Linearly polarized light of intensity I0 shines through two polarizing sheets. The second of the sheets has its transmission axis perpendicular to the polarization of the light before it passes through the first sheet. Must the intensity transmitted through the second sheet be zero, or is it possible that some light gets through? Explain.
> A grating with 5550 slits/cm has red light of 0.680 µm incident on it. The light shines through the grating onto a screen that is 5.50 m away. (a) What is the distance between adjacent slits on the grating? (b) How far from the central bright spot is th
> Natural gas is sold by volume. In the United States, the price charged is usually per cubic foot. Given the price per cubic foot, what other information would you need in order to calculate the price per mole?
> A spaceship is traveling away from Earth at 0.70c. The astronauts report home by radio every 4.0 h (by their own clocks). (a) At what interval are the reports sent to Earth, according to Earth clocks? (b) At what interval are the reports received by Ea
> Show that U = −2K for any gravitational circular orbit. [Hint: Use Newton’s second law to relate the gravitational force to the acceleration required to maintain uniform circular motion.]
> (a) Use dimensional analysis to show that the electric power output of a wind turbine is proportional to the cube of the wind speed. The relevant quantities on which the power can depend are the length L of the rotor blades, the density p of air (SI unit
> A clay roof tile of mass 2.7 kg slides down a roof inclined at 48° with respect to the horizontal. If the tile starts from rest 3.2 m from the edge of the roof and friction is negligible, how fast is it moving when it reaches the edge?
> The particle in a box model is often used to make rough estimates of energy level spacings. For a metal wire 10 cm long, treat a conduction electron as a particle confined to a one-dimensional box of length 10 cm. (a) Sketch the wave function ψ as a fun
> Water droplets in air create rainbows. Describe the physical situation that causes a rainbow. Should you look toward or away from the Sun to see a rainbow? Why is the secondary rainbow fainter than the primary rainbow?
> Repeat Problem 8 using the component (algebraic) method.
> Vector / has magnitude 7.1 and direction 14° below the +x-axis. Vector/ has x-component Cx = −1.8 and y-component Cy = −6.7. Compute: (a) the x- and y-components of /; (b) the magnitude and direction of / ; (c) the magnitude and direction of / ; (d
> A helicopter of mass M is lowering a truck of mass m onto the deck of a ship. (a) At first, the helicopter and the truck move downward together (the length of the cable doesn’t change). If their downward speed is decreasing at a rate of 0.10g, what is t
> Superman is standing 120 m horizontally away from Lois Lane. A villain drops a rock from 4.0 m directly above Lois. (a) If Superman is to intervene and catch the rock just before it hits Lois, what should be his minimum constant acceleration? (b) How f
> A parallel plate capacitor has a charge of 0.020 µC on each plate with a potential difference of 240 V. The parallel plates are separated by 0.40 mm of bakelite. What is the capacitance of this capacitor?
> In the Bohr model of the hydrogen atom, an electron moves in a circular orbit around a stationary proton. In its lowest-energy state (the ground state), the orbital radius is 0.0529 nm. (a) What are the electric forces on the electron and on the proton?
> A copper wire of length 3.0 m is observed to stretch by 2.1 mm when a weight of 120 N is hung from one end. (a) What is the diameter of the wire and what is the tensile stress in the wire? (b) If the tensile strength of copper is 400 MPa, what is the m
> The graph shows the tension in a rubber band as it is first stretched and then allowed to contract. As you stretch a rubber band, the tension at a particular length (on the way to a maximum stretch) is larger than the tension at that same length as you l
> In a color TV tube, electrons are accelerated through a potential difference of 20.0 kV. Some of the electrons strike the metal mask (instead of the phosphor dots behind holes in the mask), causing x- rays to be emitted. What is the smallest wavelength o
> If the electric field between plates (A) is 1.0 × 103 N/C in the +x- direction, what is the horizontal deflection (Δx) of the beam as it exits the region between plates (A)?
> By what factor is the momentum of a particle moving at 0.60c greater than the momentum of the same particle moving at 0.30c?
> Object A has mass 90.0 g and hangs from an insulated thread. When object B, which has a charge of +130 nC, is held nearby, A is attracted to it. In equilibrium, A hangs at an angle θ = 7.20° with respect to the vertical and is 5.00 cm to the left of B.
> Two springs with equal spring constants k are connected first in series (one after the other) and then in parallel (side by side) with an object hanging from the bottom of the combination. What is the effective spring constant of the two different arrang
> Vector / is directed along the positive y-axis is directed along the negative x-axis and has magnitude 1.0 unit. (a) What are the magnitude and direction of / ? (b) What are the x- and y-components of/ ?
> Many brass instruments have valves that increase the total length of the pipe from mouthpiece to bell. When a valve is depressed, is the fundamental frequency raised or lowered? What happens to the pitch?
> Electrons in an old television's CRT (see Sec. 16.5) are accelerated from rest by an electric field through a potential difference of 2.5 kV. In contrast to an oscilloscope, where the electron beam is deflected by an electric field, the beam is deflected
> A spring used in an introductory physics laboratory stores 10.0 J of elastic potential energy when it is compressed 0.20 m. Suppose the spring is cut in half. When one of the halves is compressed by 0.20 m, how much potential energy is stored in it? [Hin
> Two tuning forks, A and B, excite the next-to-lowest resonant frequency in two air columns of the same length, but A's column is closed at one end and B's column is open at both ends. What is the ratio of A's frequency to B's frequency?
> Your friend needs advice on her newest “acoustic sculpture.” She attaches one end of a steel wire, of diameter 4.00 mm and density 7860 kg/m3, to a wall. After passing over a pulley, located 1.00 m from the wall, the other end of the wire is attached to
> A circular loop of wire can be used as an antenna to sense the changing magnetic fields in an electromagnetic wave (such as a radio transmission). What is the advantage of using a coil with many turns rather than a single loop?
> When a block is suspended from a vertically hanging spring, it stretches the spring from its original length of 4.5 cm to a total length of 6.0 cm. The spring with the same block attached is then placed on a horizontal frictionless surface. The block is
> A lead rod and a common glass rod both have the same length when at 20.0°C. The lead rod is heated to 50.0°C. To what temperature must the glass rod be heated so that they are again at the same length?
> The fundamental frequency of the highest note on the piano is 4.186 kHz. Most musical instruments do not go that high; only a few singers can produce sounds with fundamental frequencies higher than around 1 kHz. Yet a good-quality stereo system must repr
> Six copper wires are characterized by their dimensions and by the current they carry. Rank the wires in order of decreasing drift velocity. (a) diameter 2 mm, length 2 m, current 80 mA (b) diameter 1 mm, length 1 m, current 80 mA (c) diameter 4 mm, lengt
> Using Faraday’s law, explain why it is impossible to have a magnetic wave without any electric component.
> Why do some telescopes produce an inverted image?
> Answer the questions in Problem 121 for a particle with total mechanical energy +100 J initially moving to the left at x = 15.0 cm.
> Two vectors, each of magnitude 4.0 cm, are inclined at a small angle a below the horizontal as shown. Let /. Sketch the direction of / and estimate its magnitude.
> A model sailboat is slowly sailing west across a pond at 0.33 m/s. A gust of wind gives the sailboat a constant acceleration of 0.30 m/s2 directed 28° south of west during a time interval of 2.0 s. (a) If the net force on the sailboat during the 2.0 s i
> The particle has a total mechanical energy of −100 J. At time t = 0, the particle is located at x = 8.0 cm and is moving to the left. (a) What is the particle’s potential energy at t = 0? What is its kinetic energy at this time? (b) What are the particl
> Suppose that current flows to the left through the inductor in Fig. 21.7a so that i is negative. (a) If the current is increasing in magnitude, what is the sign of Δi/Δt? (b) In what direction is the induced emf that opposes the increase in current? (
> A hair breaks under a tension of 1.2 N. What is the diameter of the hair? The tensile strength is 200 MPa.
> A 0.50 kg block, starting at rest, slides down a 30.0° incline with static and kinetic friction coefficients of 0.35 and 0.25, respectively (see the figure with Problem 75). After sliding 85 cm along the incline, the block slides across a frictionless ho
> Convert these to radian measure: (a) 30.0°, (b) 33.3 revolutions.
> A spaceship of mass m is traveling away from Earth at speed v. Its momentum has magnitude 2.5mv. (a) Find v. (b) An astronaut on the spaceship has a watch that ticks once every second. How often does the watch tick as measured by an Earth observer?
> In a simple model, the electron in a hydrogen atom orbits the proton at a radius of 53 pm and at a constant speed of 2.2 × 106 m/s. The orbital motion of the electron gives it an orbital magnetic dipole moment. (a) What is the current I in this current
> Find the radius and volume of the / nucleus.
> An object with a charge of 0.890 µC is placed at the center of a cube. What is the electric flux through one surface of the cube?
> Luke is trying to catch a pesky animal that keeps eating vegetables from his garden. He is building a trap and needs to use a spring to close the door to his trap. He has a spring in his garage, and he wants to determine the spring constant of the spring
> An electromagnetic flowmeter is to be used to measure blood speed. A magnetic field of 0.115 T is applied across an artery of inner diameter 3.80 mm. The Hall voltage is measured to be 88.0 μV. What is the average speed of the blood flowing in the artery
> If a clothes washer’s drum has a radius of 25 cm and spins at 4.0 rev/s, what is the strength of the apparent gravitational field to which the clothes are subjected? Ignore Earth’s gravity and express your answer as a multiple of g.
> Some feathers of the ruby-throated hummingbird have an iridescent green color due to interference. A simplified model of the step structure of the feather is shown in the figure. If the strongest reflection for normal incidence is at λ = 520
> What fundamental particles make up an atom?
> The power supply for a pacemaker is a small amount of radioactive 238Pu. This nuclide decays by alpha decay with a half-life of 87.7 yr. The pacemaker is typically replaced every 10.0 yr. (a) By what percentage does the activity of the 238Pu source decr
> Human feet and legs store elastic energy when walking or running. They are not nearly as efficient at doing so as kangaroo legs, but the effect is significant nonetheless. If not for the storage of elastic energy, a 70 kg man running at 4 m/s would lose
> It has only been fairly recently that 1.0 F capacitors have been readily available. A typical 1.0 F capacitor can withstand up to 5.00 V. To get an idea why it isn't easy to make a 1.0 F capacitor, imagine making a 1.0 F parallel plate capacitor using ti
> Why must we use absolute temperature (temperature in kelvins) in the ideal gas law (PV = NkBT)? Explain how using the Celsius scale would give nonsensical results.
> A jogger runs counterclockwise around a path of radius 90.0 m at constant speed. He makes 1.00 revolution in 188.4 s. At t = 0, he is heading due east. (a) What is the jogger’s instantaneous velocity at t = 376.8 s? (b) What is his instantaneous veloci
> A Canada goose floats with 25% of its volume below water. What is the average density of the goose?
> Jane is running from the ivory hunters in the jungle. Cheetah throws a 7.0 m long vine toward her. Jane leaps onto the vine with a speed of 4.0 m/s. When she catches the vine, it makes an angle of 20° with respect to the vertical. (a) When Jane is at he
> Why is the receiving antenna of a satellite dish placed at a set distance from the dish?
> A toroid is like a solenoid that has been bent around in a circle until its ends meet. The field lines are circular, as shown in the figure. What is the magnitude of the magnetic field inside a toroid of N turns carrying current I? Apply Ampere's law, fo
> Tarzan is running toward a deep gully. A tree branch with a vine hangs over the gully. Tarzan must grab the vine and swing across the gully to the other side, where the ground surface is 1.7 m higher. How fast does Tarzan have to be running to accomplish
> How far along the incline does the object travel before coming to rest and then sliding back down?
> An astronaut of mass 60.0 kg and a small asteroid of mass 40.0 kg are initially at rest with respect to the space station. The astronaut pushes the asteroid with a constant force of magnitude 250 N for 0.35 s. Gravitational forces are negligible. (a) Ho
> A string of 25 decorative lights has bulbs rated at 9.0 W, and the bulbs are connected in parallel. The string is connected to a 120 V power supply. (a) What is the resistance of each of these lights? (b) What is the current through each bulb? (c) Wha
> Consider a 60.0 W incandescent lightbulb and a 100.0 W incandescent lightbulb designed for use in a household lamp socket at 120 V. (a) What are the resistances of these two bulbs? (b) If they are wired together in a series circuit, which bulb shines b
> The bottom of a thundercloud is at a potential of −1.00 × 108 V with respect to Earth's surface. If a charge of −25.0 C is transferred to Earth during a lightning strike, find the electric potential energy released. (Assume that the system acts like a ca
> Beatrice needs to drag her suitcase again (see Example 3.8). This time she pulls with a force of 105 N at 38.0° with the horizontal. The coefficients of static and kinetic friction between the suitcase and the floor are 0.273 and 0.117, respectively. (a
> An airplane lands and starts down the runway at a southwest velocity of 55 m/s. What constant acceleration allows it to come to a stop in 1.0 km? Sketch a graph of vx(t).
> (a) At what temperature (if any) does the numerical value of the temperature in Celsius degrees equal its numerical value in Fahrenheit degrees? (b) At what temperature (if any) does the numerical value of the temperature in kelvins equal its numerical
> The electric potential at a distance of 20.0 cm from a point charge is +1.0 kV (assuming V = 0 at infinity). (a) Is the point charge positive or negative? (b) At what distance is the potential +2.0 kV?
> What is the speed of the object when it has moved 0.10 m along the incline?
> Find the magnetic field at the center of the square.
> Near Earth's surface the air contains both negative and positive ions due to radioactivity in the soil and cosmic rays from space. As a simplified model, assume there are 600.0 singly charged positive ions per cubic centimeter and 500.0 singly charged ne
> In an adventure movie, a 62.5 kg stunt woman falls 8.10 m and lands in a huge air bag. Her speed just before she hits the air bag is 10.5 m/s. (a) What is the total work done on the stunt woman during the fall? (b) How much work is done by gravity on t
> What does it mean if the power factor is 1? What does it mean if it is zero?
> A spring gun (k = 28 N/m) is used to shoot a 56 g ball horizontally. Initially the spring is compressed by 18 cm. The ball loses contact with the spring and leaves the gun when the spring is still compressed by 12 cm. What is the speed of the ball when i
> A 6.0 kg block, starting from rest, slides down a frictionless incline of length 2.0 m. When it arrives at the bottom of the incline, its speed is vf. At what distance from the top of the incline is the speed of the block 0.50vf?
> In a cathode ray tube, electrons are accelerated from rest by a constant electric force of magnitude 6.4 × 10−17 N during the first 2.0 cm of the tube's length; then they move at essentially constant velocity another 45 cm before hitting the screen. (a)
> A sigma baryon at rest decays into a lambda baryon and a photon: Σ0 → Λ0 + γ. The rest energies of Σ0 and Λ0 are 1192 MeV and 1116 MeV, respectively. What is the photon wavelength?
> One way to loosen the lid on a glass jar is to run it under hot water. How does that work?
> A car moving at 30 mi/h is stopped by jamming on the brakes and locking the wheels. The car skids 50 ft before coming to rest. How far would the car skid if it were initially moving at 60 mi/h? [Hint: You will not have to do any unit conversions if you s
> A hang glider moving at speed 9.5 m/s dives to an altitude 8.2 m lower. Ignoring drag, how fast is it then moving?
> A manufacturer is designing a shaving mirror, which is intended to be held close to the face. If the manufacturer wants the image formed to be upright and as large as possible, what characteristics should he choose? (Should the mirror be convex or concav
> A charged particle is observed to have a total energy of 0.638 MeV when it is moving at 0.600c. If this particle enters a linear accelerator and its speed is increased to 0.980c, what is the new value of the particle's total energy?
> The surface of the water in a swimming pool is completely still. Describe what you would see looking straight up toward the surface from under water. [Hint: Sketch some rays. Consider both reflected and transmitted rays at the water surface.]
> Yosemite Falls in California is about 740 m high, (a) What average power would it take for a 70 kg person to hike up to the top of Yosemite Falls in 1.5 h? (b) The human body is about 25% efficient at converting chemical energy to mechanical energy. Ho
> A point source of light is in front of a plane mirror. (a) Show that all the reflected rays, when extended back behind the mirror, intersect in a single point. [Hint: See Fig. 23.27a and use similar triangles.] (b) Show that the image point lies on a l
> A projectile with mass of 500 kg is launched straight up from Earth’s surface with an initial speed vi. What magnitude of vi enables the projectile to just reach a maximum height of 5RE, measured from the center of Earth? Ignore air friction as the proje
> A spaceship traveling at speed 0.13c away from Earth sends a radio transmission to Earth. (a) According to Galilean relativity, at what speed would the transmission travel relative to Earth? (b) Using Einstein's postulates, at what speed does the trans
> /can alpha decay to the ground state of / , or to any of the four excited states of / shown in Fig. 29.7. The maximum kinetic energy of the alpha particles emitted by / is 6.090 MeV. What other alpha particle kinetic energies are possible? [Hint: Estim
> Explain what is meant by a phase difference. Sketch graphs of i(t) and vC(t), given that the current leads the voltage by π/2 radians.
> A solenoid with a radius of 8.0 × 10−3 m and 200 turns/cm is used as an inductor in a circuit. When the solenoid is connected to a source of 15 V rms at 22 kHz, an rms current of 3.5 × 10−2 A is measured. Assume the resistance of the solenoid is negligib
> How long a pipe is needed to make a tuba whose lowest note is low C (frequency 130.8 Hz)? Assume that a tuba is a long straight pipe open at both ends.
> The electric field between plates (A) is zero. As the beam exits the space between plates (B), it has been deflected 2.0 mm downward (Δy = −2.0 mm). In what direction is the beam moving now?
> Two cows, with approximately 1.8 m between their front and hind legs, are standing under a tree during a thunderstorm. See the diagram with Conceptual Question 16. (a) If the equipotential surfaces about the tree just after a lightning strike are as sho
> A spaceship is moving away from Earth with a constant velocity of 0.80c with respect to Earth. The spaceship and an Earth station synchronize their clocks, setting both to zero, at an instant when the ship is near Earth. By prearrangement, when the clock
> A marble column with a cross-sectional area of 25 cm2 supports a load of 7.0 × 104 N. The marble has a Young’s modulus of 60 GPa and a compressive strength of 200 MPa. (a) What is the stress in the column? (b) What is the strain in the column? (c) If
> An elevator starts at rest on the ninth floor. At t = 0, a passenger pushes a button to go to another floor. The graph for this problem shows the acceleration ay of the elevator as a function of time. Let the y-axis point upward. (a) Has the passenger g
> An accelerometer—a device to measure acceleration—can be as simple as a small pendulum hanging in an airplane cockpit. An essentially similar accelerometer is found in the inner ear of vertebrates. Suppose you are flyi
> A tower outside the Houses of Parliament in London has a famous clock commonly referred to as Big Ben, the name of its 13 ton chiming bell. The hour hand of each clock face is 2.7 m long and has a mass of 60.0 kg. Assume the hour hand to be a uniform rod
