kg/m'. The tanker runs aground on a sandbar. To reflect the tanker, its oil cargo is pumped out into steel barrels, each of which has a mass...

(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 1150 N/C just outside the surface of...

The rubber worn from tires mostly enters the atmosphere as particulate pollution. Estimate how much rubber (in kg) is put into the air in the United States every year. To get started a good estimate...

At t = 0 a 1.0 kg ball is thrown from a tall tower with v = (18 m/s)i + (24m/s)j. What is U of the ball-Earth system between t = 0and t = 6.0s (still free fall)?

A flowerpot falls off a windowsill and falls past the window below. You may ignore air resistance. It takes the pot 0.420 s to pass this window, which is 1.90 m high. How far is the top of the window...

An aluminum tea kettle with mass 1.50 kg and containing 1.80 kg of water is placed on a stove. If no heat is lost to the surroundings, how much heat must be added to raise the temperature from 20.0C...

The electric potential of some configuration is given by the expression where A and are constants. Find the electric field E(r), the charge density p(r), and the total charge Q. ir ir V (r) = A

A parallel-plate capacitor consists of square plates of edge length that are separated by a distance d, where d < < . A potential difference V is maintained between the plates. A material of...

Suppose our Sun is about to explode. In an effort to escape, we depart in a spacecraft at v = 0.800c and head toward the star Tau Ceti, 12.0 ly away. When we reach the midpoint of our journey from...

Martian Athletics in the long jump, an athlete launches herself at an angle above the ground and lands at the same height, trying to travel the greatest horizontal distance. Suppose that on earth she...

A parallel-plate capacitor has capacitance C = 12.5 pF when the volume between the plates is filled with air. The plates are circular, with radius 3.00 cm. The capacitor is connected to a battery and...

A position-time graph for a particle moving along the x axis is shown in Figure P2.7. (a) Find the average velocity in the time interval t = 1.50 s to t = 4.00 s (b) Determine the instantaneous...

A ground retaining wall is shown in Fig. 9-36a. The ground, particularly when wet, can exert a significant force F on the wall. (a) What force produces the torque to keep the wall upright? (b)...

At time t, r = 4.0t2i - (2.0t + 6.0t2) j gives the position of a 3.0 kg particle relative to the origin of an xy coordinate system (r is in meters and t is in seconds). (a) Find an expression for the...

In Figure uniform beams A and B are attached to a wall with hinges and loosely bolted together (there is no torque of one on the other). Beam A has length LA = 2.40 m and mass 54.0 kg; beam B has...

A daring ranch hand sitting on a tree limb wishes to drop vertically onto a horse galloping under the tree. The constant speed of the horse is 10.0 m/s, and the distance from the limb to the level of...

Estimate how many molecules of air are in each 2.0-L breath you inhale that was also in the last breath Galileo took.

Two charges, Q0 and 3Q0, are a distance l apart. These two charges are free to move but do not because there is a third charge nearby. What must be the charge and placement of the third charge for...

A73 kg man stands on a level bridge of length L. He is at distance L/4 from one end. The bridge is uniform and weighs 2.7kN what are the magnitudes of the vertical forces on the bridge from its...

A ball is shot vertically upward from the surface of another planet. A plot of y versus t for the ball is shown in Figure, where y is the height of the ball above its starting point and t = 0 at the...

An elevator is moving upward at a constant speed of 2.50 m/s. A bolt in the elevator ceiling 3.00 m above the elevator floor works loose and falls. (a) How long does it take for the bolt to fall to...

Blocks A, B, and C are placed as in Fig. 5.56 and connected by ropes of negligible mass. Both A and B weigh 25.0 N each, and the coefficient of kinetic friction between each block and the surface is...

Three thin lenses, each with a focal length of 40.0 cm, are aligned on a common axis; adjacent lenses are separated by 52.0cm. Find the position of the image of a small object on the axis, 80.0cm to...

Atwood's Machine A 15.O-kg load of bricks hangs from one end of a rope that passes over a small, frictionless pulley. A 28.O-kg counterweight is suspended from the other end of the rope. As shown in...

In Fig 21-12, the rod moves with a speed of 1.6 m/s, is 30.0 cm long, and has a resistance of 2.5 . The magnetic field is 0.35 T, and the resistance of the U-shaped conductor is 25.0 at a given...

A uniform disk of radius R is cut in half so that the remaining half bas mass M (Fig. 931a). (a) What is the moment of inertia of this half about an axis perpendicular to its plane through point A?...

A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s. What is the...

Find the frequency of small oscillations for a thin homogeneous plate if the motion takes place in the plane of the plate and if the plate has the shape of an equilateral triangle and is suspended...

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...

It has been proposed that a spaceship might be propelled in the solar system by radiation pressure, using a large sail made of foil. How large must the surface area of the sail be if the radiation...

For the system of capacitors shown in Figure P26.54, find (a) The equivalent capacitance of the system, (b) The potential across each capacitor, (c) The charge on each capacitor, and (d) The total...

A 0.20-F capacitor is desired. What area must the plates have if they are to be separated by a 2.2-mm air gap?

An object is moved along the central axis of a spherical mirror while the lateral magnification m of it is measured. Figure gives m versus object distance p for the range pa = 2.0 cm to pb = 8.0 cm....

A battery has an emf of 15.0 V. The terminal voltage of the battery is 11.6 V when it is delivering 20.0 W of power to an external load resistor R. (a) What is the value of R? (b) What is the...

In Example 12.5 (Section 12.3) we ignored the gravitational effects of the moon on a spacecraft en route from the earth to the moon. In fact, we must include the gravitational potential energy due to...

A boy is initially seated on the top of a hemispherical ice mound of radius R = 13.8 m. He begins to slide down the ice, with a negligible initial speed (Figure g).Approximate the ice as being...

A sample of an ideal gas is taken through the cyclic process abca shown in Figure. The scale of the vertical axis is set by p?? = 7 .5 kPa and pb = 2.5 kPa. At point a, T = 200 K. (a) How many moles...

In a 250-turn automobile alternator, the magnetic flux in each turn is B = (2.50 x 10-4 Wb) cos (wt), where w is the angular speed of the alternator. The alternator is geared to rotate three times...

A 110-kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 350N. For the first 15m the floor is frictionless, and for the next 15m the coefficient of friction is...

Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 0.60m/s through a pipe 5.0cm in diameter, the pipe tapers down to 2.6cm in diameter by the top floor,...

Two cables are tied together at C and are loaded as shown. Determine the tension (a) In cable AC, (b) In cable BC. 75 75 200 k

A point charge Q = +4.60 C is held fixed at the origin. A second point charge q = + 1.20 C with mass of 2.80 X 10-4 kg is placed on the x-rods, 0.250 m from the origin. (a) What is the electric...

Figure shows an end view of two long, parallel wires perpendicular to the xy-plane, each carrying a current I but in opposite directions. (a) Copy the diagram, and draw vectors to show the B field of...

A particle is described by the normalized wave function (x, y, z) = Axe-ax2 e -y2 e-yz2', where A, a, , and are all real, positive constants. The probability that the particle will be found in the...

A 50 kg passenger rides in an elevator cab that starts from rest on the ground floor of a building at t = 0 and rises to the top floor during a 10 s interval. The cab's acceleration as a function of...

A thermodynamic system is taken from stare a to state c in Fig. 19.29 along either path abc or path adc. Along path abc, the work W done by the system is 450 J. Along path adc, W is 120 J. The...

A negative charge -0.550C exerts an upward 0.200-N force on an unknown charge 0.300 m directly below it. (a) What is the unknown charge (magnitude and sign)? (b) What are the magnitude and direction...

A cardiac defibrillator is used to shock a heart that is beating erratically. A capacitor in this device is charged to 5.0kV and stores 1200 J of energy. What is its capacitance?

An insulating rod having linear charge density 1 = 40.0 μC/m and linear mass density μ = 0.100 kg/m is released from rest in a uniform electric field E = 100 V/m directed perpendicular to the...

Two long, straight, parallel wires are 1.00 m apart (Fig.). The wire on the left carries a current I1of 6.00 A into the plane of the paper. (a) What must the magnitude and direction of the current s...

A flatbed truck is carrying a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still...

What fraction of a piece of aluminum will be submerged when it floats in mercury?

An electron and a positron collide head on, annihilate, and create two 0.90-MeV photons traveling in opposite directions. What were the initial kinetic energies of electron and positron?

A swimming pool has dimensions 30.0 m X 10.0 m and a flat bottom. When the pool is filled to a depth of 2.00 m with fresh water, what is the force caused by the water on the bottom? On each end? On...

Binding Energy of the Hydrogen Molecule when two hydrogen atoms of mass m combine to form a diatomic hydrogen molecule (H2), the potential energy of the system after they combine is -fl., where fl....

A cylinder with a movable piston contains 3.00 mol of N2 gas (assumed to he have like an ideal gas). (a) The N2 is heated at constant volume until 1557 J of heat have been added. Calculate the change...

(a) Calculate the characteristic rotational energy, h2/2I, for the O2 molecule whose bond length is 0.121nm, (b) What are the energy and wavelength of photons emitted in a L = 2 to L = 1 transition?

A square wire loop with 2.00 m sides is perpendicular to a uniform magnetic field, with half the area of the loop in the field as shown in Figure. The loop contains an ideal battery with emf ? = 20.0...

A uniformly charged ring of radius 10.0 cm has a total charge of 75.0 C. Find the electric field on the axis of the ring at (a) 1.00 cm, (b) 5.00 cm, (c) 30.0 cm, and (d) 100 cm from the center of...

Two people carry a heavy electric motor by placing it on a light board 2.00 m long. One person lifts at one end with a force of 400 N, and the other lifts the opposite end with a force of 600 N. (a)...

Alpha particles of charge q = +2e and mass m = 6.6 X 10-27 kg are emitted from a radioactive source at a speed of 1.6 X 107 m/s. what magnetic field strength would be required to bend them into a...

Two train whistles, A and B, each have a frequency of 392 Hz. A is stationary and B is moving toward the right (away from A) at a speed of35.0 m/s. A listener is between the two whistles and is...

A car at the Indianapolis 500 accelerates uniformly from the pit area, going from rest to 320 km/h in a semicircular are with a radius of 22m. Determine the tangential and radial acceleration of the...

A 340-kg marble boulder rolls off the top of a cliff and falls a vertical height of 140m before striking the ground. Estimate the temperature rise of the rock if 50% of the heat generated remains in...

Estimate the total binding energy copper and then estimate the energy, in joules, needed to break a 3.0-g copper penny into its constituent nucleons.

The atmospheric density at an altitude of 2500 km is about 1 molecule/cm3. (a) Assuming the molecular diameter of 2.0 x 10-8 cm, find the mean free path predicted by Eq. 19-25. (b) Explain whether...

Two parallel rails with negligible resistance are 10.0 cm apart and are connected by a 5.00-Ω resistor. The circuit also contains two metal rods having resistances of 10.0 Ω and 15.0...

A frictionless pulley has the shape of a uniform solid disk of mass 2.50 kg and radius 20.0 cm. A l.50-kg stone is attached to a very light wire that is wrapped around the rim of the pulley (Fig....

Three point charges are arranged on a line. Charge q3 = + 5.00 nC and is at the origin. Charge q2 = - 3.00 nC and is at x = +4.00cm. Charge q1 is at x = +2.00cm. What is q1 (magnitude and sign) if...

In a certain particle accelerator, protons travel around a circular path of diameter 23.0 m in an evacuated chamber, whose residual gas is at 295 K and 1.00 x 10-6 torr pressure. (a) Calculate the...

(a) Show that the electric field at point (0, 0, h) due to the rectangle described by ? a x a, ? b y b, z = 0 carrying uniform charge ? s C/m 2 is (b) If a = 2, b?= 5, ? s =?10 ?5 , find the total...

Two rods are identical in all respects except one: one rod is made from aluminum and the other from tungsten. The rods are joined end to end, in order to make a single rod that is twice as long as...

As in Figure P10.57, toppling chimneys often break apart in mid-fall because the mortar between the bricks cannot withstand much shear stress. As the chimney begins to fall, shear forces must act on...

A length of wire is cut in half and the two lengths are wrapped together side by side to make a thicker wire. How does the resistance of this new combination compare to the resistance of the original...

Figure shows a metallic block, with its faces parallel to coordinate axes. The block is in a uniform magnetic field of magnitude 0.020 T. One edge length of the block is 25 cm; the block is not drawn...

High-power lasers in factories are used to cut through cloth and metal (Fig. P34.23). One such laser has a beam diameter of 1.00 mm and generates an electric field having amplitude of 0.700 MV/m at...

A rocket is fired in deep space, where gravity is negligible. If the rocket has an initial mass of 6000 kg and ejects gas at a relative velocity of magnitude 2000 m/s, how much gas must it eject in...

A spacecraft is to be launched from the surface of the earth so that it will escape from the solar system altogether. (a) Find the speed relative to the center of the earth with which the spacecraft...

Water stands at a depth H in a large, open tank whose side walls are vertical (Fig. 14.42). A hole is made in one of the walls at a depth h below the water surface. (a) At what distance R from the...

A hydrogen atom is in the 6s state. Determine (a) The principal quantum number, (b) The energy of the state, (c) The orbital angular momentum and its quantum number l, and (d) The possible values for...

Two 2.00-C point charges are located on the x axis. One is at x = 1.00 m, and the other is at x = -1.00 m. (a) Determine the electric field on the y axis at y = 0.500 m. (b) Calculate the electric...

A small block with mass m is placed inside an inverted cone that is rotating about a vertical axis such that the time for one revolution of the cone is T (Fig. 5.83). The walls of the cone make an...

Two moles of an ideal gas occupy a volume V. The gas expands isothermally and reversibly to a volume 3V. (a) Is the velocity distribution changed by the isothermal expansion? Explain. (b) Use Eq....

A 145-g baseball is dropped from a tree 13.0 m above the ground. (a) With what speed would it hit the ground if air resistance could be ignored? (b) If it actually hits the ground with a speed of...

Consider a ladder with a painter climbing up it (Fig. 9-61). If the mass of the ladder is 12.0 kg, the mass of the painter is 55.0 kg, and the ladder begins to slip at its base when her feet are 70%...

Phasor Diagram for Eight Slits an interference pattern is produced by eight equally spaced, narrow slits. Figure 36.14 shows phasor diagrams for the cases in which the phase difference between light...

A block having mass m and charge + Q is connected to a spring having constant k. The block lies on a frictionless horizontal track, and the system is immersed in a uniform electric field of magnitude...

If r = bt2i + Ct3j, where b and c are positive constants, when does the velocity vector make an angle of 45.00 with the x and y- axes?

A car traveling at 53 km/h hits a bridge abutment. A passenger in the car moves forward a distance of 65 cm (with respect to the road) while being brought to rest by an inflated air bag. What...

Three point charges are placed on the y-axis: a charge q at y = a, a charge - 2q at the origin, and a charge q at y = -a. Such an arrangement is called an electric quadrupole. (a) Find the magnitude...

Two small, copper spheres each have radius 1.00 mm. (a) How many atoms does each sphere contain? (b) Assume that each copper atom contains 29 protons and 29 electrons. We know that electrons and...

A tourist purchases a car in England and ships it home to the United States. The car sticker advertised that the car's fuel consumption was at the rate of 40 miles per gallon on the open road. The...

A block weighing 75.0 N rests on a plane inclined at 25.0 to the horizontal. A force F is applied to the object at 40.0 to the horizontal, pushing it upward on the plane. The coefficients of static...

Find the radius a star image forms on the retina of the eye if the aperture diameter (the pupil) at night is 0.700 cm and the length of the eye is 3.00 cm. Assume the representative wavelength of...

A truck with mass m has a brake failure while going down an icy mountain road of constant downward slope angle a (Fig. 7.40). Initially the truck is moving downhill at speed vo. After careening...

In Figure a French submarine and a U.S. submarine move toward each other during maneuvers in motionless water in the North Atlantic. The French sub moves at speed vF = 50.00 km/h, and the U.S. sub at...

A thin flake of mica (n = 1.58) is used to cover one slit of a double-slit interference arrangement. The central point on the viewing screen is now occupied by what had been the seventh bright side...