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 transmitted through the second polarizer, from greatest to least. (a) θ1 = 0°, θ2 = 30°; (b) θ1 = 30°, θ2 = 30°; (c) θ1 = 0°, θ2 = 90°; (d) θ1 = 60°, θ2 = 0°; (e) θ1 = 30°, θ2 = 60°.
> Find the magnetic force on the electron at point a.
> The figure shows a simplified circuit diagram for an automobile. The equivalent resistor R represents the total electrical load due to spark plugs, lights, radio, fans, starter, rear window defroster, and the like in parallel. If R = 0.850 â„&
> Two blocks are connected by an ideal cord that passes over a frictionless pulley. If m1 = 3.6 kg and m2 = 9.2 kg, and block 2 is initially at rest 140 cm above the floor, how long does it take block 2 to reach the floor?
> Rank the electrons in order of the magnitude of the magnetic force on them, from greatest to least.
> A rocket engine can accelerate a rocket launched from rest vertically up with an acceleration of 20.0 m/s2. However, after 50.0 s of flight the engine fails. Ignore air resistance. (a) What is the rocket's altitude when the engine fails? (b) When does
> Consider the camera flash in Problem 96. If the flash really discharges according to Eq. (18-48), then it takes an infinite amount of time to discharge. When Problem 96 assumes that the capacitor discharges in 4.0 × 10−3 s, we mean that the capacitor has
> In Example 6.1, find the work done by the movers as they slide the chest up the ramp if the coefficient of friction between the chest and the ramp is 0.20.
> The average speed of blood in the aorta is 0.3 m/s, and the radius of the aorta is 1 cm. There are about 2 × 109 capillaries with an average radius of 6 μm. What is the approximate average speed of the blood flow in the capillaries?
> A parallel plate capacitor used in a flash for a camera must be able to store 32 J of energy when connected to 300 V. (Most electronic flashes actually use a 1.5 to 6.0 V battery, but increase the effective voltage using a dc-dc inverter.) (a) What shou
> Consider the circuit in the diagram. After the switch S has been closed for a long time, what are the current through the 12 Ω resistor and the voltage across the capacitor?
> In each of five situations, two point charges (Q1, Q2) are separated by a distance d. Rank them in order of the electric potential energy, from highest to lowest. (a) Q1 = 1 µC, Q2 = 2 µC, d = 1 m (b) Q1 = 2 µC, Q2 = −1 µC, d = 1 m (c) Q1 = 2 µC, Q2 = −4
> A naval aviator had to eject from her plane before it crashed at sea. She is rescued from the water by helicopter and dangles from a cable that is 45 m long while being carried back to the aircraft carrier. What is the period of her vibration as she swin
> A 20 µF capacitor is discharged through a 5.0 kΩ resistor. The initial charge on the capacitor is 200 µC. (a) Sketch a graph of the current through the resistor as a function of time. Label both axes with numbers and units. (b) What is the initial powe
> Using a mass spectrometer, the mass of the / ion is found to be 238.050 24 u. (a) Use this result to calculate the mass of the / nucleus. (b) Now find the binding energy of the / nucleus.
> A proton moves in a helical path at speed v = 4.0 × 107 m/s high above the atmosphere, where Earth's magnetic field has magnitude B = 1.0 × 10−6 T. The proton's velocity makes an angle of 25° with the magnetic field. (a) Find the radius of the helix. [H
> (a) In a charging RC circuit, how many time constants have elapsed when the capacitor has 99.0% of its final charge? (b) How many time constants have elapsed when the capacitor has 99.90% of its final charge? (c) How many time constants have elapsed wh
> An automobile traveling at a speed of 30.0 m/s applies its brakes and comes to a stop in 5.0 s. If the automobile has a mass of 1.0 × 103 kg, what is the average horizontal force exerted on it during braking? Assume the road is level.
> In the circuit, the initial energy stored in the capacitor is 25 J. At t = 0 the switch is closed. (a) Sketch a graph of the voltage across the resistor (VR) as a function of t. Label the vertical axis with key numerical value(s) and units. (b) At what
> (a) Light of wavelength 300 nm is incident on a metal that has a work function of 1.4 eV. What is the maximum speed of the emitted electrons? (b) If light of wavelength 800 nm is incident on a metal that has a work function of 1.6 eV, are any electrons
> Explain why the displacement of air elements at condensations and rarefactions is zero.
> A 1.5 hp motor operates on 120 V. Ignoring I2R losses, how much current does it draw?
> In the circuit, the capacitor is initially uncharged. At t = 0, switch S is closed. Find the currents I1 and I2 and voltages V1 and V2 (assuming V3 = 0) at points 1 and 2 at (a) t = 0 (i.e., just after the switch is closed) and at (b) t = 1.0 ms.
> To get to a concert in time, a harpsichordist has to drive 122 mi in 2.00 h. (a) If he drove at an average speed of 55.0 mi/h in a due west direction for the first 1.20 h, what must be his average speed if he drives 30.0° south of west for the remaining
> Five conducting spheres are charged as shown. All have the same magnitude net charge except E, whose net charge is zero. Which pairs are attracted to each other and which are repelled by each other when they are brought near each other, but well away fro
> In Fig. 3.39, two blocks are connected by a lightweight cord that does not stretch and that passes over an ideal pulley. (a) If m1 = 3.0 kg and m2 = 5.0 kg, what are the accelerations of each block? (b) What is the tension in the cord?
> Show that Eq. (26-23) reduces to the nonrelativistic relationship between momentum and kinetic energy, K ≈ p2/(2m), for K ≪ E0.
> In a defibrillator (see Example 17.12), a charged capacitor is connected to paddles that make electrical contact with the patient's skin. If gel is applied to the patient's chest to make a good connection between the paddles and the skin, the effective r
> (a) What is the position of the peak of the pulse shown in the figure at t = 3.00 s? (b) When does the peak of the pulse arrive at x = 4.00 m?
> In the circuit of Problem 88, at what time after switch S is closed is the voltage across the combination of three capacitors 50% of its final value?
> Consider the circuit shown with R1 = 25 Ω, R2 = 33 Ω, C1 = 12 µF, C2 = 23 µF, C3 = 46 µF, and V = 6.0 V. (a) Draw an equivalent circuit with one resistor and one capacitor an
> In the circuit, R = 30.0 kΩ and C = 0.10 µF. The capacitor is allowed to charge fully, and then the switch is changed from position a to position b. What will the voltage across the resistor be 8.4 ms later?
> In the Cornell Electron Storage Ring, electrons and positrons circulate in opposite directions with kinetic energies of 6.0 GeV each. When an electron collides with a positron and the two annihilate, one possible (though unlikely) outcome is the producti
> A wind turbine converts some of the kinetic energy of the wind into electric energy. Suppose that the blades of a small wind turbine have length L = 4.0 m. (a) When a 10 m/s (22 mi/h) wind blows head-on, what volume of air (in m3) passes through the cir
> In the circuit shown, assume the battery emf is 20.0 V, R = 1.00 MΩ, and C = 2.00 µF. The switch is closed at t = 0. At what time t will the voltage across the capacitor be 15.0 V?
> A tangent galvanometer is an instrument, developed in the nineteenth century, designed to measure current based on the deflection of a compass needle. A coil of wire in a vertical plane is aligned in the magnetic north-south direction. As illustrated, a
> An ammeter with a full-scale deflection for I = 10.0 A has an internal resistance of 24 Ω. We need to use this ammeter to measure currents up to 12.0 A. The lab instructor advises that we get a resistor and use it to protect the ammeter. (a) What size r
> Show that c2 = 931.494 MeV/u. [Hint: Start with the conversion factors to SI units for MeV and atomic mass units.]
> A 0.15 kg baseball traveling in a horizontal direction with a speed of 20 m/s hits a bat and is popped straight up with a speed of 15 m/s. (a) What is the change in momentum (magnitude and direction) of the baseball? (b) If the bat was in contact with
> Find the potential at the sodium ion, Na+, which is surrounded by two chloride ions, Cl−, and a calcium ion, Ca2+, in water as shown in the diagram. The effective charge of the positive sodium ion in water is 2.0 × 10â
> Consider the circuit in the diagram. Given: I1 = 2.50 A /, / , R1 = 8.00 Ω, and R2 = 5.00 Ω. Find the values of I2, I3, and R3.
> Two cars, a Porsche Boxster convertible and a Toyota Scion xB, are traveling at constant speeds in the same direction, although the Boxster is 186 m behind the Scion. The speed of the Boxster is 24.4 m/s and the speed of the Scion is 18.6 m/s. Sketch gra
> Iodine is eliminated from the body through biological processes with an effective half-life of about 140 days. The radioactive half-life of iodine-131 is 8 days. Suppose some radioactive 131I nuclei are present in the body. Assuming that no new 131I nucl
> A BMW of mass 2.0 × 103 kg is traveling at 42 m/s. It approaches a 1.0 × 103 kg Volkswagen going 25 m/s in the same direction and strikes it in the rear. Neither driver applies the brakes. Ignore the relatively small frictional forces on the cars due to
> Transverse waves travel on five stretched strings with the following properties. Rank the strings according to the time it takes a transverse wave pulse to travel from one end to the other, from largest to smallest. (a) length L, total mass m, tension F
> Derive Eq. (12-5): (a) Starting with Eq. (12-4), substitute T = TC + 273.15. (b) Apply the binomial approximation to the square root (see Appendix A.9) and simplify.
> The longest “string” (a thick metal wire) on a particular piano is 2.0 m long and has a tension of 300.0 N. It vibrates with a fundamental frequency of 27.5 Hz. What is the total mass of the wire?
> 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
> 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) Plot a graph for versus x at t = 0 and at / . From the plots determine the amplitude, wavelength, and speed of the wave. (b) For the same function, plot a graph of y(x, t) versus t at x = 0 and find the period of the vibration. Show that X = vT.
> 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.
