A portable radio requires an emf of 4.5 V. Olivia has only two nonrechargeable 1.5 V batteries, but she finds a larger 6.0 V battery. (a) How can she arrange the batteries to produce an emf of 4.5 V? Draw a circuit diagram. (b) Is it advisable to use this combination with her radio? Explain.
> The rogue starship Galaxa is being chased by the battle cruiser Millenia. The Millenia is catching up to the Galaxa at a rate of 0.55c when the captain of the Millenia decides it is time to fire a missile. First the captain shines a laser range finder to
> One cold and windy winter day, Zach notices a humming sound coming from his chimney, which is open at the top and closed at the bottom. He opens the chimney at the bottom and notices that the sound changes. He goes over to the piano to try to match the n
> Is the electric field inside a conductor always zero? If not, when is it not zero? Explain.
> If E = 0 everywhere throughout a region of space, what do we know is true about the potential at points in that region?
> A road with a radius of 75.0 m is banked so that a car can navigate the curve at a speed of 15.0 m/s without any friction. When a car is going 20.0 m/s on this curve, what minimum coefficient of static friction is needed if the car is to navigate the cur
> A sound wave of frequency 1231 Hz travels through air directly toward a wall, then through the wall out into air again. If the initial speed of the sound wave is 341 m/s and its speed in the wall is 620 m/s, what are (a) the initial wavelength of the so
> An object is placed on a scale. Under what conditions does the scale read something other than the object's weight, even though the scale is functioning properly and is calibrated correctly? Explain.
> Can the average speed and the magnitude of the average velocity ever be equal? If so, under what circumstances?
> For divers going to great depths, the composition of the air in the tank must be modified. The ideal composition is to have approximately the same number of O2 molecules per unit volume as in surface air (to avoid oxygen poisoning), and to use helium ins
> On a graph of vx versus time, what quantity does the area under the graph represent?
> The columns built by the ancient Greeks and Romans to support temples and other structures are tapered; they are thicker at the bottom than at the top. This certainly has an aesthetic purpose, but is there an engineering purpose as well? What might it be
> You are driving your car along a country road at a speed of 27.0 m/s. As you come over the crest of a hill, you notice a farm tractor 25.0 m ahead of you on the road, moving in the same direction as you at a speed of 10.0 m/s. You immediately slam on you
> Verify that the units of the rotational form of Newton's second law [Eq. (8-19)] are consistent. In other words, show that the product of a rotational inertia expressed in kg·m2 and an angular acceleration expressed in rad/s2 is a torque expressed in N·m
> An electron moving in the positive x-direction passes through a slit of width Δy = 85 nm. What is the minimum uncertainty in the electron's velocity in the y-direction?
> While testing speakers for a concert, Tomás sets up two speakers to produce sound waves at the same frequency, which is between 100 Hz and 150 Hz. The two speakers vibrate in phase with each other. He notices that when he listens at certain locations, th
> Two identical circular coils of wire are separated by a fixed center-to- center distance. Describe the orientation of the coils that would (a) maximize or (b) minimize their mutual inductance.
> Two loops of wire are next to each other in the same plane. (a) If the switch S is closed, does current flow in loop 2? If so, in what direction? (b) Does the current in loop 2 flow for only a brief moment, or does it continue? (c) Is there a magnetic
> What is the de Broglie wavelength of a proton with kinetic energy 1.0 TeV?
> An object moves in the positive x-direction under the influence of a force Fx. A graph of Fx versus vx is shown. (a) What is the instantaneous power (i.e., the rate at which the force does work on the object) when its speed is 10 m/s? (b) What is the i
> Objects that are at rest relative to Earth’s surface are in circular motion due to Earth’s rotation. What is the radial acceleration of an African baobab tree located at the equator?
> If E = 0 at a single point, then a point charge placed at that point will feel no electric force. What does it mean if the potential is zero at a point? Are there any assumptions behind your answer?
> 21. A stone is thrown at an angle of 20° below the horizontal from the top of a cliff. Assume no air resistance. One second after being thrown, the stone's velocity is at angle θ below the horizontal. Which is true? (a) θ = 0 (b) θ = 20° (c) 0 < θ < 20°
> Why are all parts of a conductor at the same potential in electrostatic equilibrium?
> Coherent green light with a wavelength of 520 nm and coherent violet light with a wavelength of 412 nm are incident on a double slit with slit separation of 0.020 mm. The interference pattern is displayed on a screen 72.0 cm away. (a) Find the separatio
> An electron in an atom has an angular momentum quantum number of 2. (a) What is the magnitude of the angular momentum of this electron in terms of ħ? (b) What are the possible values for the z- components of this electron's angular momentum? (c) Draw a
> Magnetic induction is the principle behind the operation of mechanical speedometers used in automobiles and bicycles. In the drawing, a simplified version of the speedometer, a metal disk is free to spin about the vertical axis passing through its center
> An electron is accelerated from rest through a potential difference ΔV. If the electron reaches a speed of 7.26 × 106 m/s, what is the potential difference? Be sure to include the correct sign. (Does the electron move through an increase or a decrease in
> Objects that are at rest relative to Earth’s surface are in circular motion due to Earth’s rotation. What is the radial acceleration of a painting hanging in the Prado Museum in Madrid, Spain, at a latitude of 40.2&Aci
> A point charge moves to a region of higher potential and yet the electric potential energy decreases. How is this possible?
> At the Stanford Linear Accelerator, electrons and positrons collide together at very high energies to create other elementary particles. Suppose an electron and a positron, each with rest energies of 0.511 MeV, collide to create a proton (rest energy 938
> In the United States, the ac household current oscillates at a frequency of 60 Hz. In the time it takes for the current to make one oscillation, how far has the electromagnetic wave traveled from the current- carrying wire? This distance is the wavelengt
> A circular conducting loop with radius 1.8 cm is placed in a uniform magnetic field of 0.88 T with the plane of the coil perpendicular to the magnetic field as shown. The magnetic field decreases to 0.36 T in a time interval of 29 ms. What is the average
> A parallel plate capacitor has a capacitance of 2.0 µF and plate separation of 1.0 mm. (a) How much potential difference can be placed across the capacitor before dielectric breakdown of air occurs (Emax = 3 × 106 V/m)? (b) What is the magnitude of the
> Points A and B are at the same potential. What is the total work that must be done by an external agent to move a charge from A to B? Does your answer mean that no external force need be applied? Explain.
> A charged particle is accelerated from rest through a potential difference ΔV. The particle then passes straight through a velocity selector (field magnitudes E and B). Derive an expression for the charge-to-mass ratio (q/m) of the particle in terms of Δ
> What are some of the advantages of using mirrors rather than lenses for astronomical telescopes?
> 11. A woman stands on a bathroom scale in an elevator that is not moving. The scale reads 500 N. The elevator then moves downward at a constant velocity of 4.5 m/s. What does the scale read while the elevator descends with constant velocity? (a) 100 N (b
> In a reciprocating saw, a Scotch yoke converts the rotation of the motor into the back-and-forth motion of the blade. The Scotch yoke is a mechanical device used to convert oscillatory motion to circular motion or vice versa. A wheel with a fixed knob ro
> The motion of a simple pendulum is approximately SHM only if the amplitude is small. Consider a simple pendulum that is released from a horizontal position (θi = 90° in Fig. 10.23). (a) Using conservation of energy, find the speed of the pendulum bob at
> The f-stop of a camera lens is defined as the ratio of the focal length of lens to the diameter of the aperture. A large f-stop therefore means a small aperture. If diffraction is the only consideration, would you use the largest or the smallest f-stop t
> An object is subjected to two constant forces that are perpendicular to each other. Can a set of x- and y-axes be chosen so that the acceleration of the object has only one nonzero component? If so, how? Explain.
> Suppose some astronauts have landed on Mars. When the astronauts ask a question of mission control personnel on Earth, what is the shortest possible time they have to wait for a response? The average distance from Mars to the Sun is 2.28 × 1011 m.
> Two sheets of ideal polarizing material are placed with their transmission axes at right angles to each other. A third polarizing sheet is placed between them with its transmission axis at 45° to the axes of the other two. (a) If unpolarized light of in
> Four long straight wires, each with current I, overlap to form a square with side 2r. (a) Find the magnetic field at the center of the square. (b) Compare your answer with the magnetic field at the center of a circular loop of radius r carrying current
> A 1500 kg car moving east at 17 m/s collides with a 1800 kg car moving south at 15 m/s, and the two cars stick together. (a) What is the velocity of the cars right after the collision? (b) How much kinetic energy was converted to another form during th
> If a capacitor has a capacitance of 10.2 µF and we wish to lower the potential difference across the plates by 60.0 V, what magnitude of charge will we have to remove from each plate?
> In aviation, a standard rate turn proceeds at an angular speed of 180° per minute. What is the radius of a standard rate turn for a plane moving at 240 m/s?
> Roger is in a ship offshore and listening to a baseball game on his radio. He notices that there is destructive interference when seaplanes from the nearby Coast Guard station are flying directly overhead at elevations of 780 m, 975 m, and 1170 m. The br
> (a) If you measure the ship that passes you in Problem 76 to be 24 m long, how long will the observers on Earth measure that ship to be? (b) If there is a rod on your spaceship that you measure to be 24 m long, how long will the observers on Earth measu
> Zach insists that the seasons are caused by the elliptical shape of Earth’s orbit. He says that it is summer when Earth is closest to the Sun and winter when it is farthest away from the Sun. What evidence can you think of to show that the seasons are no
> In musical acoustics, a frequency ratio of 2:1 is called an octave. Humans with extremely good hearing can hear sounds ranging from 20 Hz to 20 kHz, which is approximately 10 octaves (since 210 = 1024 ≈ 1000). (a) Approximately how many octaves of visib
> (a) In double-slit interference, how does the slit separation affect the distance between adjacent interference maxima? (b) How does the distance between the slits and screen affect that separation? (c) If you are trying to resolve two closely spaced m
> The International Space Station (ISS) has a mass of 4.5 × 105 kg and orbits Earth at a speed of 7.7 km/s. By what percentage does the approximate momentum of the ISS calculated nonrelativistically differ from the relativistic momentum? [Hint: Use one of
> A positive charge is initially at rest in an electric field and is free to move. Does the charge start to move toward a position of higher or lower potential? What happens to a negative charge in the same situation?
> Light visible to humans consists of electromagnetic waves with wavelengths (in air) in the range 400–700 nm (4.0 × 10−7 m to 7.0 × 10−7 m). The speed of light in air is 3.0 × 108 m/s. What are the frequencies of electromagnetic waves that are visible?
> Using the results of Problem 75, we can find the electric field at any radius for any spherically symmetrical charge distribution. A solid sphere of charge of radius R has a total charge of q uniformly spread throughout the sphere. (a) Find the magnitud
> What is the potential energy if a third point charge q = −4.2 nC is placed at point b?
> 1. Which one of these statements is true? (a) The principal quantum number of the electron in a hydrogen atom does not affect its energy. (b) The principal quantum number of an electron in its ground state is zero. (c) The orbital angular momentum quantu
> A curve in a stretch of highway has radius 512 m. The road is unbanked. The coefficient of static friction between the tires and road is 0.70. (a) What is the maximum speed that a car can travel around the curve without skidding? (b) Explain what happe
> A beam of neutrons has the same de Broglie wavelength as a beam of photons. Is it possible that the energy of each photon is equal to the kinetic energy of each neutron? If so, at what de Broglie wavelength(s) does this occur? [Hint: For the neutron, use
> Glenda drops a coin from ear level down a wishing well. The coin falls a distance of 7.00 m before it strikes the water. If the speed of sound is 343 m/s, how long after Glenda releases the coin will she hear a splash?
> Find the molar mass of ammonia (NH3).
> A thin film of oil with index of refraction of 1.50 sits on top of a pool of water with index of refraction of 1.33. When light is incident on this film, a maximum is observed in reflected light at 480 nm and a minimum is observed in reflected light at 6
> If rays from points on an object are converging as they enter a lens, is the object real or virtual?
> Why must projectors and cameras form real images? Does the lens in the eye form real or virtual images on the retina?
> The windings of an electromagnet have inductance L = 8.0 H and resistance R = 2.0 Ω. A 100.0 V dc power supply is connected to the windings by closing switch S2. (a) A few minutes later, what is the current in the windings? (b) The electrom
> A car drives around a curve with radius 410 m at a speed of 32 m/s. The road is banked at 5.0°. The mass of the car is 1400 kg. (a) What is the frictional force on the car? (b) At what speed could you drive around this curve so that the force of fricti
> What causes chromatic aberration? What can be done to compensate for chromatic aberration?
> A star is moving away from Earth at a speed of 2.4 × 108 m/s. Light of wavelength 480 nm is emitted by the star. What is the wavelength as measured by an Earth observer?
> For an ideal inductor in an ac circuit, explain why the voltage across the inductor must be zero when the current is maximum.
> A hot air balloon is floating in equilibrium with the surrounding air. (a) How does the pressure inside the balloon compare with the pressure outside? (b) How does the density of the air inside compare to the density outside?
> A parallel plate capacitor has a capacitance of 1.20 nF. There is a charge of 0.80 µC on each plate. How much work must be done by an external agent to double the plate separation while keeping the charge constant?
> The graph shows x(t) for an object traveling along the x-axis. Plot vx as a function of time for this object from t = 0 to t = 8 s.
> A man requires reading glasses with +2.0 D refractive power to read a book held 40.0 cm away with a relaxed eye. Assume the glasses are 2.0 cm from his eyes. (a) What is his uncorrected far point? (b) What refractive power lenses should he use for dist
> A solid copper disk of radius R rotates at angular velocity ω in a perpendicular magnetic field B. The figure shows the disk rotating clockwise and the magnetic field into the page. (a) Is the charge that accumulates on the edge of the disk p
> An African swallow carrying a very small coconut is flying horizontally with a speed of 18 m/s. (a) If it drops the coconut from a height of 10 m above Earth, how long will it take before the coconut strikes the ground? (b) At what horizontal distance
> A bird is perched on a high-voltage power line whose potential varies between −100 kV and +100 kV. Why is the bird not electrocuted?
> A charged parallel plate capacitor has the space between the plates filled with air. The capacitor has been disconnected from the battery that charged it. Describe quantitatively what happens to the capacitance, the potential difference, the charge on th
> In some textbooks, the electric field is called the flux density. Explain the meaning of this term. Does flux density mean the flux per unit volume? If not, then what does it mean?
> A parallel plate capacitor has the space between the plates filled with a slab of dielectric with κ = 3. While the capacitor is connected to a battery, the dielectric slab is removed. Describe quantitatively what happens to the capacitance, the potential
> An instrument known as an atomic force microscope (AFM) can be used to measure forces between atoms or molecules at the nanometer scale. Suppose you find the elasticity of biological membranes by measuring the indentation of the force probe into the memb
> At a grocery store, a spring scale (spring constant = 450 N/m) hangs near the produce section. The spring hangs vertically with a 0.250 kg pan suspended from its lower end. Jenna drops a 2.20 kg bag of oranges from a height of 30.0 cm above the pan. The
> The particle in a box model is often used to make rough estimates of ground-state energies. Suppose that you have a neutron confined to a one-dimensional box of length equal to a nuclear diameter (say 10−14 m). What is the ground-state energy of the conf
> In a transformer, two coils are wound around an iron core; an alternating current in one coil induces an emf in the second. The core is normally made of either laminated iron—thin sheets of iron with an insulating material between them—or a bundle of par
> Photons of wavelength 350 nm are incident on a metal plate in a photocell, and electrons are ejected. A stopping potential of 1.10 V is able to just prevent any of the ejected electrons from reaching the opposite electrode. What is the maximum wavelength
> How far does a beam of light travel in 1 ns?
> Dry air breaks down for an electric field of about 3000 V/mm. Is it possible to build a parallel plate capacitor with a plate spacing of 1 mm that can be charged to a potential difference greater than 3000 V? If so, explain how.
> The figure shows a schematic diagram of a defective eye. What is this defect called?
> 1. A leopard starts from rest at t = 0 and runs in a straight line with a constant acceleration until t = 3.0 s. The distance covered by the leopard between t = 1.0 s and t = 2.0 s is (a) the same as the distance covered during the first second. (b) twic
> A neutron, with rest energy 939.6 MeV, has momentum 935 MeV/c downward. What is its total energy?
> Two long, straight wires, each with a current of 12.0 A, are placed on two corners of an equilateral triangle with sides of length 2.50 cm as shown. Both of the wires have a current into the page. (a) What is the magnetic field at the third corner of th
> You are asked to hang a uniform beam and sign using a cable that has a breaking strength of 417 N. The store owner desires that it hang out over the sidewalk as shown. The sign has a weight of 200.0 N and the beam's weight is 50.0 N. The beam's length is
> A beam of electrons traveling with a speed of 3.0 × 107 m/s enters a uniform, downward electric field of magnitude 2.0 × 104 N/C between the deflection plates of an oscilloscovpe. The initial velocity of the electrons is perpend
> A stone is launched straight up by a slingshot. Its initial speed is 19.6 m/s, and the stone is 1.50 m above the ground when launched. (a) How high above the ground does the stone rise? (b) How much time elapses before the stone hits the ground?
> Humans can hear sounds with frequencies up to about 20.0 kHz, but dogs can hear frequencies up to about 40.0 kHz. Dog whistles are made to emit sounds that dogs can hear but humans cannot. If the part of a dog whistle that actually produces the high freq
> The electric field just above Earth's surface on a clear day in an open field is about 150 V/m downward. Which is at a higher potential: Earth or the upper atmosphere?
> In Fig. 17.13, why is the person touching the dome of the van de Graaff generator not electrocuted even though there may be a potential difference of hundreds of thousands of volts between him and the ground?
> Under favorable conditions, the human eye can detect light waves with intensities as low as 2.5 × 10−12 W/m2. (a) At this intensity, what is the average power incident on a pupil of diameter 9.0 mm? (b) If this light is produced by an isotropic source 1
> At what time is energy stored in the inductor 0.10 times its initial value?
> Another example of motional emf is a rod attached at one end and rotating in a plane perpendicular to a uniform magnetic field. We can analyze this motional emf using Faraday’s law. (a) Consider the area that the rod sweeps out in each
