Suppose that an ideal capacitor and an ideal inductor are connected in series in an ac circuit. (a) What is the phase difference between vC(t) and vL(t)? [Hint: Since they are in series, the same current i(t) flows through both.] (b) If the rms voltages across the capacitor and inductor are 5.0 V and 1.0 V, respectively, what would an ac voltmeter (which reads rms voltages) connected across the series combination read?
> 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
> A uniform string of length 10.0 m and weight 0.25 N is attached to the ceiling. A weight of 1.00 kN hangs from its lower end. The lower end of the string is suddenly displaced horizontally. How long does it take the resulting wave pulse to travel to the
> If we know the potential at a single point, what (if anything) can we say about the magnitude of the electric field at that same point?
> It takes a flea 1.0 × 10−3 s to reach a peak speed of 0.74 m/s. (a) If the mass of the flea is 0.45 × 10−6 kg, what is the average power required? (b) Insect muscle has a maximum output of 60 W/kg. If 20% of the flea’s weight is muscle, can the muscle
> A lens is placed at the end of a bundle of optical fibers in an endoscope. The purpose of the lens is to make the light rays parallel before they enter the fibers (in other words, to put the image at infinity). What is the advantage of using a lens with
> A 6.2 cm by 2.2 cm parallel plate capacitor has the plates separated by a distance of 2.0 mm. (a) When 4.0 × 10−11 C of charge is placed on this capacitor, what is the electric field between the plates? (b) If a dielectric with dielectric constant of 5
> An axon has the outer part of its membrane positively charged and the inner part negatively charged. The membrane has a thickness of 4.4 nm and a dielectric constant κ = 5. If we model the axon as a parallel plate capacitor whose area is 5 µm2, what is i
> Show that the amplitudes of the graphs you made in Problem 89 satisfy the equation A′ = 2A cos (ωt), where A′ is the amplitude of the wave you plotted and A is 5.0 cm, the amplitude of the waves that were added together.
> A converging lens made from dense flint glass is placed into a container of transparent glycerin. Describe what happens to the focal length.
> Why must a blood pressure cuff be wrapped around the arm at the same vertical level as the heart?
> An electron is placed in a uniform electric field of strength 232 N/C. If the electron is at rest at the origin of a coordinate system at t = 0 and the electric field is in the positive x-direction, what are the x- and y-coordinates of the electron at t
> During a thunderstorm, some cows gather under a large tree. One cow stands facing directly toward the tree. Another cow stands at about the same distance from the tree, but it faces sideways (tangent to a circle centered on the tree). Which cow do you th
> The ball is released from rest when the thread makes an angle of 32° with the vertical. How fast is it moving when the thread is vertical?
> Calculate the kinetic energy of the alpha particle in Problem 25. This time, do not assume that the / nucleus is at rest after the reaction. Start by figuring out the ratio of the kinetic energies of the alpha particle and the / nucleus.
> A photoelectric experiment illuminates the same metal with six different ultraviolet sources. Both the wavelength and the intensity vary from one source to another. Rank the six situations in order of the stopping potential, largest to smallest. (a) λ =
> A curve in a stretch of highway has radius 610 m. The road is banked at angle 5.8° to the horizontal. The coefficient of static friction between the tires and road is 0.50. What is the fastest speed that a car can travel through the curve without skiddin
> The voltage across an inductor and the current through the inductor are related by vL = L Δi/Δt. Suppose that i(t) = I sin ωt. (a) Sketch a graph of i(t), showing at least one full cycle. (b) Using a small-angle approximation (Appendix A.9), find the s
> If an object is traveling at a constant velocity, is it necessarily traveling in a straight line? Explain.
> Repeat Problem 22, but now the copper washer and the steel bolt are both raised to the same temperature. At what temperature will the washer fit on the bolt?
> What are some of the advantages of a UV microscope over a visible light microscope? What are some of the disadvantages?
> An old highway is built out of concrete blocks of equal length. A car traveling on this highway feels a little bump at the joint between blocks. The passengers in the car feel that the ride is uncomfortable at a speed of 45 mi/h, but much smoother at spe
> Your friend balances a package with mass m = 10 kg on top of his head while standing. The mass of his upper body is M = 55 kg (about 65% of his total mass). Because the spine is vertical rather than horizontal, the force exerted by the sacrum on the spin
> A solenoid with 8500 turns per meter has radius 65 cm. The current in the solenoid is 25.0 A. A circular loop of wire with 100 turns and radius 8.00 cm is put inside the solenoid. The current in the circular loop is 2.20 A. What is the maximum possible m
> If a piece of white cardboard is placed at the location of a virtual object, what (if anything) would be seen on the cardboard?
> Estimate the minimum total kinetic energy of the 2H and 3H nuclei necessary to allow the fusion reaction of Eq. (29-49) to take place.
> A horizontal segment of pipe tapers from a cross-sectional area of 50.0 cm2 to 0.500 cm2. The pressure at the larger end of the pipe is 1.20 × 105 Pa, and the speed is 0.040 m/s. What is the pressure at the narrow end of the segment?
> The charge on a capacitor doubles. What happens to its capacitance?
> Four people sit in a car. The masses of the people are 45 kg, 52 kg, 67 kg, and 61 kg. The car’s mass is 1020 kg. When the car drives over a bump, its springs cause an oscillation with a frequency of 2.00 Hz. What would the frequency be if only the 45 kg
> You are hiking through a lush forest with some of your friends when you come to a large river that seems impossible to cross. However, one of your friends notices an old metal barrel sitting on the shore. The barrel is shaped like a cylinder and is 1.20
> You will be hiking to a lake with some of your friends by following the trails indicated on a map at the trail-head. The map says that you will travel 1.6 mi directly north, then 2.2 mi in a direction 35° east of north, then finally 1.1 mi in a direction
> A sphere of copper is subjected to 100 MPa of pressure. The copper has a bulk modulus of 130 GPa. By what fraction does the volume of the sphere change? By what fraction does the radius of the sphere change?
> A light wave passes through a hazy region in the sky. If the electric field vector of the emerging wave is one quarter that of the incident wave, what is the ratio of the transmitted intensity to the incident intensity?
> In Fig. 20.2, the distance between the rails is L = 5.0 cm. The metal rod is sliding to the right at v = 16 cm/s and the magnetic field has magnitude B = 0.75 T. The rod and rails have negligible resistance compared with the resistor (R = 180 Ω). Find (
> 1. Which of these statements are postulates of Einstein's special relativity? (1) The speed of light is the same in all inertial reference frames. (2) Moving clocks run slow. (3) Moving objects are contracted along the direction of motion. (4) The laws o
> An above-ground swimming pool is filled with water (total mass M) to a height h. Explain why the gravitational potential energy of the water (taking U = 0 at ground level) is /. Where does the factor of / come from? How much work must be done to fill t
> When we talk about the potential difference between the plates of a capacitor, shouldn't we really specify two points, one on each plate, and talk about the potential difference between those points? Or doesn't it matter which points we choose? Explain.
> A uniform magnetic field of 0.50 T is directed to the north. At some instant, a particle with charge +0.020 μC is moving with velocity 2.0 m/s in a direction 30° north of east. (a) What is the magnitude of the magnetic force on the charged particle? (b
> A gold wire of 0.50 mm diameter has 5.90 × 1028 conduction electrons per cubic meter. If the drift speed is 6.5 µm/s, what is the current in the wire?
> Color printers always use at least three different colors of ink or toner. Televisions and computer monitors have pixels of at least three different colors. Why are at least three necessary? [Hint: See Fig. 24.9.]
> Sheena can row a boat at 3.00 mi/h in still water. She needs to cross a river that is 1.20 mi wide with a current flowing at 1.60 mi/h. Not having her calculator ready, she guesses that to go straight across, she should head upstream at an angle of 25.0°
> A circular metal loop carries a current I as shown. The points are all in the plane of the page and the loop is perpendicular to the page. Sketch the loop, and draw vector arrows at the points A, B, C, D, and E to show the direction of the magnetic field
> Finola has a circuit with a 4.00 kΩ resistor, a 0.750 H inductor, and a capacitor of unknown value connected in series to a 440.0 Hz ac source. With an oscilloscope, she measures the phase angle to be 25.0°. (a) What is the value of the unknown capacito
> At a point due south of the transmitter, what is the direction of the wave’s magnetic field?
> A constant force, acting for 3.6 × 104 s (10 h), brings a spaceship of mass 2200 kg from rest to speed 0.70c. (a) What is the magnitude of the force? [Hint: Use the impulse-momentum theorem.] (b) What is the initial acceleration of the spaceship? Comme
> Why does a mirror hanging in a vertical plane seem to interchange left and right but not up and down? [Hint: Refer to Fig. 23.28. Instead of calling Grant's hands left and right, call them east and west. In Grant's image, are the east and west hands reve
> A transverse wave on a string is described by Plot the displacement y and the velocity vy versus t for one complete cycle of the point x = 0 on the string.
> Point P is at a potential of 500.0 kV, and point S is at a potential of 200.0 kV. The space between these points is evacuated. When a charge of +2e moves from P to S, by how much does its kinetic energy change?
> How much work is done by an applied force that moves two charges of 6.5 µC that are initially very far apart to a distance of 4.5 cm apart?
> If a uniform electric field exists in a region of space, is the potential the same at all points in the region? Explain.
> We can model some of the electrical properties of an unmyelinated axon as an electric cable covered with defective insulation so that current leaks out of the axon to the surrounding fluid. We assume the axon consists of a cylindrical membrane filled wit
> Four masses are arranged as shown. They are connected by rigid, massless rods of lengths 0.75 m and 0.50 m. What torque must be applied to cause an angular acceleration of 0.75 rad/s2 about the axis shown?
> (a) When ice floats in water at 0°C, what percent of its volume is submerged? (b) What is the specific gravity of ice?
> At a rock concert, the engineer decides that the music isn't loud enough. He turns up the amplifiers so that the amplitude of the sound, where you're sitting, increases by 50.0%. (a) By what percentage does the intensity increase? (b) How does the inte
> In a velocity selector, the electric and magnetic forces cancel if . Show that / must be in the same direction as / [Hint: Since is perpendicular to both and in a velocity selector, there are only two possibilities for the direction of /:
> A circular conducting loop with radius 3.40 cm is placed in a uniform magnetic field of 0.880 T with the plane of the loop perpendicular to the magnetic field, as shown. The loop is rotated 180° about the axis in 0.222 s. (a) As the loop begi
> Dash is standing on his frictionless skateboard with three balls, each with a mass of 100 g, in his hands. The combined mass of Dash and his skateboard is 60 kg. How fast should Dash throw the balls forward if he wants to move backward with a speed of 0.
> How many different hadrons are stable (as far as we know)?
> According to Maxwell, why is it impossible to have an electric wave without any magnetic component?
> Find the energy for a hydrogen atom in the stationary state n = 4.
> Stan and Ollie are standing next to a train track. Stan puts his ear to the steel track to hear the train coming. He hears the sound of the train whistle through the track 2.1 s before Ollie hears it through the air. How far away is the train?
> A stretched string has a fundamental frequency of 847 Hz. What is the fundamental frequency if the tension is increased by a factor of 3.0?
> You are bicycling along a straight north-south road. Let the x-axis point north. Describe your motion in each of the following cases. Example: ax > 0 and vx > 0 means you are moving north and speeding up. (a) ax > 0 and vx < 0. (b) ax = 0 and vx < 0.
> Under what special circumstances can kelvins or Celsius degrees be used interchangeably?
> At a point P, a distance R0 from a positive charge Q0, the electric field has a magnitude E0 = 100 N/C and the electric potential is V0 = 10 V. The charge is now increased by a factor of three, becoming 3Q0. (a) At what distance, RE, from the charge 3Q0
> An electroscope consists of a conducting sphere, conducting pole, and two metal foils (see Fig. 16.10). The electroscope is initially uncharged. (a) A positively charged rod is allowed to touch the conducting sphere and then is removed. What happens to
> The eyepiece of a Galilean telescope is a diverging lens. The focal points Fo and F′e coincide. In one such telescope, the lenses are a distance d = 32 cm apart and the focal length of the objective is 36 cm. A rhinoceros is viewed from
> An RC filter is shown. The filter resistance R is variable between 180 Ω and 2200 Ω and the filter capacitance is C = 0.086 µF. At what frequency is the output amplitude equal to times the input amplitude if R = (a
> A radio wave with a wavelength of 1200 m follows two paths to a receiver that is 25.0 km away. One path goes directly to the receiver and the other reflects from an airplane that is flying above the point that is exactly halfway between the transmitter a
