In air under ordinary conditions (room temperature and atmospheric pressure), the average intermolecular distance is about 4 nm and the mean free path is about 0.1 µm. The diameter of a nitrogen molecule is about 0.3 nm. What would it mean if the intermolecular distance and the molecular diameter were about the same? In that case, would it make sense to speak of a mean free path? Explain.
> A lens (n = 1.51) has an antireflective coating of MgF2 (n = 1.38). Which of the first two reflected rays has a phase shift of 180°? Suppose a different antireflective coating on a similar lens had n = 1.62. Now which of the first two reflected rays has
> Make a sketch (similar to Fig. 25.15b) of the reflected rays from two adjacent steps of the Morpho butterfly wing for a large angle of incidence (around 45°). Refer to your sketch to explain why the wavelength at which constructive interference occurs de
> Find the electric field at point C, the center of the square.
> The fuselage of an Airbus A340 has a circumference of 17.72 m on the ground. The circumference increases by 26 cm when it is in flight. Part of this increase is due to the pressure difference between the inside and outside of the plane and part is due to
> An RLC series circuit is built with a variable capacitor. How does the resonant frequency of the circuit change when the area of the capacitor is increased by a factor of 2?
> A uniform magnetic field directed upward exists in some region of space. In what direction(s) could an electron be moving if its trajectory is (a) a straight line? (b) a circle? Assume that the electron is subject only to magnetic forces.
> In order to decrease the fundamental frequency of a guitar string by 4.0%, by what percentage should you reduce the tension?
> A violin is tuned by adjusting the tension in the strings. Brian's A string is tuned to a slightly lower frequency than Jennifer's, which is correctly tuned to 440.0 Hz. (a) What is the frequency of Brian's string if beats of 2.0 Hz are heard when the t
> Three identical incandescent lightbulbs are connected with wires to an ideal battery. The two terminals on each socket connect to the two terminals of its lightbulb. Wires do not connect with one another where they appear to cross in the picture. Ignore
> You want to build a cyclotron to accelerate protons to a speed of 3.0 × 107 m/s for use in proton beam therapy. The largest magnetic field you can attain is 1.5 T. What must be the minimum radius of the dees in your cyclotron? Show how your answer comes
> What effect places a lower limit on the size of an object that can be clearly seen with the best optical microscope?
> Explain, using Huygens's principle, why the Poisson spot is expected.
> A slide projector forms a real image of the slide on a screen using a converging lens. If the bottom half of the lens is blocked by covering it with opaque tape, does the bottom half of the image disappear, or does the top half disappear, or is the entir
> A glass tube is closed at one end and has a diaphragm covering the other end. The tube is filled with gas and some very fine sawdust has been scattered along inside the tube. When the diaphragm is driven at a frequency of 1457 Hz, the sawdust forms small
> Refer to Example 26.1. Ashlin travels at speed 0.800c to a star 30.0 ly from Earth. (a) Find the distance between Earth and the star in the astronaut's frame of reference. (b) How long (as measured by the astronaut) does it take to travel this distance
> A copper wire is connected to an ideal battery at room temperature. The current increases by a factor of 78 when the wire is immersed in liquid nitrogen (temperature 77 K). Ignoring changes in the wire's dimensions, and assuming that the number of conduc
> A 0.020 kg bullet is shot horizontally and collides with a 2.00 kg block of wood. The bullet embeds in the block, and the block slides along a horizontal surface for 1.50 m. If the coefficient of kinetic friction between the block and surface is 0.400, w
> An image of a biological sample is to have a resolution of 5 nm. (a) What is the kinetic energy of a beam of electrons with a de Broglie wavelength of 5.0 nm? (b) Through what potential difference should the electrons be accelerated to have this wavele
> The piano strings that vibrate with the lowest frequencies consist of a steel wire around which a thick coil of copper wire is wrapped. Only the inner steel wire is under tension. What is the purpose of the copper coil?
> A 12 Ω resistor has a potential difference of 16 V across it. What current flows through the resistor?
> The spectators at a sports stadium are “doing the wave”: they stand and raise their arms simultaneously with those in front of them and slightly after their neighbors on one side. This gives the appearance of a wave pulse propagation around the stadium.
> Nuclei in a radium-226 radioactive source emit photons whose energy is 186 keV. These photons are scattered by the electrons in a metal target; a detector measures the energy of the scattered photons as a function of the angle θ through which they are sc
> Electrons in a cathode ray tube start from rest and are accelerated through a potential difference of 12.0 kV. They are moving in the +x- direction when they enter the space between the plates of a parallel plate capacitor. There is a potential differenc
> A spherical conductor with a radius of 75.0 cm has an electric field of magnitude 8.40 × 105 V/m just outside its surface. What is the electric potential just outside the surface, assuming the potential is zero far away from the conductor?
> The amplitudes of an EM wave are related by Em = cBm. Since c = 3.00 × 108 m/s, a classmate says that the electric field in an EM wave is much larger than the magnetic field. How would you reply?
> (a) Show that it was valid to ignore the gravitational force in Problem 110. (b) What are the components of velocity of the particle when it emerges from the plates?
> Audio speakers must be connected with the correct polarity so that, if the same electrical signal is sent, they move in the same direction. If the wires going to one speaker are reversed, the listener hears a noticeably weaker bass (low frequencies). Exp
> Simple ear-protection devices use materials that reflect or absorb sound before it reaches the ears. A newer technology, sometimes called noise cancellation, uses a microphone to produce an electrical signal that mimics the noise. The signal is modified
> Find the maximum current that a fully charged D-cell can supply—if only briefly—such that its terminal voltage is at least 1.0 V. Assume an emf of 1.5 V and an internal resistance of 0.10 Ω.
> An RLC series circuit is connected to an ac power supply with a 12 V amplitude and a frequency of 2.5 kHz. If R = 220 Ω, C = 8.0 µF, and L = 0.15 mH, what is the average power dissipated?
> Is the vibration of a string in a piano, guitar, or violin a sound wave? Explain.
> Several possibilities are listed for what might or might not happen if the insulation in the current-carrying wires of the figure breaks down and point b makes electrical contact with point c. Discuss each possibility. (1) The person touching the microw
> You are working as an electrical engineer designing transformers for transmitting power from a generating station producing 2.5 × 106 W to a city 120 km away. The power will be carried on two transmission lines to complete a circuit, each line constructe
> Find the x-coordinate of the CM of the composite object shown in the figure. The sphere, cylinder, and rectangular solid all have a uniform composition. Their masses and dimensions are: sphere: 200 g, diameter = 10 cm; cylinder: 450 g, length = 17 cm, ra
> Does it take more force to tear a longer tendon or a shorter tendon? Assume the tendons are identical except for their lengths and are ideal—there are no weak points. Does it take more energy to tear the long tendon or the short tendon? Explain.
> To escape a burning building, Arnold has to jump from a third- story window that is about 10 m above the ground. Arnold is worried about breaking his leg. The largest bone in Arnold’s leg is the femur, which has a minimum cross-sectional area of about 5
> A 0.030 kg bullet is fired vertically at 200 m/s into a 0.15 kg baseball that is initially at rest. The bullet lodges in the baseball and, after the collision, the baseball/bullet rise to a height of 37 m. (a) What was the speed of the baseball/bullet r
> Three identical incandescent lightbulbs are connected in a circuit as shown in the diagram. (a) What happens to the brightness of the remaining bulbs if bulb A is removed from the circuit and replaced by a wire? (b) What happens to the brightness of th
> A 500 W electric heater unit is designed to operate with an applied potential difference of 120 V. (a) If the local power company imposes a voltage reduction to lighten its load, dropping the voltage to 110 V, by what percentage does the heat output of t
> Six wires are characterized by their dimensions and by the metal they are made from. Assume the tungsten alloy has exactly twice the resistivity of aluminum. Rank the wires in order of decreasing resistance. (a) diameter 2 mm, length 1 m, tungsten alloy
> Four identical incandescent lightbulbs are placed in two different circuits with identical batteries. Bulbs A and B are connected in series with the battery. Bulbs C and D are connected in parallel across the battery. (a) Rank the brightness of the bulb
> Rank the points in order of kinetic energy, from greatest to least, assuming no friction or air resistance.
> (a) Calculate the change in potential energy of 1 kg of water as it passes over Niagara Falls (a vertical descent of 50 m). (b) At what rate is gravitational potential energy lost by the water of the Niagara River? The rate of flow is 5.5 ×
> (a) If the resistance R1 decreases, what happens to the voltage drop across R3? The switch S is still open, as in the figure. (b) If the resistance R1 decreases, what happens to the voltage drop across R2? The switch S is still open, as in the figure.
> Describe what happens to a single-slit diffraction pattern as the width of the slit is slowly decreased.
> An acrobat of mass 55 kg is going to hang by her teeth from a steel wire and she does not want the wire to stretch beyond its elastic limit. The elastic limit for the wire is 250 MPa. What is the minimum diameter the wire should have to support her?
> An electron is suspended at a distance of 1.20 cm above a uniform line of charge. What is the linear charge density of the line of charge? Ignore end effects.
> Are you more likely to find steel rods in a horizontal concrete beam or in a vertical concrete column? Is concrete more in need of reinforcement under tensile or compressive stress?
> A bar magnet is held near the electron beam in an oscilloscope. The beam passes directly below the south pole of the magnet. In what direction will the beam move on the screen? (Don't try this with the CRT in a color TV. There is a metal mask just behind
> A strip of copper carries current in the +x-direction. There is an external magnetic field directed out of the page. What is the direction of the Hall electric field?
> An electron beam is deflected upward through 3.0 mm while traveling in a vacuum between two deflection plates 12.0 mm apart. The potential difference between the deflecting plates is 100.0 kV, and the kinetic energy of each electron as it enters the spac
> Harvey claims that he annihilated a 1.00 lb bag of chocolate-chip cookies after playing basketball for 3 h. (a) If Harvey had truly annihilated the mass in the cookies, how much energy would be produced? (b) How many kilowatt-hours of electric energy i
> Sketch the magnetic field as it would appear inside the coil of wire to an observer, looking into the coil from the position shown.
> What is the wavelength of the microwaves transmitted by a cell phone at 900 MHz? (Microwaves travel at 3.0 × 108 m/s.)
> A barge of mass 5.0 × 104 kg is pulled along the Erie Canal by two mules, walking along towpaths parallel to the canal on either side of it. The ropes harnessed to the mules make angles of 45° to the canal. Each mule is pulling on its rope with a force o
> A series circuit with a resistor and a capacitor has a time constant of 0.25 ms. The circuit has an impedance of 350 Ω at a frequency of 1250 Hz. What are the capacitance and the resistance?
> An ultraviolet microscope locates an electron in an atom to within a distance of 0.5 nm. What is the order of magnitude of the minimum uncertainty in the momentum of the electron located in this way?
> A 2.0 kg toy locomotive is pulling a 1.0 kg caboose. The frictional force of the track on the caboose is 0.50 N backward along the track. If the train’s acceleration forward is 3.0 m/s2, what is the magnitude of the force exerted by the locomotive on the
> Because iodine accumulates in the thyroid, radioactive iodine-131 can be used to kill cancerous thyroid tissue with minimal damage to other tissue. Sometimes the dose is administered in an outpatient setting and the patient is allowed to go home, with in
> The trajectory of a charged particle in a uniform magnetic field is a helix if / has components both parallel to and perpendicular to the field. Explain how the two other cases (circular motion for v∣∣ = 0 and straight line motion for v⊥ = 0) can each b
> Explain how the period of a mass-spring system can be independent of amplitude, even though the distance traveled during each cycle is proportional to the amplitude.
> When a tuning fork is held over the open end of a very thin tube, as in Fig. 12.7, the smallest value of L that produces resonance is found to be 30.0 cm. (a) What is the wavelength of the sound? [Hint: Assume that the displacement antinode is at the op
> Estimate the number of H2O molecules in a human body of mass 80.2 kg. Assume that, on average, water makes up about 62% of the mass of a human body.
> In Section 6.2, Rosie lifts a trunk weighing 220 N up 4.0 m. If it takes her 40 s to lift the trunk, at what average rate does she do work?
> A charged particle moves through a region of space at constant velocity. Ignore gravity. In the region, is it possible that there is (a) a magnetic field but no electric field? (b) an electric field but no magnetic field? (c) a magnetic field and an e
> Agnes Pockels (1862–1935) was able to determine Avogadro's number using only a few household chemicals, in particular oleic acid, whose formula is C18H34O2. (a) What is the molar mass of this acid? (b) The mass of one drop of oleic acid is 2.3 × 10−5 g
> A point charge q = −2.5 nC is initially at rest adjacent to the negative plate of a capacitor. The charge per unit area on the plates is 4.0 µC/m2 and the space between the plates is 6.0 mm. (a) What is the potential difference between the plates? (b)
> Refer to the bubble chamber tracks in Fig. 19.16a. Suppose that particle 2 moves in a smaller circle than particle 1. Can we conclude that ∣q2∣ > ∣q1∣? Explain.
> Explain why a constant magnetic field does no work on a point charge moving through the field. Since the field does no work, what can we say about the speed of a point charge acted on only by a magnetic field?
> A metal bar is shown at two different times. The arrows represent the alignment of the dipoles within each magnetic domain. (a) What happened between t1 and t2 to cause the change? (b) Is the metal a paramagnet, diamagnet, or ferromagnet? Explain.
> The phenomenon of Brownian motion is the random motion of microscopically small particles as they are buffeted by the still smaller molecules of a fluid in which they are suspended. For a particle of mass 1.0 × 10−16 kg, the fluctuations in velocity are
> A doorbell uses a transformer to deliver an amplitude of 8.5 V when it is connected to a 170 V amplitude line. If there are 50 turns on the secondary, (a) what is the turns ratio? (b) How many turns does the primary have?
> A magnifying glass can be held over a piece of white paper and its position adjusted until the image of an overhead light is formed on the paper. Explain.
> If a magnet is held near the screen of a CRT (see Sec. 16.5), the picture is distorted. [Don't try this—see part (b).] (a) Why is the picture distorted? (b) With a color CRT, the distortion remains even after the magnet is removed. Ex
> A copper wire and an aluminum wire of the same length have the same resistance. What is the ratio of the diameter of the copper wire to that of the aluminum wire?
> (a) What is the buoyant force on 0.90 kg of ice floating freely in liquid water? (b) What is the buoyant force on 0.90 kg of ice held completely submerged under water?
> An ac circuit has a single resistor, capacitor, and inductor in series. The circuit uses 100 W of power and draws a maximum rms current of 2.0 A when operating at 60 Hz and 120 V rms. The capacitive reactance is 0.50 times the inductive reactance. (a) F
> The dipole is released from rest at θ = 90.0°. What is its angular speed when it reaches θ = 0? [Hint: First find the work done on each point charge.]
> A block of wood is compressed 2.0 nm when inward forces of magnitude 120 N are applied to it on two opposite sides. (a) Assuming Hooke’s law holds, what is the effective spring constant of the block? (b) Assuming Hooke’s law still holds, how much is th
> Two soap bubbles of different radii are formed at the ends of a tube with a closed valve in the middle. What happens to the bubbles when the valve is opened? (If the alveoli in the lung did not have a surfactant that reduces surface tension in the smalle
> Two wires at right angles in a plane carry equal currents. At what points in the plane is the magnetic field zero?
> One iron nail does not necessarily attract another iron nail, although both are attracted by a magnet. Explain.
> According to the special theory of relativity, no object that has mass can travel faster than the speed of light. Yoo Jin says she knows something that moves faster than the speed of light. She tells you to consider a rotating beacon on Earth with a powe
> An AM radio station broadcasts at 570 kHz. (a) What is the wavelength of the radio wave in air? (b) If a radio is tuned to this station and the inductance in the tuning circuit is 0.20 mH, what is the capacitance in the tuning circuit? (c) In the vici
> Small animals eat much more food per kilogram of body mass than do larger animals. The basal metabolic rate (BMR) is the minimal energy intake necessary to sustain life in a state of complete inactivity. The table lists the BMR in kilocalories per day, t
> To make an order-of-magnitude estimate of the energy level spacings in the nucleus, assume that a nucleon is confined to a one- dimensional box of width 10 fm (a typical nuclear diameter). Calculate the energy of the ground state.
> The nucleus of a helium atom contains two protons that are approximately 1 fm apart. How much work must be done by an external agent to bring the two protons from an infinite separation to a separation of 1.0 fm?
> Explain why there is almost no hydrogen (H2) or helium (He) in Earth's atmosphere, yet both are present in Jupiter's atmosphere. [Hint: Escape velocity from Earth is 11.2 km/s and escape velocity from Jupiter is 60 km/s.]
> The potential difference across a cell membrane from outside to inside is initially at −90 mV (when in its resting phase). When a stimulus is applied, Na+ ions are allowed to move into the cell such that the potential changes to +20 mV for a short interv
> Computer speakers that are intended to be placed near a CRT computer monitor are magnetically shielded—either they don't use magnets or they are designed so that their magnets produce only a small magnetic field nearby. Why is the shielding important? Wh
> In an experiment to measure the speed of sound in air, standing waves are set up in a narrow pipe open at both ends using a speaker driven at 702 Hz. The length of the pipe is 2.0 m. What is the air temperature inside the pipe (assumed reasonably near ro
> A circular loop of current carries a steady current. (a) Sketch the magnetic field lines in a plane perpendicular to the plane of the loop. (b) Which side of the loop is the north pole of the magnetic dipole and which is the south pole?
> The magnetic field due to a long straight wire carrying steady current is measured at two points, P and Q. Where is the wire and in what direction does the current flow?
> In 1988 the shroud of Turin, a piece of cloth that some people believe is the burial cloth of Jesus, was dated using 14C. The measured 14C activity of the cloth was about 0.23 Bq/g. According to this activity, when was the cloth in the shroud made?
> A horizontal wire that runs east-west carries a steady current to the east. A C-shaped magnet (see Fig. 19.3a) is placed so that the wire runs between the poles, with the north pole above the wire and the south pole below. What is the direction of the ma
> Abductin, an elastic protein found in the ligaments of scallops, has a Young’s modulus of 4.0 MPa. The inner hinge ligament has a cross-sectional area of 0.78 mm2 and a relaxed length of 1.0 mm. When the muscles in the shell relax, the shell opens. This
> In her bag, a photographer is carrying three camera lenses with focal lengths of 400.0 mm, 50.0 mm, and 28.0 mm. Which lens should she use for (a) wide angle shots (a cathedral, taken from the square in front), (b) everyday use (children at play), and
> A 5.0 kg block of wood is attached to a spring with a spring constant of 150 N/m. The block is free to slide on a horizontal frictionless surface once the spring is stretched and released. A 1.0 kg block of wood rests on top of the first block. The coeff
> A dc motor is connected to a constant emf of 12.0 V. The resistance of its windings is 2.0 ΩAt normal operating speed, the motor takes in 6.0 W of electrical power. (a) What is the initial current drawn by the motor when it is first started up? (b) Wha
> Two magnifying glasses are labeled with their angular magnifications. Glass A has a magnification of “2×” (M = 2) and glass B has a magnification of 4×. Which has the longer focal length? Explain.
