The potential energy of a diatomic molecule (a two-atom system like H2 or O) is given by where r is the separation of the two atoms of the molecule and A and B are positive constants. This potential...

A charge + q is at the origin. A charge -2q is at x = 2.00 m on the x axis. For what finite value(s) of x is (a) The electric field zero? (b) The electric potential zero?

Superconducting power transmission the use of superconductors has been proposed for power transmission lines. A single coaxial cable (Fig P32.78) could carry 1.00 x 103 MW (the output of a large...

An Earth satellite has a perigee of 300 km and an apogee of 3,500 km above Earths surface. How far is the satellite above Earth when (a) It has rotated 90o around Earth from perigee and (b) It has...

Estimate the binding energy of the H2 molecule, assuming the two H nuclei are 0.074nm apart and the two electrons spend 33% of their time midway between them.

An alien spacecraft is flying overhead at a great distance as you stand in your backyard. You see its searchlight blink on for 0.190 s. The first officer on the spacecraft measures that the...

(a) Explain what happens to the balls of Problem 54 if one of them is discharged (loses its charge q to, say, the ground).(b) Find the new equilibrium separation x, using the given values of L and m...

The radar system of a navy cruiser transmits at a wavelength of 1.6 cm, from a circular antenna with a diameter of 2.3 m. At a range of 6.2 km, what is the smallest distance that two speedboats can...

A crate of eggs is located in the middle of the flat bed of a pickup truck as the truck negotiates an un-banked curve in the road. The curve may be regarded as an arc of a circle of radius 35.0 m. If...

A uniformly charged disk like the disk in Fig. 21.26 has radius 2.50 cm and carries a total charge of 4.0 X 10-12 C. (a) Find the electric field (magnitude and direction) on the x-axis at x = 20.0...

(a) Calculate the rate at which body heat is conducted through the clothing of a skier in a steady-state process, given the following data: the body surface area is 1.8 m2, and the clothing is 1.0 cm...

Using the definition of the scalar product, find the angles between (a) A = 3i 2j and B = 4i 4j; (b) A = 2i + 4j and B = 3i + 4j + 2k; (c) A = i 2j + 2k and B = 3j + 4 k.

Three resistors having resistances of 1.60, 2.40 , and 4.80 are connected in parallel to a 28.0-V battery that has negligible internal resistance. Find (a) The equivalent resistance of the...

A particle is projected with an initial velocity v0 up a slope that makes an angle a with the horizontal. Assume frictionless motion and find the time required for the particle to return to its...

Red light with wavelength 700 nm is passed through a two slit apparatus. At the same time, monochromatic visible light with another wavelength passes through the same apparatus. As a result, most of...

A roller-coaster car has a mass of 1200 kg when fully loaded with passengers. As the car passes over the top of a circular hill of radius 18 m, its speed is not changing. At the top of the hill, what...

A glass flask whose volume is 1000.00 cm3 at 0.0oC is completely filled with mercury at this temperature.When flask and mercury are warmed to 55.0oC, 8.95 cm3 of mercury overflow. If the coefficient...

A Stirling-Cycle Engine the Stirling cycle is similar to the Otto cycle, except that the compression and expansion of the gas are done at constant tem- perature, not adiabatically as in c the Otto...

Suppose a truck loaded with sand accelerates along a highway. If the driving force on the truck remains constant, what happens to the trucks acceleration if its trailer leaks sand at a constant rate...

An oscillator consists of a block of mass 0.500 kg connected to a spring. When set into oscillation with amplitude 35.0 cm, the oscillator repeats its motion every 0.500 s. Find the (a) Period, (b)...

Two identical parallel-plate capacitors, each with capacitance C, are charged to potential difference V and connected in parallel. Then the plate separation in one of the capacitors is doubled. (a)...

Two coils, held in fixed positions, have a mutual inductance of 100 H. What is the peak voltage in one when a sinusoidal current given by I (t) = (10.0 A) sin (1 000t) is in the other coil?

A 25-turn 12.5 cm-diameter coil is placed between the pole pieces of an electromagnet. When the magnet is turned on, the flux through the coil changes, inducing and emf at what rate (in T/s) must the...

A particle is constrained to move (without friction) on a circular wire rotating with constant angular speed w about a vertical diameter. Find the equilibrium position of the particle, and calculate...

Two streams merge to form a river. One stream has a width of 8.2 m, depth of 3.4m, and current speed of 2.3 m/s. The other stream is 6.8 m wide and 3.2m deep, and flows at 2.6 m/s. If the river has...

Two very long, straight wires carry currents as shown in Fig. For each case, find all locations where the net magnetic field is zero 10.0 A 20.0 A 10.0A 3.0 A 10.0 A 20.0 A (b) (c) (a)

If a projectile is fired due east from a point on the surface of Earth at a northern latitude λ with a velocity of magnitude V0 and at an angle of inclination to the horizontal of a, show that...

Displacement Current in a Wire A long, straight, copper wire with a circular cross-sectional area of 2.1 mm2 carries a current of16 A. The resistivity of the material is 2.0 X 10-8 m. (a) What is the...

Pipe A, which is 1.20 m long and open at both ends, oscillates at its third lowest harmonic frequency, it is filled with air for which the speed of sound is 343 m/s. Pipe B, which is closed at one...

A sample of gas expands from V1 = 1.0 m3 and P1 = 40 Pa to V2 = 4.0 m3 and P2 = 10 Pa along path B in the p-V diagram in Figure. It is then compressed back to V1 along either path A or path C....

A sinusoidal wave traveling in the x direction (to the left) has an amplitude of 20.0 cm, a wavelength of 35.0 cm, and a frequency of 12.0 Hz. The transverse position of an element of the medium at t...

Show that the amount of work required to assemble four identical point charges of magnitude Q at the corners of a square of side s is 5.41keQ2/s.

A very large flat sheet carries a uniformly distributed electric current with current per unit width Js. Example 30.6 demonstrated that the current creates a magnetic field on both sides of the...

The accommodation limits for Nearsighted Nicks eyes are 18.0 cm and 80.0 cm. When he wears his glasses, he can see faraway objects clearly. At what minimum distance is he able to see objects clearly?

A small rock moves in water, and the force exerted on it by the water is given by Eq. (5.7). The terminal speed of the rock is measured and found to be 2.0 m/s. The rock is projected upward at an...

One lens of a nearsighted persons eyeglasses has a focal length of -22.0 cm, and the lens is 81.8 cm from the eye. If the person switches to contact lenses that are placed directly on the eye, what...

A disk, initially rotating at 120 rad/s, is slowed down with a constant angular acceleration of magnitude 4.0 rads2. (a) How much time does the disk take to stop? (b) Through what angle does the disk...

Figure shows a thin plastic rod of length L = 13.5 cm and uniform charge 43.6fC. (a) In terms of distance d, find an expression for the electric potential at point Pr. (b) Next, substitute variable x...

(a) Find a quantitative expression for the thermal equilibrium concentration n = n+ = n in the particle-antiparticle reaction A+ + A = 0. The reactants may be electrons and positrons; protons and...

A magnetic field of 0.200 T exists within a solenoid of 500 turns and a diameter of 10.0 cm. How rapidly (that is, within what period of time) must the field be reduced to zero, if the average...

It is not possible to see very small objects, such as viruses, using an ordinary light microscope. An electron microscope can view such objects using an electron beam instead of a light beam....

Two forces have the same magnitude F. What is the angle between the two vectors if their sum bas a magnitude of (a) 2F? (b) 2F? (c) zero? Sketch the three vectors in each case.

Calculate the percent difference between your weight in Sacramento, near sea level, and at the top of Mount Everest, which is 8800 m above sea level.

Assuming that air resistance is unimportant, calculate the minimum velocity a particle must have at the surface of Earth to escape from Earths gravitational field. Obtain a numerical value for the...

Measuring Wavelengths with a CD A laser beam of wavelength = 632.8 nm shines at normal incidence on the reflective side of a compact disc. The tracks of tiny pits in which information is coded onto...

Suppose the electric field in some region is found to be E = kr3r, in spherical coordinates (k is some constant). (a) Find the charge density p. (b) Find the total charge contained in a sphere of...

A space vehicle is traveling at 4300 km/h relative to Earth when the exhausted rocket motor (mass 4m) is disengaged and sent backward with a speed of 82 km/h relative to the command module (mass...

The lowest possible temperature in outer space is 2.7 K. What is the rms speed of hydrogen molecules at this temperature? (The molar mass is given in Table 19-1.)

Two stunt drivers drive directly toward each other. At time t = 0 the two cars are a distance D apart, car 1 is at rest, and car 2 is moving to the left with speed Va. Car 1 begins to move at t = 0,...

Longitudinal Standing Waves in a Solid Longitudinal standing waves can be produced in a solid rod by holding it at some point between the fingers of one hand and stroking it with the other band. The...

One molecule of water (H2O) contains two atoms of hydrogen and one atom of oxygen. A hydrogen atom has a mass of 1.0 u and an atom of oxygen has a mass of 16 u, approximately. (a) What is the mass in...

The accompanying figure shows three different crystallographic planes for a unit cell of a hypothetical metal. The circles represent atoms: (a) To what crystal system does the unit cell belong? (b)...

A uniform solid disk of mass 3.00 kg and radius 0.200 m rotates about a fixed axis perpendicular to its face. If the angular frequency of rotation is 6.00 rad/s, calculate the angular momentum of the...

Block A in Fig. 8.35 has mass 1.00 kg, and block B has mass 3.00 kg. The blocks are forced together, compressing a spring S between them; then the system is released from rest on a level,...

How far from a very small 100-kg ball would a particle have to be placed so that the ball pulled on the particle just as hard as the earth does? Is it reasonable that you could actually set up this...

The shock-wave cone created by the space shuttle at one instant during its reentry into the atmosphere makes an angle of 58.0 with its direction of motion. The speed of sound at this altitude is 331...

A radioactive nucleus at rest decays into a second nucleus, and electron, and a neutrino. The electron and neutrino are emitted at right angles and have moment a of 9.30 x 10-23 kg m/s and 5.40 x...

A gas is allowed to expand (a) Adiabatically and (b) Isothermally. In each process, does the entropy increase, decrease, or stay the same? Explain.

One round face of a 3.25-m, solid, cylindrical plastic pipe is covered with a thin black coating that completely blocks light. The opposite face is covered with a fluorescent coating that glows when...

Three forces act on a particle that moves with unchanging velocity v = (2 m/s)i (7 m/s)i. Two of the forces are F1 = (2 N)i + (3 N)j + ( 2N)k and F2 = ( 5N)i + (8 N)j + ( 2 N)k. What is the third...

A sample of ideal gas is expanded to twice its original volume of 1.00 m3 in a quasi-static process for which P =V 2, with = 5.00 atm/m6, as shown in Figure P20.23. How much work is done on the...

A 2.9-kg piece of wood slides on the surface shown in Fig. 7.33 The curved sides are perfectly smooth, but the rough horizontal bottom is 30 m long and has a kinetic friction coefficient of 0.20 with...

A square steel plate is 10.0 cm on a side and 0.500 cm thick. (a) Find the sbear strain that results if a force of magnitude 9.0 X 10" N is applied to each of the four sides, parallel to the side....

Testing a Space Radio Transmitter you are a NASA mission specialist on your first flight aboard the space shuttle. Thanks to your extensive training in physics, you have been assigned to evaluate the...

The volume of air space in the passenger compartment of an 1800 kg car is 5.00 m3. The volume of the motor and front wheels is 0.750 m3, and the volume of the rear wheels, gas tank, and trunk is...

A certain electric dipole is placed in a uniform electric field E of magnitude 20 N/C. Figure gives the potential energy U of the dipole versus the angle 0 between E and the dipole moment p. The...

Use mesh analysis to find i1, i2, and i3 in the circuit of Fig. 3.97? Figure 3.97 6) 8 3 A 121. i3

A mass less spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest in a position yi such that the spring is at its rest length. The object...

A piece of aluminum with mass 1.00 kg and density 2 700 kg/m3 is suspended from a string and then completely immersed in a container of water (Figure P14.25). Calculate the tension in the string (a)...

Eight solid plastic cubes, each 3.00 cm on each edge, are glued together to form each one of the objects (i, ii, iii, and iv) shown in Figure P23.37. (a) Assuming each object carries charge with...

Calculate the resistance in an RL circuit in which L = 2.50 H and the current increases to 90.0% of its final value in 3.00 s.

The capacity of a storage battery, such as those used in automobile electrical systems, is rated in ampere-hours (A h). A 50- A h battery can supply a current of 50 A for 1.0 h, or 25 A for 2.0 h,...

The oscillator of a 96.1-MHz FM station has a inductance of 1.8 H. What value must the capacitance be?

A small fly of mass 0.25 g is caught in a spiders web. The web vibrates predominately with a frequency of 4.0 Hz. (a) What is the value of the effective spring stiffness constant k for the web? (b)...

A toroid is a solenoid in the shape of a circle (Fig. 20-62). Use Amperes law along the circular path, shown dashed in fig, 20-62a, to determine that the magnetic field. (a) Inside the toroid is B =...

A beam of light strikes a sheet of glass at an angle of 57.0o with the normal in air. You observe that red light makes an angle of 38.1 with the normal in the glass, while violet light makes a 36.7...

L-C Oscillations. A capacitor with capacitance 6.00 X 10-5 F is charged by connecting it to a 12.0-V battery. The capacitor is disconnected from the battery and connected across an inductor with L =...

The position function x(r) of a particle moving along an x axis is x = 4.0 6.0 t 2 , with x in meters and t in seconds. (a) At what time and (b) Where does the particle (momentarily) stop? At what...

Calculate the rotational inertia of a meter stick, with mass 0.56 kg, about an axis perpendicular to the stick and located at the 20 cm mark. (Treat the stick as a thin rod.)

A projectile is launched with speed Vo at an angle ao above the horizontal. The launch point is a height h above the ground. (a) Show that if air resistance is ignored, the horizontal distance that...

Two organ pipes open at one end but closed at the other, are each 1.14 m long. One is now lengthened by 2.00 cm. Find the frequency of the beat they produce when playing together in their fundamental.

The ideas of average and root-mean-square value can be applied to any distribution. A class of 150 students had the following scores on a 100-point quiz: (a) Find the average score for the class. (b)...

A force of 48.0N is required to start a 50-kg box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor? (b) If the 48.0-N force...

Will a grandfather clock, accurate at 20oC, run fast or slow on a hot day (30oC)? Explain. The clock uses a pendulum supported on a long, thin brass rod.

The diameter of Mars is 6794 km, and its minimum distance from the ear1h is 5.58 x 107 km. When Mars is at this distance find the diameter of the image of Mars formed by a spherical, concave,...

A golfer tees off from the top of a rise, giving the golf ball an initial velocity of 43 m/s at an angle of 30 above the horizontal. The ball strikes the fairway a horizontal distance of 180 m from...

In Figure, a nonconducting spherical shell of inner radius a = 2.00 cm and outer radius b = 2.40 cm has (within its thickness) a positive volume charge density = A / r, where A is a constant and r...

The reel shown in Figure P10.70 has radius R and moment of inertia I. One end of the block of mass m is connected to a spring of force constant k, and the other end is fastened to a cord wrapped...

A 18.0-F capacitor is placed across a 22.5-V battery for several seconds and is then connected across a 12.0-mH inductor that has no appreciable resistance. (a) After the capacitor and inductor are...

Suppose V = 0 and A = A0 sin(kx wt) y, where A0, w, and k are constants. Find E and B, and check that they satisfy Maxwell's equations in vacuum. What condition must you impose on w and k?

At time t = 0, a ball is struck at ground level and sent over level ground. Figure gives momentum p versus t during the flight (p0 = 6.0 kg m/s and p1 = 4.0 kg m/s). At what initial angle is the ball...

A boy can throw a ball a maximum horizontal distance of R on a level field. How far can he throw the same ball vertically upward? Assume that his muscles give the ball the same speed in each case.

Consider a siphon which transfers water from one vessel to a second (lower) one, as in Fig. 10-58. Determine the rate of flow if the tube has a diameter of 1.2cm and the difference in water levels of...

Two rooms, each a cube 4.0m per side, share a 12-cm-thick brick wall. Because of a number of 100-W lightbulbs in one room, the air is at 30oC, while in the other room it is at 10oC. How many of the...

Continuation of Problems 2 and 39, another explanation is that the stones move only when the water dumped on the playa during a storm freezes into a large, thin sheet of ice. The stones are trapped...

A golf ball is launched at an angle of 20 to the horizontal, with a speed of 60 m/s and a rotation rate of 90 rad/s. Neglecting air drag, determine the number of revolutions the ball makes by the...

In Figure, light is incident at angle 1 = 40.1? on a boundary between two transparent materials. Some of the light travels down through the next three layers of transparent materials while some of it...

A thin rod of length l lies on the + x-axis with its left end at the origin. A string pulls on the rod with a force F directed toward a point P a distance h above the rod. Where along the rod should...

A potato of mass 0.5 kg moves under Earths gravity with an air resistive force of kmv. (a) Find the terminal velocity if the potato is released from rest and k = 0.01 s1. (b) Find the maximum height...

Construct the energy-level diagram for the He+ ion (See Fig 27-27).