A plastic water bottle open at the top is three-fourths full of water and is placed on a scale. The bottle has an indentation for a label midway up the side, and a strap has been placed around this indentation. If the strap is tightened, so the bottle is squeezed in at the middle and the water level is forced to rise, what happens to the reading on the scale? Is the water pressure at the bottom of the bottle the same?
> A pendulum bob hung from a string of length L is released from height h above the bottom of its swing. The pendulum’s swing is interrupted by a horizontal peg at height r above the bottom of the pendulum’s swing (point
> A photon is incident on an electron at rest. The scattered photon has a wavelength of 2.81 pm and moves at an angle of 29.5° with respect to the direction of the incident photon. (a) What is the wavelength of the incident photon? (b) What is the final
> Why are several layers of clothing warmer than one coat of equal weight?
> A certain pipe has resonant frequencies of 234 Hz, 390 Hz, and 546 Hz, with no other resonant frequencies between these values. (a) Is this a pipe open at both ends or closed at one end? (b) What is the fundamental frequency of this pipe? (c) How long
> Why is drinking water in a camp located near the equator often kept in porous jars?
> A 40 Hz sound wave is barely audible at a sound intensity level of 60 dB. What is the displacement amplitude of this sound wave? Compare it with the average distance between molecules in air at room temperature, about 3 nm.
> If the angle of incidence is greater than the angle of refraction for a light beam passing an interface, what can be said about the relative values of the indices of refraction and the speed of light in the first and second media?
> In the diagram, regions A and C extend far to the left and right, respectively. The electric field due to the two point charges is zero at some point in which region or regions? Explain.
> The Bohr theory of the hydrogen atom ignores gravitational forces between the electron and the proton. Make a calculation to justify this omission. [Hint: Find the ratio of the gravitational and electrostatic forces acting on the electron due to the prot
> The tension in a guitar string is increased by 15%. What happens to the fundamental frequency of the string?
> (a) Assume Earth is a uniform solid sphere. Find the kinetic energy of Earth due to its rotation about its axis. (b) Suppose we could somehow extract 1.0% of Earth's rotational kinetic energy to use for other purposes. By how much would that change the
> A 0.67 mH inductor and a 130Ω. resistor are placed in series with a 24 V battery. (a) How long will it take for the current to reach 67% of its maximum value? (b) What is the maximum energy stored in the inductor? (c) How long will it take for the ene
> A pendulum consists of a bob of mass m attached to the end of a cord of length L. The pendulum is released from a point at a height of L/2 above the lowest point of the swing. What is the tension in the cord as the bob passes the lowest point?
> In a game of pool, suppose that the cue ball initially moves in the −x- direction. After a collision with the 4-ball of equal mass, the cue ball moves at 52.0° above the −x-axis and the 4-ball moves at 38.0° below the −x-axis. Find the ratio of the balls
> A particle collides with a hydrogen atom in the n = 2 state, transferring 15.0 eV of energy to the atom. As a result, the electron breaks away from the hydrogen nucleus. What is the kinetic energy of the electron when it is far from the nucleus?
> A 750 kg automobile is moving at 20.0 m/s at a height of 5.0 m above the bottom of a hill when it runs out of gasoline. The car coasts down the hill and then continues coasting up the other side until it comes to rest. Ignoring frictional forces and air
> The figure shows the lowest six energy levels of the outer electron in sodium. In the ground state, the electron is in the “3s” level. (a) What is the ionization energy of sodium? (b) What is the wavelength of the ra
> Two copper wires, one double the diameter of the other, have the same current flowing through them. If the thinner wire has a drift speed ν1 and the thicker wire has a drift speed ν2, how do the drift speeds of the charge carriers compare?
> Why do we call the temperature 0 K “absolute zero”? How is 0 K fundamentally different from 0°C or 0°F?
> A 60.0 kg woman stands at one end of a 120 kg raft that is 6.0 m long. The other end of the raft is 0.50 m from a pier. (a) The woman walks toward the pier until she gets to the other end of the raft and stops there. Now what is the distance between the
> When a virtual image is formed by a mirror, is it in front of the mirror or behind it? What about a real image?
> A capacitor and a resistor are connected in parallel across an ac source. The reactance of the capacitor is equal to the resistance of the resistor. Assuming that iC(t) = I sin ωt, sketch graphs of iC(t) and iR(t) on the same axes.
> A transverse wave on a string is described by Find the maximum velocity and the maximum acceleration of a point on the string. Plot graphs for displacement y versus t, velocity vy versus t, and acceleration ay versus t at x = 0.
> A neutron (mass 939.565 MeV/c2) disintegrates into a proton (mass 938.272 MeV/c2), an electron (mass 0.5110 MeV/c2), and an antineutrino (mass negligibly small). What is the sum of the kinetic energies of the particles produced, if the neutron was at res
> The diameter of a certain artery has decreased by 25% due to arteriosclerosis. (a) If the same amount of blood flows through it per unit time as when it was unobstructed, by what percentage has the blood pressure difference between its ends increased?
> An x-ray photon of initial frequency 3.0 × 1019 Hz collides with a free electron at rest; the scattered photon moves off at 90°. What is the frequency of the scattered photon?
> Two parallel long straight wires are suspended by strings of length L = 1.2 m. Each wire has mass per unit length 0.050 kg/m. When one wire carries 25.0 A of current and the other carries 100.0 A, the wires swing apart. (a) How far apart are the wires i
> Grant jumps 1.3 m straight up into the air to slam-dunk a basketball into the net. With what speed did he leave the floor?
> An electron beam in an oscilloscope is deflected by the electric field produced by oppositely charged metal plates. If the electric field between the plates is 2.00 × 105 N/C directed downward, what is the force on each electron when it passes between th
> Why do lakes and rivers freeze first at their surfaces?
> (a) Calculate the capacitance per unit length of an axon of radius 5.0 µm (see Fig. 17.14). The membrane acts as an insulator between the conducting fluids inside and outside the neuron. The membrane is 6.0 nm thick and has a dielectric constant of 7.0.
> (a) Why is the coolant fluid in an automobile kept under high pressure? (b) Why do radiator caps have safety valves, allowing you to reduce the pressure before removing the cap? [Hint: See Fig. 14.7a, the phase diagram for water.]
> Where would you place a third small object with the same charge so that the electric field is zero at the corner of the square labeled A?
> For human eyes, about 70% of the refraction occurs at the cornea; less than 25% occurs at the two surfaces of the lens. Why? [Hint: Consider the indices of refraction.] Is the same thing true for fish eyes?
> Objects that are at rest relative to Earth’s surface are in circular motion due to Earth’s rotation. (a) What is the radial acceleration of an object at the equator? (b) Is the object’s apparent weight greater or less than its weight? Explain. (c) By
> In a conventional exterior wall, a 2 × 6 wooden stud is placed every 16 in. (A stud is an upright support.) The stud runs all the way from the exterior siding to the interior wall and the spaces between studs are filled with insulation. In o
> A hollow metal sphere carries a charge of 6.0 µC. A second hollow metal sphere with a radius that is double the size of the first carries a charge of 18.0 µC. The two spheres are brought into contact with each other, then separated. How much charge is on
> For a capacitor in an ac circuit, explain why the current must be zero when the voltage across the capacitor is maximum.
> Why is the passenger's side mirror in many cars convex rather than plane or concave?
> A karate student hits downward on a stack of concrete blocks supported at both ends. A block breaks. Explain where it starts to break first, at the bottom or at the top. (The block experiences shear, compressive, and tensile stresses. Recall that concret
> Even though heat is not a fluid, Eq. (14-13) has a close analogy in Poiseuille's law, which describes the viscous flow of a fluid through a pipe (see Problem 9.68). (a) Explain the analogy. (b) For two or more thermal conductors in series, the total th
> Two objects with the same surface area are inside an evacuated container. The walls of the container are kept at a constant temperature. Suppose one object absorbs a larger fraction of incident radiation than the other. Explain why that object must emit
> The vertical displacement d of light rays parallel to the axis of a lens is measured as a function of the vertical displacement h of the incident ray from the principal axis as shown in part (a) of the figure. The data are graphed in part (b) of the fi
> In a nuclear reactor, a neutron moving at speed vi in the positive x- direction strikes a deuteron, which is at rest. The neutron is deflected by 90.0° and moves off with speed 0.577vi in the positive y-direction. Find the x- and y-components of the deut
> A thin circular hoop is suspended from a knife edge. Its rotational inertia about the rotation axis (along the knife) is I = 2mr2. Show that it oscillates with the same frequency as a simple pendulum of length equal to the diameter of the hoop.
> Many homes are heated with “radiators,” which are hollow metal devices filled with hot water or steam and located in each room of the house. They are sometimes painted with metallic, high-gloss silver paint so that they look well polished. Does this make
> A town is considering using its lake as a source of power. The average temperature difference from the top to the bottom is 15°C, and the average surface temperature is 22°C. (a) Assuming that the town can set up a reversible engine using the surface an
> The diagram shows a simplified household circuit. Resistor r1 = 240.0 Ω represents a lightbulb; resistor r2 = 12.0 Ω represents a hair dryer. The resistors r = 0.50 Ω (each) represent the resistance of the wiring in th
> How many moles of He are in 13 g of He?
> A man with a mass of 70 kg stands on one foot. His femur has cross-sectional area of 8.0 cm2 and uncompressed length 50 cm. (a) How much shorter is the femur when he stands on one foot? (b) What is the fractional length change of the femur when the per
> What is the velocity of the scattered electron in Problem 26?
> A room in which the air temperature is held constant may feel warm in the summer but cool in the winter. Explain. [Hint: The walls are not necessarily at the same temperature as the air.]
> (a) Write an equation for a surface seismic wave moving in the −x- direction with amplitude 2.0 cm, period 4.0 s, and wavelength 4.0 km. Assume the wave is harmonic, x is measured in meters, and t is measured in seconds. (b) What is the maximum speed of
> The coefficient of linear expansion of brass is 1.9 × 10−5 °C−1. At 20.0°C, a hole in a sheet of brass has an area of 1.00 mm2. How much larger is the area of the hole at 30.0°C?
> The George Washington Bridge crosses the Hudson River between New York and New Jersey. The span of the steel bridge is about 1.6 km. If the temperature can vary from a low of −15°F in winter to a high of 105°F in summer, by how much might the length of t
> Suppose your handheld calculator will show six places beyond the decimal point. At what minimum speed would an object have to be traveling so that gamma can be seen to be different from 1 on your calculator display? That is, how fast should an object tra
> An astronaut has spent a long time in the International Space Station (ISS) traveling at 7.66 km/s. When he returns to Earth, he is 50 ms younger than his twin brother. How long was he on the ISS? [Hint: Use an approximation from Appendix A.9]
> An object connected to an ideal spring is oscillating without friction on a horizontal surface. Sketch graphs of the kinetic energy, potential energy, and total energy as functions of time for one complete cycle.
> A number of wires carry currents into or out of the page as indicated in the figure. (a) Using loop 1 for Ampere's law, what is the net current through the interior of the loop? (b) Repeat for loop 2.
> A certain fixed length L of wire carries a current I. (a) Show that if the wire is formed into a square coil, then the maximum torque in a given magnetic field B is developed when the coil has just one turn. (b) Show that the magnitude of this torque is
> An apparatus is designed to study insects at an acceleration of magnitude 980 m/s2 (= 100g). The apparatus consists of a 2.0 m rod with insect containers at either end. The rod rotates about an axis perpendicular to the rod and at its center. (a) How fa
> A tiny hole is made in the center of the negatively and positively charged plates of a capacitor, allowing a beam of electrons to pass through and emerge from the far side. If 40.0 V are applied across the capacitor plates and the electrons enter through
> If the frictional force on the sliding crate has magnitude 19.4 N and the tension in the rope is 121.5 N, find the total work done on the sliding crate.
> What is the ground state energy, according to Bohr theory, for (a) He+, (b) Li2+, (c) deuterium (an isotope of hydrogen whose nucleus contains a neutron as well as a proton)?
> Which possesses more total internal energy, the water within a large, partially ice-covered lake in winter or a 6 cup teapot filled with hot tea? Explain.
> (a) What is the pressure amplitude of a sound wave with an intensity level of 120.0 dB in air? (b) What maximum force does this wave exert on an eardrum of area 0.550 × 10−4 m2?
> When an old movie has a scene of someone ironing, the person is often shown testing the heat of a hot flat iron with a moistened finger. Why is this safe to do?
> If the mass of the drop is 1.0 × 10−15 kg and it remains stationary when the potential difference between the plates is 9.76 kV, what is the magnitude of the charge on the drop? (Ignore the small buoyant force on the drop.)
> Consider the following decay process: π+ → μ+ + ν. The mass of the pion (π+) is 139.6 MeV/c2, the mass of the muon (μ+) is 105.7 MeV/c2, and the mass of the neutrino (ν) is negligible. If the pion is initially at rest, what is the total kinetic energy of
> A study of food preservation in Britain discovered that the temperature of meat that is kept in transparent plastic packages and stored in open and lighted freezers can be as much as 12°C above the temperature of the freezer. Why is this? How could this
> An electromagnet is made by inserting a soft iron core into a solenoid. The solenoid has 1800 turns, radius 2.0 cm, and length 15 cm. When 2.0 A of current flows through the solenoid, the magnetic field inside the iron core has magnitude 0.42 T. What is
> The drawing shows a snapshot of a transverse wave moving to the left on a string. The wave speed is 10.0 m/s. At the instant the snapshot is taken, (a) in what direction is point A moving? (b) In what direction is point B moving? (c) At which of these
> When a double slit is illuminated with light of wavelength 510 nm, the interference maxima on a screen 2.4 m away gradually decrease in intensity on either side of the 2.40 cm wide central maximum and reach a minimum in a spot where the fifth-order maxim
> Would heat loss be reduced or increased by increasing the air gap, usually about 1 cm, between commercially made double-paned windows? Explain your reasoning. [Hint: Consider convection.]
> A gibbon, hanging onto a horizontal tree branch with one arm, swings with a small amplitude. The gibbon’s CM is 0.40 m from the branch, and its rotational inertia divided by its mass is I/m = 0.25 m2. Estimate the frequency of oscillation.
> The focal length of a concave mirror is 4.00 m and an object is placed 3.00 m in front of the mirror. Describe the image in terms of real, virtual, upright, and inverted.
> A harpsichord string of length 1.50 m and linear mass density 25.0 mg/m vibrates at a fundamental frequency of 450.0 Hz. (a) What is the speed of the transverse string waves? (b) What is the tension? (c) What are the wavelength and frequency of the so
> An electron is suspended in a vacuum between two oppositely charged horizontal parallel plates. The separation between the plates is 3.00 mm. (a) What are the signs of the charge on the upper and on the lower plates? (b) What is the voltage across the
> An object moves in SHM. Its position as a function of time is x(t) = A cos ωt. (a) Apply conservation of energy to show that vx(t) = ±ωA sin ωt. [Hint: See Appendix A.7 for a useful trigonometric identity.] (b) Then refer to a graph of x(t) to explain
> The tension in a ligament in the human knee is approximately proportional to the extension of the ligament, if the extension is not too large. If a particular ligament has an effective spring constant of 150 N/mm as it is stretched, (a) what is the tens
> A volunteer firefighter holds the end of a firehose as a strong jet of water emerges. (a) The hose exerts a large backward force on the firefighter. Explain the origin of this force. (b) If another firefighter steps on the hose, forming a constriction
> A 3000 kg truck is about to tow a 1250 kg car up a hill that makes an angle of α = 10° with respect to the horizontal. The rope attached from the truck to the car makes an angle of β = 25° with respect to t
> A mica sheet 1.00 µm thick is suspended in air. In reflected light, there are gaps in the visible spectrum just at 450, 525, and 630 nm. Calculate the index of refraction of the mica sheet.
> Explain why there is a phase difference between the current in an ac circuit and the potential difference across a capacitor in the same circuit.
> What is the difference between a virtual and a real image? Describe a method for demonstrating the presence of a real image.
> A square loop of wire with side 0.60 m carries a current of 9.0 A as shown in the side-view diagram. When there is no applied magnetic field, the plane of the loop is horizontal and the nonconducting, nonmagnetic spring (k = 550 N/m) is unstretched. A ho
> A study was done observing the ability of the eye to rapidly rotate in order to follow a moving object by placing contact lenses that contain accelerometers on a subject’s eye. The eyeball has radius 1.25 cm. Suppose that, while the subject watches a mov
> At t = 0, the wave pulses shown are moving toward each other on a string. The wave speed is 20 m/s. Use the principle of superposition to sketch the shape of the string at t = 2.0 ms.
> A glass prism bends a ray of blue light more than a ray of red light since its index of refraction is slightly higher for blue than for red. Does a diverging glass lens have the same focal point for blue light and for red light? If not, for which color i
> 1. The speed of an electromagnetic wave in vacuum depends on (a) the amplitude of the electric field but not on the amplitude of the magnetic field. (b) the amplitude of the magnetic field but not on the amplitude of the electric field. (c) the amplitude
> 1. For an ac circuit, graphs (1, 2) could represent: (a) the (1-voltage, 2-current) for a capacitor. (b) the (1-current, 2-voltage) for a capacitor. (c) the (1-voltage, 2-current) for a resistor. (d) the (1-current, 2-voltage) for a resistor. (e) the (1-
> 1. An electric current is induced in a conducting loop by all but one of these processes. Which one does not produce an induced current? (a) rotating the loop so that it cuts across magnetic field lines (b) placing the loop so that its area is perpendicu
> The United States and Canada use 120 V rms as the standard household voltage, whereas most of the rest of the world uses 240 V rms for the household standard. What are the advantages and disadvantages of the two systems?
> Explain the theory behind the pressure cooker. How does it speed up cooking times?
> High-voltage power lines run along the edge of a farmer’s field. Describe how the farmer might be able to steal electric power without making any electrical connection to the power line. (Yes, it works. Yes, it has been done. Yes, it is illegal.)
> Samantha goes kayaking on a straight river. After she has paddled upstream for a while, she realizes she dropped a lifejacket overboard when she launched so she turns around and paddles downstream to retrieve it. The lifejacket has been drifting along wi
> You throw a ball up with initial speed vi, and when it reaches its high point at height h, you throw another ball into the air with the same initial speed vi. Will the two balls cross at half the height h, more than half, or less than half? Explain.
> Wires that carry telephone signals or Internet data are twisted. The twisting reduces the noise on the line from nearby electric devices that produce changing currents. How does the twisting reduce noise pickup?
> Consider the three ideal polarizing filters shown in the figure. The angles listed indicate the direction of the transmission axis of each polarizer with respect to the vertical. (a) If unpolarized light of intensity I0 is incident from the left, what i
> Write the symbol (in the form / ) for the nuclide that has 78 neutrons and 53 protons.
