Light travels through tanks filled with various substances. The indices of refraction of the substances n and the lengths of the tanks are given. Rank them in order of the time it takes light to traverse the tank, from greatest to smallest. (a) n = 5/4, length = 1 m; (b) n = 1, length = 4/5 m; (c) n = 1, length = 1 m; (d) n = 3/2, length = 1 m; (e) n = 3/2, length = 5/4 m; (f) n = 3/2, length = 4/5 m.
> A ball weighing 20.0 N is tied to a string fixed to the ceiling. The string makes a 30.0° angle with the ceiling. Initially, the ball is held in place by a force / that is perpendicular to the string. (a) What is the magnitude of the force
> Refer to Problems 11–14. Find the final speed of the sliding crate if the incline is frictionless.
> A graph is plotted of the vertical velocity component vy of an elevator versus time. The y-axis points up. (a) How high is the elevator above the starting point (t = 0) after 20 s have elapsed? (b) When is the elevator at its highest location above the
> Two blocks are connected by a light string passing over an ideal pulley. The block with mass m1 = 20.0 kg slides on a frictionless horizontal surface, while the block with mass m2 = 1.0 kg hangs vertically. The radius of the pulley is 6.0 cm. (a) Assumi
> A circuit has a resistor and an unknown component in series with a 12 V (rms) sinusoidal ac source. The current in the circuit decreases by 25% when the frequency increases from 150 Hz to 250 Hz. What is the second component in the circuit? Explain your
> Find the orbital radius of a geostationary satellite without using the speed found in Example 5.9. Start by writing an equation that relates the period, radius, and speed of the orbiting satellite. Then apply Newton’s second law to the satellite. You wil
> If the electric force on the drop is found to be 9.6 × 10−16 N and the potential difference between the plates is 480 V, what is the magnitude of the charge on the drop in terms of the elementary charge e? Ignore the small buoyant force on the drop.
> An airplane of mass 2800 kg has just lifted off the runway. It is gaining altitude at a constant 2.3 m/s while the horizontal component of its velocity is increasing at a rate of 0.86 m/s2. Assume g = 9.81 m/s2. (a) Find the direction of the force exert
> The magnetic field between the poles of a magnet has magnitude 0.55 T. A circular loop of wire with radius 3.2 cm is placed between the poles so the field makes an angle of 22° with the plane of the loop. What is the magnetic flux through the loop?
> Two different monochromatic light sources, one yellow (580 nm) and one violet (425 nm), are used in a photoelectric effect experiment. The metal surface has a photoelectric threshold frequency of 6.20 × 1014 Hz. (a) Are both sources able to eject photoe
> (a) What is the reactance of a 10.0 mH inductor at the frequency f = 250.0 Hz? (b) What is the impedance of a series combination of the 10.0 mH inductor and a 10.0 Ω resistor at 250.0 Hz? (c) What is the maximum current through the same circuit when th
> Three capacitors (2.0 µF, 3.0 µF, 6.0 µF) are connected in series to an ac voltage source with amplitude 12.0 V and frequency 6.3 kHz. (a) What are the peak voltages across each capacitor? (b) What is the peak current that flows in the circuit?
> A small object of mass 0.50 kg is attached by a 0.50 m long cord to a pin set into the surface of a frictionless table top. The object moves in a circle on the horizontal surface with a speed of 2.0π m/s. (a) What is the magnitude of the radial accelera
> Earth’s orbit around the Sun is nearly circular. The period is 1 yr = 365.25 d. (a) In an elapsed time of 1 d, what is Earth’s angular displacement in radians? (b) What is the change in Earth’s velocity, /? (c) What is Earth’s average acceleration du
> Consider two protons (charge +e), separated by a distance of 2.0 × 10−15 m (as in a typical atomic nucleus). The electric force between these protons is equal in magnitude to the gravitational force on an object of what mass near Earth’s surface?
> A helicopter is lifting two crates simultaneously. One crate with a mass of 200 kg is attached to the helicopter by a cable. The second crate with a mass of 100 kg is hanging below the first crate and attached to the first crate by a cable. As the helico
> Credit cards have a magnetic strip that encodes information about the credit card account. Why do devices that read the magnetic strip often include the instruction to swipe the card rapidly? Why can’t the magnetic strip be read if the card is swiped too
> 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. Which two distances should we com
> The principal component of natural gas is methane (CH4). How many moles of CH4 are present in 144.36 g of methane?
> The maximum strain of a steel wire with Young’s modulus 200 GPa, just before breaking, is 0.20%. What is the stress at its breaking point, assuming that strain is proportional to stress up to the breaking point?
> At a baseball game, a spectator is 60.0 m away from the batter. How long does it take the sound of the bat connecting with the ball to travel to the spectator's ears? The air temperature is 27.0°C.
> The circuit is used to study the charging of a capacitor. (a) At t = 0, the switch is closed. What initial charging current is measured by the ammeter? (b) After the current has decayed to zero, what are the voltages at points A, B, and C?
> Derive the rotational form of Newton's second law as follows. Consider a rigid object that consists of a large number N of particles. Let Fn, mn, and rn represent the tangential component of the net force acting on the nth particle, the mass of that part
> A vertical metal rod of length 20 cm moves south at constant speed 2.6 m/s in a 0.60 T magnetic field directed west. (a) Which end of the rod has an accumulation of excess electrons? (b) What is the potential difference between the ends of the rod?
> A laboratory observer measures an electron's kinetic energy to be 1.02 × 10−13 J. What is the electron's speed?
> Compare the amount of energy released when 1.0 kg of the uranium isotope 235U undergoes the fission reaction of Eq. (29-47) with the energy released when 1.0 kg of hydrogen undergoes the fusion reaction of Eq. (29-49).
> A variable inductor with negligible resistance is connected to an ac voltage source. How does the current in the inductor change if the inductance is increased by a factor of 3.0 and the driving frequency is increased by a factor of 2.0?
> Why is the muon sometimes called a “heavy electron”?
> Before a lightning strike can occur, the breakdown limit for damp air must be reached. If this occurs for an electric field of 3.33 × 105 V/m, what is the maximum possible height above Earth for the bottom of a thundercloud, which is at a potential 1.00
> Two atomic clocks are synchronized. One is put aboard a spaceship that leaves Earth at t = 0 at a speed of 0.750c. (a) When the spaceship has been traveling for 48.0 h (according to the atomic clock on board), it sends a radio signal back to Earth. When
> An airplane is traveling from New York to Paris, a distance of 5.80 × 103 km. Ignore the curvature of Earth. (a) If the cruising speed of the airplane is 350.0 km/h, how much time will it take for the airplane to make the round-trip on a calm day? (b)
> A horizontal desk surface measures 1.3 m × 1.0 m. If Earth’s magnetic field has magnitude 0.044 mT and is directed 65° below the horizontal, what is the magnetic flux through the desk surface?
> A block (mass m) hangs from a spring (spring constant k). The block is released from rest a distance d above its equilibrium position. (a) What is the speed of the block as it passes through the equilibrium point? (b) What is the maximum distance below
> (a) Explain why a transformer works for ac but not for dc. (b) Explain why a transformer designed to be connected to an emf of amplitude 170 V would be damaged if connected to a dc emf of 170 V.
> A submarine of mass 2.5 × 106 kg and initially at rest fires a torpedo of mass 250 kg. The torpedo has an initial speed of 100.0 m/s. What is the initial recoil speed of the submarine? Ignore the drag force of the water.
> A man is doing push-ups. He has a mass of 68 kg and his center of gravity is located at a horizontal distance of 0.70 m from his palms and 1.00 m from his feet. Find the forces exerted by the floor on his palms and feet.
> Suppose you are facing due north at sunrise. Sunlight is reflected by a store's display window as shown. Is the reflected light partially polarized? If so, in what direction?
> The Hubble Space Telescope uses a mirror of radius 1.2 m. Is its resolution better when detecting visible light or UV? Explain.
> A drag racer crosses the finish line of a 400.0 m track with a final speed of 104 m/s. (a) Assuming constant acceleration during the race, find the racer's time and the minimum coefficient of static friction between the tires and the road. (b) If, beca
> The charge on a capacitor in an ac circuit is q(t) = Q sin ωt. Using a small-angle approximation (Appendix A.9), we can write q(t) ≈ Qωt for times |t| ≪ 1/ω. What is the slope of the graph of q(t) at t = 0? This is equal to the current at t = 0, which is
> The number density of free electrons in silver is 5.85 × 1028 m−3. A strip of silver of thickness 0.050 mm and width 20.0 mm is placed in a magnetic field of 0.80 T. A current of 10.0 A is sent down the strip. (a) What is t
> If the magnetic fields produced by the x-, y-, and z-coils in an MRI (see Section 19.8) are changed too rapidly, the patient may experience twitching or tingling sensations. What do you think might be the cause of these sensations? Why does the much stro
> The mayor of a city proposes a new law to require that magnetic fields generated by the power lines running through the city be zero outside of the electric company's right of way. What would you say at a public discussion of the proposed law?
> In astronomy it is common to expose a photographic plate to a particular portion of the night sky for quite some time in order to gather plenty of light. Before leaving a plate exposed to the night sky, Matt decides to test his technique by exposing two
> At a point due north of the transmitter, how should a magnetic dipole antenna be oriented to serve as a receiver?
> On a cold, autumn day, Tuan is staring out of the window watching the leaves blow in the wind. One bright yellow leaf is reflecting light that has a predominant wavelength of 580 nm. (a) What is the frequency of this light? (b) If the window glass has
> A helium atom (mass 4.00 u) moving at 618 m/s to the right collides with an oxygen molecule (mass 32.0 u) moving in the same direction at 412 m/s. After the collision, the oxygen molecule moves at 456 m/s to the right. What is the velocity of the helium
> A string 2.0 m long is held fixed at both ends. If a sharp blow is applied to the string at its center, it takes 0.050 s for the pulses to travel to the ends of the string and return to the middle. What are the lowest three standing wave frequencies for
> A patient’s heart pumps 5.0 L of blood per minute into the aorta, which has a diameter of 1.8 cm. The average force exerted by the heart on the blood is 16 N. What is the average mechanical power output of the heart?
> Suppose you have a filling in one of your teeth, and, while eating some ice cream, you suddenly realize that the filling came out. One of the reasons the filling may have become detached from your tooth is the differential contraction of the filling rela
> A rotating flywheel slows down with constant angular acceleration due to friction in its bearings. At t = 0, its angular velocity is 420 rad/s. At t = 60 s, its angular velocity is 340 rad/s. (a) What is the angular velocity at t = 180 s? (b) Through h
> Two objects with masses m1 and m2 approach each other head-on with equal and opposite momenta so that the total momentum is zero. Show that, if the collision is elastic, the final speed of each object must be the same as its initial speed. (The final vel
> Estimate the magnetic field required at the LHC to make 7.0 TeV protons travel in a circle of circumference 27 km. Start by deriving an expression, using Newton's second law, for the field magnitude B in terms of the particle's momentum p, its charge q,
> The solar energy arriving at the top of Earth's atmosphere from the Sun has intensity 1.4 kW/m2. (a) How much mass does the Sun lose per day? (b) What percent of the Sun's mass is this?
> A flat square of side s0 at temperature T0 expands by Δs in both length and width when the temperature increases by ΔT. The original area is and the final area is (s0 + Δs)2 = A. Show that if Δs â
> Figure 29.7 is an energy level diagram for 208Tl. What are the energies of the photons emitted for the six transitions shown?
> At a point due north of the transmitter, how should a second ipole antenna be oriented to serve as a receiver?
> Find the height h of the pits on a CD (Fig. 25.6a). When the laser beam reflects partly from a pit and partly from land (the flat aluminum surface) on either side of the pit, the two reflected beams interfere destructively; h is chosen to be the smallest
> The inside of a cell membrane is at a potential of 90.0 mV lower than the outside. How much work does the electric field do when a sodium ion (Na+) with a charge of +e moves through the membrane from outside to inside?
> What is the maximum possible value of the angular momentum for an outer electron in the ground state of a bromine atom?
> Telescopes used in astronomy have large lenses (or mirrors). One reason is to let a lot of light in—important for seeing faint astronomical bodies. Can you think of another reason why it is an advantage to make these telescopes so large?
> Atmospheric pressure is about 1.0 × 105 Pa on average. (a) What is the downward force of the air on a desktop with surface area 1.0 m2? (b) Convert this force to pounds to help others understand how large it is. (c) Why does this huge force not cause
> Two gears A and B are turning in mesh. Gear A’s radius to the point of contact between the gears is 8.0 cm and that of gear B is 4.0 cm. (a) What is the linear speed of the contact point when gear A’s angular velocity
> Show, from XC = 1/(ωC), that the units of capacitive reactance are ohms.
> Aliens from the planet Jeenkah have based their temperature scale on the boiling and freezing temperatures of ethyl alcohol. These temperatures are 78°C and −114°C, respectively. The people of Jeenkah have six digits on each hand, so they use a base-12 n
> Imagine a person standing naked in a room at 23.0°C. The walls are well insulated, so they also are at 23.0°C. The person's surface area is 2.20 m2, and his basal metabolic rate is 2167 kcal/day. His emissivity is 0.97. (a) If the person's skin temperat
> A certain amount of energy must be supplied to increase the current through an inductor from 0 mA to 10 mA. Does it take the same amount of energy, more, or less to increase the current from 10 mA to 20 mA?
> A metal plate is attached to the end of a rod and positioned so that it can swing into and out of a perpendicular magnetic field pointing out of the plane of the paper as shown. In position 1, the plate is just swinging into the field; in position 2, the
> Why do eyeglasses, camera lenses, and binoculars with antireflective coatings often look faintly purple?
> Why does a crystal act as a three-dimensional grating for x-rays but not for visible light?
> In the microwave experiment of Example 25.1 and in the Michelson interferometer, we ignored phase changes due to reflection from a metal surface. Microwaves and light are inverted when they reflect from metal. Why were we able to ignore the 180° phase sh
> Resilin is a rubber-like protein that helps insects to fly more efficiently. The resilin, attached from the wing to the body, is relaxed when the wing is down and is extended when the wing is up. As the wing is brought up, some elastic energy is stored i
> 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
