Question: 1. For an ac circuit, graphs (1,

> 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 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

> 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. 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.

> 11. The magnetic forces that two parallel wires with unequal currents flowing in opposite directions exert on each other are (a) attractive and unequal in magnitude. (b) repulsive and unequal in magnitude. (c) attractive and equal in magnitude. (d) repul

> The armature of an ac generator is a rectangular coil 2.0 cm by 6.0 cm with 80 turns. It is immersed in a uniform magnetic field of magnitude 0.45 T. If the amplitude of the emf in the coil is 17.0 V, at what angular speed is the armature rotating?

> A 1500 W electric hair dryer is designed to work in the United States, where the ac voltage is 120 V rms. What power is dissipated in the hair dryer when it is plugged into a 240 V rms socket in Europe? What may happen to the hair dryer in this case?

> A conducting sphere is placed within a conducting spherical shell. The conductors are in electrostatic equilibrium. The inner sphere has a radius of 1.50 cm, the inner radius of the spherical shell is 2.25 cm, and the outer radius of the shell is 2.75 cm

> On a warm day, a piano is tuned to match an organ in an auditorium. Will the piano still be in tune with the organ the next morning, when the room is cold? If not, will the organ be higher or lower in pitch than the piano? (Assume that the piano's tuning

> A radioactive sample of radon-222 has an activity of 2050 Bq. How many kilograms of radon are present?

> Multiple-Choice Questions 1–4. In the figure, four point charges move in the directions indicated in the vicinity of a bar magnet. The magnet, charge positions, and velocity vectors all lie in the plane of this page. Answer choices: (a)

> A 640 nm laser emits a 1.0 s pulse in a beam with a diameter of 1.5 mm. The rms electric field of the pulse is 120 V/m. How many photons are emitted per second?

> A 220 W laser fires a 0.250 ms pulse of light with a wavelength of 680 nm. (a) What is the energy of each photon in the laser beam? (b) How many photons are in this pulse?

> The carbon isotope 15C decays much faster than 14C. (a) Using Appendix B.8, write a nuclear reaction showing the decay of 15C. (b) How much energy is released when 15C decays?

> 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. Explain how the mean free path ca

> Two identical long straight conducting wires with a mass per unit length of 25.0 g/m are resting parallel to each other on a table. The wires are separated by 2.5 mm and are carrying currents in opposite directions. (a) If the coefficient of static fric

> An electromagnetic rail gun can fire a projectile using a magnetic field and an electric current. Consider two horizontal conducting rails that are 0.500 m apart with a 50.0 g conducting projectile that slides along the two rails. A magnetic field of 0.7

> The radio telescope at Arecibo, Puerto Rico, has a reflecting spherical bowl of 305 m (1000 ft) diameter. Radio signals can be received and emitted at various frequencies with the appropriate antennae at the focal point. If two Moon craters 499 km apart

> Describe the polarization of radio waves transmitted from a horizontal electric dipole antenna that travel parallel to Earth’s surface.

> A particle is initially moving at 0.60c. If its momentum increases by a factor of 2.0, what is its speed?

> A 2.0 kg block is moving to the right at 1.0 m/s just before it strikes and sticks to a 1.0 kg block initially at rest. What is the total momentum of the two blocks after the collision?

> An ideal transformer with 1800 turns on the primary and 300 turns on the secondary is used in an electric slot car racing set to reduce the input voltage amplitude of 170 V from the wall output. The current in the secondary coil is of amplitude 3.2 A. Wh

> The radius of a wheel is 0.500 m. A rope is wound around the outer rim of the wheel. The rope is pulled with a force of magnitude 5.00 N, unwinding the rope and making the wheel spin CCW about its central axis. Ignore the mass of the rope. (a) How much

> 1. A transverse wave travels on a string of mass m, length L, and tension F. Which statement is correct? (a) The energy of the wave is proportional to the square root of the wave amplitude. (b) Every point on the string moves with the same speed. (c) The

> On a warm summer day, the air temperature is 84°F. Express this temperature in (a) °C and (b) kelvins.

> An anchor, made of cast iron of bulk modulus 60.0 GPa and of volume 0.230 m3, is lowered over the side of the ship to the bottom of the harbor where the pressure is greater than sea level pressure by 1.75 MPa. Find the change in the volume of the anchor.

> Why do cooking directions on packages advise different timing to be followed for some locations?

> Three point charges are placed on the x-axis. A charge of 3.00 µC is at the origin. A charge of −5.00 µC is at 20.0 cm, and a charge of 8.00 µC is at 35.0 cm. What is the force on the charge at the origin?

> 11. The drawing shows a complex wave moving to the right along a cord. At the instant shown, which points on the cord are moving downward? (a) A (b) B (c) C (d) A and C (e) A, B, and C

> A uniform door weighs 50.0 N and is 1.0 m wide and 2.6 m high. What is the magnitude of the torque due to the door's own weight about a horizontal axis perpendicular to the door and passing through a corner?

> Mars has a mass of about 6.42 × 1023 kg. The length of a day on Mars is 24 h and 37 min, a little longer than the length of a day on Earth. Your task is to put a satellite into a circular orbit around Mars so that it stays above one spot on the surface,

> A ray of light passes from air into water, striking the surface of the water with an angle of incidence of 45°. Which of these quantities change as the light enters the water: wavelength, frequency, speed of propagation, direction of propagation?

> 1. In an ionic solution, sodium ions (Na+) are moving to the right and chloride ions (Cl−) are moving to the left. In which direction is the current due to the motion of (1) the sodium ions and (2) the chloride ions? (a) Both are to the

> The graph shows ground vibrations recorded by a seismograph 180 km from the focus of a small earthquake. It took the waves 30.0 s to travel from their source to the seismograph. Estimate the wavelength.

> A series RLC circuit has a 0.20 mF capacitor, a 13 mH inductor, and a 10.0 Ω resistor, and is connected to an ac source with amplitude 9.0 V and frequency 60 Hz. (a) Calculate the voltage amplitudes VL, VC, VR, and the phase angle. (b) Draw the phasor

> Electric power is distributed long distances over transmission lines by using high ac voltages and therefore small ac currents. What is the advantage of using high voltages instead of safer low voltages?

> Explain the differences between average current, rms current, and peak current in an ac circuit.

> An asteroid hits the Moon and ejects a large rock from its surface. The rock has enough speed to travel to a point between Earth and the Moon where the gravitational forces on it from Earth and the Moon are equal in magnitude and opposite in direction. A

> 11. In the diagram, which two points are closest to being at the same potential? (a) A and D (b) B and C (c) B and D (d) A and C 12. In the diagram, which point is at the lowest potential? (a) A (b) B (c) C (d) D

> A certain capacitor stores 450 J of energy when it holds 8.0 × 10−2 C of charge. What is (a) the capacitance of this capacitor and (b) the potential difference across the plates?

> X-rays illuminate a target and the scattered x-rays are detected. Given the wavelength λ of the incident x-rays and the scattering angle θ, rank the scattered x-rays from largest wavelength to smallest wavelength. (a) λ = 1.0 pm, θ = 90°; (b) λ = 1.0 p

> A piece of gold wire of length L has a resistance R0. Suppose the wire is drawn out so that its length increases by a factor of 3. What is the new resistance R in terms of the original resistance?

> 1. Among these choices, which is/are correct units for electric field? (a) N/kg only (b) N/C only (c) N only (d) N·m/C only (e) V/m only (f) both N/C and V/m 2. Two charges are located at opposite corners (A and C) of a square. We do not k

> A spring fixed at one end is compressed from its relaxed position by a distance of 0.20 m. See the graph of the applied external force Fx versus the compression x of the spring. (a) Find the work done by the external force in compressing the spring 0.20

> 1. An alpha particle (charge +2e and mass 4mp) is on a collision course with a proton (charge +e and mass mp). Assume that no forces act other than the electrical repulsion. Which one of these statements about the accelerations of the two particles is tr

> 11. Given 1 mole of an ideal gas, in a state characterized by PA, VA, a change occurs so that the final pressure and volume are equal to PB, VB, where VB > VA. Which of these is true? (a) The heat supplied to the gas during the process is completely dete