Question:

> A guitar's E-string has length 65 cm and is stretched to a tension of 82 N. It vibrates at a fundamental frequency of 329.63 Hz. Determine the mass per unit length of the string.

> A shark is able to detect the presence of electric fields as small as 1.0 µV/m. To get an idea of the magnitude of this field, suppose you have a parallel plate capacitor connected to a 1.5 V battery. How far apart must the parallel plates be to have an

> Tension is maintained in a string by attaching one end to a wall and by hanging a 2.20 kg object from the other end of the string after it passes over a pulley that is 2.00 m from the wall. The string has a mass per unit length of 3.55 mg/m. What is the

> Randomly polarized light with intensity I0 passes through two ideal polarizers, one after the other. The transmission axes of the first and second polarizers are at angles θ1 and θ2, respectively, to the horizontal. Rank the intensities of the light tran

> A source of emf / has internal resistance r. (a) What is the terminal voltage when the source supplies a current I? (b) The net power supplied is the terminal voltage times the current. Starting with P = IΔV, derive Eq. (18-39) for the net power sup

> A guitar string has a fundamental frequency of 300.0 Hz. (a) What are the next three lowest standing wave frequencies? (b) If you press a finger lightly against the string at its midpoint so that both sides of the string can still vibrate, you create a

> During a “brownout,” which occurs when the power companies cannot keep up with high demand, the voltage of the household circuits drops below its normal 120 V. (a) If the voltage drops to 108 V, what would be the power consumed by a “100 W” incandescent

> A battery has a 6.00 V emf and an internal resistance of 0.600 Ω. (a) What is the voltage across its terminals when the current drawn from the battery is 1.20 A? (b) What is the power supplied by the battery?

> Strontium-90 / is a radioactive element that is produced in nuclear fission. It decays by β− decay to yttrium (Y) with a half-life of 28.8 yr. (a) Write down the decay scheme for /. (b) What is the initial activity of 2.0 kg of /? (c) What will

> In the circuit shown, R1 = 15.0 Ω, R2 = R4 = 40.0 Ω, R3 = 20.0 Ω, and R5 = 10.0 Ω. (a) What is the equivalent resistance of this circuit? (b) What current flows through resi

> A moving source emits a sound wave that is heard by a moving observer. Imagine a thin wall at rest between the source and observer. The wall completely absorbs the sound and instantaneously emits an identical sound wave. Use this scenario to explain why

> Jason drives due west with a speed of 35.0 mi/h for 30.0 min, continues in the same direction with a speed of 60.0 mi/h for 2.00 h, and then drives farther west at 25.0 mi/h for 10.0 min. What is Jason’s average velocity? Sketch a motion diagram at 10 mi

> In lab tests it was found that rats can detect electric fields of about 5.0 kN/C or more. If a point charge of 1.0 µC is sitting in a maze, how close must the rat come to the charge in order to detect it?

> (a) If you were stranded on an island with a pair of 3.5 D reading glasses, could you make a useful telescope? If so, what would be the length of the telescope and what would be the angular magnification? (b) Answer the same questions if you also had a

> For a safe reentry into Earth's atmosphere, the pilots of a space capsule must reduce their speed from 2.6 × 104 m/s to 1.1 × 104 m/s. The rocket engine produces a backward force on the capsule of 1.8 × 105 N. The mass of the capsule is 3800 kg. For how

> In Problem 86, the +2.0 µC charge is at x = 0 and the −4.0 µC charge is at x = d. Find the x-coordinates of the point(s) where the electric field is zero.

> At what rate is energy dissipated in the 4.00 Ω and 5.00 Ω resistors in the circuit shown?

> Two conducting wires perpendicular to the page are shown in cross section as gray dots in the figure. They each carry 10.0 A out of the page. What is the magnetic field at point P?

> A long straight wire carries a 4.70 A current in the positive x- direction. At a particular instant, an electron moving at 1.00 × 107 m/s in the positive y-direction is 0.120 m from the wire. Determine the magnetic force on the electron at this instant.

> In a lab experiment, a string has a mass per unit length of 0.120 g/m. It is attached to a vibrating device and weight similar to that shown in Figure 11.23. The vibrator oscillates at a constant frequency of 110 Hz. How heavy should the weight be in ord

> In a carbon-dating experiment, a particular type of mass spectrometer is used to separate 14C from 12C. Carbon ions from a sample are first accelerated through a potential difference ΔV1 between the charged accelerating plates. Then the ions

> A 1.6 m long string fixed at both ends vibrates at resonant frequencies of 780 Hz and 1040 Hz, with no other resonant frequency between these values. The tension in the string is 1200 N. (a) What is the fundamental frequency of this string? (b) What is

> Explain why the pitch of a bassoon is more sensitive to a change in air temperature than the pitch of a cello. (That's why wind players keep blowing air through the instrument to keep it in tune.)

> Why is the number of electron neutrinos reaching Earth from the Sun smaller than had originally been predicted?

> Six sources emit sound equally in all directions with average power P. A microphone is placed at a distance d from each source. Rank the situations in order of the intensity at the location of the microphone, smallest to largest. (a) P = 10 W, d = 2 m (

> Show that A2 × Ω = W (amperes squared times ohms = watts).

> How much work are the batteries in the circuit doing in every 10.0 s time interval?

> For the train in Fig. 3.2 and Example 3.3, find the average velocity between 3:14 P.M. when the train is at 3 km east of the origin and 3:28 P.M. when it is 10 km east of the origin.

> A cord of length 1.5 m is fixed at both ends. Its mass per unit length is 1.2 g/m and the tension is 12 N. (a) What is the frequency of the fundamental oscillation? (b) What tension is required to make the n = 3 mode have a frequency of 0.50 kHz?

> In the diagram, the positive terminal of the 12 V battery is grounded —it is at zero potential. At what potential is point X?

> What is the resistance of a 40.0 W, 120 V incandescent lightbulb?

> Use Gauss’s law to derive an expression for the electric field outside the thin spherical shell of Conceptual Example 16.8.

> A negative point charge −Q is situated near a large metal plate that has a total charge of +Q. Sketch the electric field lines.

> Zorba and Boris are at a water park. There are two water slides with straight slopes that start at the same height and end at the same height. Slide A has a more gradual slope than slide B. Boris says he likes slide B better because you reach a faster sp

> A mechanic turns a wrench using a force of 25 N at a distance of 16 cm from the rotation axis. The force is perpendicular to the wrench handle. What magnitude torque does she apply to the wrench?

> A bungee jumper leaps from a bridge and comes to a stop a few centimeters above the surface of the water below. At that lowest point, is the tension in the bungee cord equal to the jumper’s weight? Explain why or why not.

> Two blocks, masses m1 and m2, are connected by a massless cord. If the two blocks are pulled with a constant tension on a frictionless surface by applying a force of magnitude T2 to a second cord connected to m2, what is the ratio of the tensions in the

> Radioactive iodine, 131I, is used in some forms of medical diagnostics, (a) If the initial activity of a sample is 64.5 mCi, what is the mass of 131I in the sample? (b) What will the activity be 4.5 d later?

> A bird (mass 31 g) is flying at 11.1 m/s when it flies into a glass window and bounces off at a speed of 4.1 m/s. The bird is in contact with the glass for 0.071 s. What is the average force on the bird during the collision?

> What is the current in a 60.0 W bulb when connected to a 120 V emf?

> The Sun emits electromagnetic waves (including light) equally in all directions. The intensity of the waves at Earth's upper atmosphere is 1.4 kW/m2. At what rate does the Sun emit electromagnetic waves? (In other words, what is the power output?)

> At what rate does the jet airplane in Problem 4 radiate energy in the form of sound waves?

> For a transverse wave on a string described by find the maximum speed and the maximum acceleration of a point on the string. Plot a graph showing one cycle of velocity vy versus t at the point x = 0.

> A 75 kg man is at rest on ice skates. A 0.20 kg ball is thrown to him. The ball is moving horizontally at 25 m/s just before the man catches it. How fast is the man moving just after he catches the ball?

> See Problem 7. During Michaela’s travel from Killarney to Cork via Mallow, her travel time is 48 min. (a) What is her average speed in m/s? (b) What is the magnitude of her average velocity in m/s?

> (a) What is the mass defect of the 1H atom due to the binding energy of the electron (in the ground state)? (b) Should we worry about this mass defect when we calculate the mass of the 1H nucleus by subtracting the mass of one electron from the mass of

> A coaxial cable consists of a wire of radius a surrounded by a thin metal cylindrical shell of radius b. The wire has a uniform linear charge density λ > 0 and the outer shell has a uniform linear charge density −Î

> A small plane is flying directly west with an airspeed of 30.0 m/s. The plane flies into a region where the wind is blowing at 10.0 m/s at an angle of 30° to the south of west. (a) If the pilot does not change the heading of the plane, what will be the

> In the construction of railroads, curvature of the track is measured in the following way. First a 100.0 ft long chord is measured. Then the curvature is reported as the angle subtended by two radii at the endpoints of the chord. (The angle is measured b

> A sine wave is traveling to the right on a cord. The lighter line in the figure represents the shape of the cord at time t = 0; the darker line represents the shape of the cord at time t = 0.10 s. (Note that the horizontal and vertical scales are differe

> Find the electric field at point B, midway between the upper left and right corners.

> Five stretched strings have the following properties. Rank the strings according to their fundamental frequencies (for transverse standing waves), from greatest to least. (a) length L, total mass m, tension F (b) length 2L, total mass m, tension F (c) le

> Rank the waves in order of maximum transverse speed, largest to smallest.

> Rank the waves in order of amplitude, largest to smallest.

> Rank the waves in order of frequency, largest to smallest.

> What is the average binding energy per nucleon for /?

> Five cars are traveling on a highway. Their masses and initial speeds are: (a) 1500 kg, 30 m/s (b) 1500 kg, 20 m/s (c) 1000 kg, 30 m/s (d) 1000 kg, 20 m/s (e) 2000 kg, 40 m/s The cars use the same braking force to slow down and stop. Rank the cars in ord

> Once Rutherford and Geiger determined the charge-to-mass ratio of the alpha particle (see Problem 93), they performed another experiment to determine its charge. An alpha source was placed in an evacuated chamber with a fluorescent screen. Through a glas

> Write the equation for a harmonic wave with amplitude 2.50 cm and angular frequency 2.90 rad/s that is moving in the +x-direction with a wave speed that is 5.00 times as fast as the maximum transverse speed of a point on the string. At t = 0, the point x

> At time t = 0, block A of mass 0.225 kg and block B of mass 0.600 kg rest on a horizontal frictionless surface a distance 3.40 m apart, with block A located to the left of block B. A horizontal force of 2.00 N directed to the right is applied to block A

> A scout troop is practicing its orienteering skills with map and compass. First they walk due east for 1.2 km. Next, they walk 45° west of north for 2.7 km. In what direction must they walk to go directly back to their starting point? How far will they h

> The intensity of the sound wave from a jet airplane as it is taking off is 100 W/m2 at a distance of 5.0 m. What is the intensity of the sound wave that reaches the ears of a person standing at a distance of 120 m from the runway? Assume that the sound w

> In a game of shuffleboard, a disk with an initial speed of 3.2 m/s travels 6.0 m before coming to rest. (a) What was the acceleration of the disk? (b) What was the coefficient of kinetic friction between the floor and the disk?

> (a) Write an equation for a harmonic wave with amplitude 0.750 mm, frequency 36.0 Hz, and wave speed 144 m/s traveling in the +x- direction. At t = 0, the point x = 0 is at its maximum displacement in the +y-direction. (b) What is the maximum accelerati

> Prove that, in an EM wave traveling in vacuum, the electric and magnetic energy densities are equal; that is, prove that at any point and at any instant of time.

> You are swimming in the ocean as water waves with wavelength 9.6 m pass by. What is the closest distance that another swimmer could be so that his motion is exactly opposite yours (he goes up when you go down)?

> What is the mass defect of the 14N nucleus?

> A mass of 1.4 kg of water at 22°C is poured from a height of 2.5 m into a vessel containing 5.0 kg of water at 22°C. (a) How much does the internal energy of the 6.4 kg of water increase? (b) Is it likely that the water temperature increases? Explain.

> Rank the points in order of mechanical energy, from greatest to least, assuming no friction or air resistance.

> Steel railroad tracks of length 18.30 m are laid at 10.0°C. How much space should be left between the track sections if they are to just touch when the temperature is 50.0°C?

> Sketch a graph of y versus x for the function for the times t = 0 and 0.96 s. Make the graphs on the same axes, using a solid line for the first and a dashed line for the second. Use the values k = (Ï€/5.0) rad/cm and ω = (Ï&#12

> The photosensitive cells (rods and cones) in the retina are most densely packed in the fovea—the part of the retina used to see straight ahead. In the fovea, the cells are all cones spaced about 1 µm apart. Would our vision have much better resolution if

> An object of mass m is hung from the base of an ideal spring that is suspended from the ceiling. The spring has a spring constant k. The object is pulled down a distance D from equilibrium and released. Later, the same system is set oscillating by pullin

> Two 35.0 cm metal rods, one made of copper and one made of aluminum, are placed end to end, touching each other. One end is fixed, so that it cannot move. The rods are heated from 0.0°C to 150°C. How far does the other end of the system of rods move?

> A 6.0 pF capacitor is needed to construct a circuit. The only capacitors available are rated as 9.0 pF. How can a combination of three 9.0 pF capacitors be assembled so that the equivalent capacitance of the combination is 6.0 pF?

> Is e the smallest fundamental unit of charge? The smallest observable unit of charge? [Hint: Try to come up with a meson or baryon with a charge that is not an integral multiple of e.] Explain.

> Isolated atoms (or atoms in a dilute gas) radiate photons at discrete energies characteristic of that atom. In dense matter, the spectrum radiated is quasi-continuous. Why doesn’t the same thing happen with nuclear spectra: why do the gamma rays have the

> What is the mass of an 16O atom in units of MeV/c2? (1 MeV/c2 is the mass of a particle with rest energy 1 MeV.)

> A 2.4 m length of copper pipe extends directly from a water heater in a basement to a faucet on the first floor of a house. If the faucet isn't fixed in place, how much will it rise when the pipe is heated from 20.0°C to 90.0°C? Ignore any increase in th

> The size of an atom is about 0.1 nm. Can a light microscope make an image of an atom? Explain.

> You are serving as a consultant for the newest James Bond film. In one scene, Bond must fire a projectile from a cannon and hit the enemy headquarters located on the top of a cliff 75.0 m above and 350 m from the cannon. The cannon will shoot the project

> A radio station wants to ensure good reception of its signal everywhere inside a city. Would it be a good idea to place several broadcasting antennas at roughly equal intervals around the perimeter of the city? Explain.

> Five slabs with temperature coefficients of expansion α have lengths L at Ti = 20°C. Their temperatures then rise to Tf. Rank them in order of how much their lengths increase, greatest to smallest. (a) L = 90 cm, Tf = 40°C, α = 8 × 10−6 K−1 (granite) (b)

> Water entering a house flows with a speed of 0.20 m/s through a pipe of 1.0 cm inside radius. What is the speed of the water at a point where the pipe tapers to a radius of 2.5 mm?

> A 1.5 V flashlight battery can maintain a current of 0.30 A for 4.0 h before it is exhausted. How much chemical energy is converted to electrical energy in this process? (Assume zero internal resistance of the battery.)

> Two antennas driven by the same electrical signal emit coherent radio waves. Is it possible for two antennas driven by independent signals to emit radio waves that are coherent with each other? If so, how? If not, why not?

> Stereo speakers should be wired with the same polarity. If by mistake they are wired with opposite polarities, the bass (low frequencies) sound much weaker than if they are wired correctly. Why? Why is the bass (low frequencies) weakened more than the tr

> Why can you easily hear sound around a corner due to diffraction, although you cannot see around the same corner?

> Estimate the number of nucleons found in the body of a 75 kg person.

> Event A happens at the spacetime coordinates (x, y, z, t) = (2 m, 3 m, 0, 0.1 s) and event B happens at the spacetime coordinates (x, y, z, t) = (0.4 × 108 m, 3 m, 0, 0.2 s). (a) Is it possible that event A caused event B? (b) If event B occurred at (0

> Hannah is standing in the middle of a room with two opposite walls that are separated by 10.0 m and covered by plane mirrors. There is a candle in the room 1.50 m from one mirrored wall. Hannah is facing the opposite mirrored wall and sees many images of

> A 2.0 kg object (the “projectile”) approaches a stationary object (the “target”) at 5.0 m/s. The projectile is deflected through an angle of 60.0° and its speed after the collision is 3.0 m/s. What is the magnitude of the momentum of the target after the

> In the LHC, protons are accelerated to a total energy of 7 TeV. (a) What is the speed of these protons? (b) The LHC tunnel is 27 km in circumference. As measured by an Earth observer, how long does it take the protons to go around the tunnel once? (c)

> What is the average binding energy per nucleon for

> The escape speed from Earth is 11.2 km/s, but that is only the minimum speed needed to escape Earth’s gravitational pull; it does not give the object enough energy to leave the solar system. What is the minimum speed for an object near Earth’s surface so

> The gravitational potential energy of a pendulum is U = mgy. (a) Taking y = 0 at the lowest point, show that y = L(1 − cos θ), where θ is the angle the string makes with the vertical. (b) If θ is s

> Kurt is measuring the speed of light in an evacuated chamber aboard a spaceship traveling with a constant velocity of 0.60c with respect to Earth. The light is moving in the direction of motion of the spaceship. Siu-Ling is on Earth watching the experime

> The Milky Way galaxy rotates about its center with a period of about 200 million yr. The Sun is 2 × 1020 m from the center of the galaxy. How fast is the Sun moving with respect to the center of the galaxy?

> The two strands of the DNA molecule are held together by hydrogen bonds between base pairs (Sec. 16.1). When an enzyme unzips the molecule to separate the two strands, it has to break these hydrogen bonds. A simplified model represents a hydrogen bond as

> Your car’s wheels are 65 cm in diameter, and the wheels are spinning at an angular velocity of 101 rad/s. How fast is your car moving in kilometers per hour (assume no slippage)?