Question: Find the magnetic field at point R,

> Two strings, each 15.0 m long, are stretched side by side. One string has a mass of 78.0 g and a tension of 180.0 N. The second string has a mass of 58.0 g and a tension of 160.0 N. A pulse is generated at one end of each string simultaneously. (a) On w

> (a) What is the density of an object that is 14% submerged when floating in water at 0°C? (b) What percentage of the object will be submerged if it is placed in ethanol at 0°C?

> The speed of waves on a lake depends on frequency. For waves of frequency 1.0 Hz, the wave speed is 1.56 m/s; for 2.0 Hz waves, the speed is 0.78 m/s. The 2.0 Hz waves from a speedboat's wake reach you 120 s after the 1.0 Hz waves generated by the same b

> Simon wishes to display a double-slit experiment for his class. His coherent light source has a wavelength of 510 nm, and the slit separation is d = 0.032 mm. He must set up the light on a desk 1.5 m away from the screen that is only 10 cm wide. How many

> Bruce is trying to remove an eyelash from the surface of his eye. He looks in a shaving mirror to locate the eyelash, which is 0.40 cm long. If the focal length of the mirror is 18 cm and he puts his eye at a distance of 11 cm from the mirror, how long i

> An electric device has the current-voltage (I-V) graph shown. What is its resistance at (a) point 1 and (b) point 2? [Hint: Use the definition of resistance.]

> When the muscles of the eye remain tensed for a significant period of time, eyestrain results. How much is this a concern for a person using (a) a microscope, (b) a telescope, and (c) a simple magnifier?

> The instantaneous sinusoidal emf from an ac generator with an rms emf of 4.0 V oscillates between what values?

> The K0 meson can decay to two pions: K0 → π+ + π−. The rest energies of the particles are: K0 = 497.7 MeV, π+ = π− = 139.6 MeV. If the K0 is at rest before it decays, what are the kinetic energies of the π+ and the π− after the decay?

> The length of a spring increases by 7.2 cm from its relaxed length when a mass of 1.4 kg is hanging in equilibrium from the spring. (a) What is the spring constant? (b) How much elastic potential energy is stored in the spring? (c) A different mass is

> Due to the similarity between Newton’s law of gravity and Coulomb’s law, a friend proposes this hypothesis: perhaps there is no gravitational interaction at all. Instead, what we call gravity might be electric forces acting between objects that are almos

> An airplane is flying at constant speed 740 km/h in a horizontal circle of radius 4.1 km. The lift force on the wings due to the air is perpendicular to the wings. At what angle to the vertical must the wings be banked to fly in this circle?

> While an elevator of mass 832 kg moves downward, the tension in the supporting cable is a constant 7730 N. Between t = 0 and t = 4.00 s, the elevator's displacement is 5.00 m downward. What is the elevator's speed at t = 4.00 s?

> A Compton scattering experiment is performed using an aluminum target. The incident photons have wavelength λ. The scattered photons have wavelengths λ′ and energies E that depend on the scattering angle θ. (a) At what angle θ are scattered photons with

> Are entropy changes always caused by the flow of heat? If not, give some other examples of processes that increase entropy.

> Why are heat pumps more often used in mild climates than in areas with severely cold winters?

> The pull cord of a lawnmower engine is wound around a drum of radius 6.00 cm. While the cord is pulled with a force of 75 N to start the engine, what magnitude torque does the cord apply to the drum?

> A discus thrower moves the discus in 1.5 complete revolutions in 1.4 s (starting from rest). The radius of the circular path of the discus is 0.90 m, and the mass of the discus is 2.0 kg. Assume a constant torque is applied to the discus by the athlete.

> Two spaceships are observed from Earth to be approaching each other along a straight line. Ship A moves at 0.40c relative to the Earth observer, and ship B moves at 0.50c relative to the same observer. What speed does the captain of ship A report for the

> Two steel wires (of the same length and different radii) are connected together, end to end, and tied to a wall. An applied force stretches the combination by 1.0 mm. How far does the midpoint move?

> A 2010 kg elevator moves with an upward acceleration of 1.50 m/s2. What is the tension in the cable that supports the elevator?

> Rank the flywheels in order of the linear speed at the rim, largest to smallest. Explain.

> No currents flow in the circuit diagrammed before the switch is closed. Consider all the circuit elements to be ideal. (a) At the instant the switch is closed, what are the values of the currents I1 and I2, the potential differences across the resistors

> Two blocks, one with mass m1 = 0.050 kg and one with mass m2 = 0.030 kg, are connected to each other by a string. The inner block is connected to a central pole by another string as shown in the figure with r1 = 0.40 m and r2 = 0.75 m. When the blocks ar

> A television set draws an rms current of 2.50 A from a 60 Hz power line. Find (a) the average current, (b) the average of the square of the current, and (c) the amplitude of the current.

> In everyday experience, visible light seems to travel in straight lines whereas radio waves do not. Explain.

> A proton is initially at rest and moves through three different regions as shown in the figure. In region 1, the proton accelerates across a potential difference of 3330 V. In region 2, there is a magnetic field of 1.20 T pointing out of the page and an

> A block of mass 2.00 kg slides eastward along a frictionless surface with a speed of 2.70 m/s. A chunk of clay with a mass of 1.50 kg slides southward on the same surface with a speed of 3.20 m/s. The two objects collide and move off together. What is th

> Most heat pumps incorporate an auxiliary electric heater. For relatively mild outdoor temperatures, the electric heater is not used. However, if the outdoor temperature gets very low, the auxiliary heater is used to supplement the heat pump. Why?

> When snorkeling, you wear goggles in order to see clearly. Why is your vision blurry without the goggles? A nearsighted person notices that he is able to see more clearly when he is underwater (without goggles or corrective lenses) than in air (without c

> The Milky Way galaxy rotates about its center with a period of about 200 million yr. The Sun is 2 × 1020 m from the center of the galaxy. (a) What is the Sun’s radial acceleration? (b) What is the net gravitational force on the Sun due to the other star

> The graph shows the force exerted on an object versus the position of that object along the x-axis. The force has no components other than along the x-axis. What is the work done by the force on the object as the object is displaced from 0 to 3.0 m?

> Table 12.2 lists 120 dB as the intensity level at the threshold of pain for humans. (a) Show that the corresponding pressure amplitude is 29 Pa. (b) What is this pressure amplitude as a fraction of atmospheric pressure?

> A block is released from rest and slides down an incline. The coefficient of sliding friction is 0.38, and the angle of inclination is 60.0°. (a) Use energy considerations to find how fast the block is sliding after it has traveled a distance of 30.0 cm

> If you leave the refrigerator door open and the refrigerator runs continuously, does the kitchen get colder or warmer? Explain.

> A transverse wave on a string is described by Sketch graphs of the transverse velocity and acceleration of the point x = 0 as functions of time, showing one complete cycle.

> What are the advantages of using hydraulic systems rather than mechanical systems to operate automobile brakes or the control surfaces of an airplane?

> Two African swallows fly toward each other, carrying coconuts. The first swallow is flying north horizontally with a speed of 20 m/s. The second swallow is flying at the same height as the first and in the opposite direction with a speed of 15 m/s. The m

> Some electric appliances are able to operate equally well with either dc or ac voltage sources, but other appliances require one type of source or the other and cannot run on both. Explain and give a few examples of each type of appliance.

> The graph shows vx in meters per second versus t in seconds for a skateboard moving along the x-axis. How far does the board move between t = 3.00 s and t = 8.00 s? Sketch a motion diagram and a graph of x(t) for the same time interval.

> A centrifuge has a rotational inertia of 6.5 × 10−3 kg·m2. How much energy must be supplied to bring it from rest to 420 rad/s (4000 rev/min)?

> When a block of ebony is placed in ethanol, what percentage of its volume is submerged?

> Consider the emission spectrum of singly ionized helium (He+). Find the longest three wavelengths for the series in which the electron makes a transition from a higher excited state to the first excited state (not the ground state).

> A bicycle is moving at 9.0 m/s. What is the angular speed of its tires if their radius is 35 cm?

> Show that the spontaneous alpha decay of 19O is not possible.

> A 4.0 N object is attached to the bottom of an ideal spring of spring constant 250 N/m. The spring is initially in its relaxed position. Write an equation to describe the motion of the object if it is released at t = 0. [Hint: Let y = 0 at the equilibri

> When supplies of fossil fuels such as petroleum and coal dwindle, people might call the situation an “energy crisis.” From the standpoint of physics, why is that not an accurate name? Can you think of a better one?

> A person in bare feet is standing under a tree during a thunderstorm, seeking shelter from the rain. A lightning strike hits the tree. A burst of current lasting 40 µs passes through the ground; during this time the potential difference between his feet

> In Section 22.3, we stated that an electric dipole antenna should be aligned with the electric field of an EM wave for best reception. If a magnetic dipole antenna is used instead, should its axis be aligned with the magnetic field of the wave? Explain.

> By what percentage does the density of water increase at a depth of 1.0 km below the surface?

> Why must all reversible engines (operating between the same reservoirs) have the same efficiency? Try an argument by contradiction: imagine that two reversible engines exist with e1 > e2. Reverse one of them (into a heat pump) and use the work output fro

> A ball of mass 0.10 kg moving with speed of 2.0 m/s hits a wall and bounces back with the same speed in the opposite direction. What is the change in the ball’s kinetic energy?

> Would a ground fault interrupter work if the circuit used dc current instead of ac? Explain.

> A cylindrical steel bar is compressed by the application of forces of magnitude F at each end. What magnitude forces would be required to compress by the same amount (a) a steel bar of the same cross- sectional area but one half the length? (b) a steel

> A car drives around a curve with radius 410 m at a speed of 32 m/s. The road is not banked. The mass of the car is 1400 kg. (a) What is the frictional force on the car? (b) Does the frictional force necessarily have magnitude μsN? Explain.

> Why is a refracting telescope with a large angular magnification longer than one with a smaller magnification?

> An electron with a velocity of 10.0 m/s in the positive y-direction enters a region where there is a uniform electric field of 200 N/C in the positive x-direction. What are the x- and y-components of the electron’s displacement 2.40 &Ac

> In the crossover network of Problem 63, the inductance L is 1.20 mH. The capacitor is variable; its capacitance can be adjusted to set the crossover point according to the frequency response of the woofer and tweeter. What should the capacitance be set t

> Suppose a uniform electric field of magnitude 100.0 N/C exists in a region of space. How far apart are a pair of equipotential surfaces whose potentials differ by 1.0 V?

> On a graph of x versus time, what quantity does the slope of the graph represent?

> A cosmic-ray proton entering the atmosphere from space has a kinetic energy of 2.0 × 1020 eV. (a) What is its kinetic energy in joules? (b) If all of the kinetic energy of the proton could be harnessed to lift an object of mass 1.0 kg near Earth's surfa

> What is the angular acceleration of the dipole at θ = 135°?

> A whimsical statement of the laws of thermodynamics—probably not one favored by gamblers—goes like this: I. You can never win; you can only lose or break even. II. You can only break even at absolute zero. III. You can never get to absolute zero. What do

> A seismic wave is described by the equation The wave travels through a uniform medium along the x-axis. (a) Is this wave moving right (+x-direction) or left (−x-direction)? (b) How far from their equilibrium positions do the particles

> The first nuclear reaction ever observed (in 1919 by Ernest Rutherford) was / . (a) Identify the reaction product “(?).” (b) For this reaction to take place, the alpha particle must come in contact with the nitrogen nucleus. Calculate the distance d bet

> An electric appliance is rated 120 V, 5 A, 500 W. The first two are rms values; the third is the average power consumption. Why is the power not 600 W (= 120 V × 5 A)?

> A beam of light in air enters a glass block at an angle of 30° to the glass surface, as shown. The glass has an index of refraction of 1.35. (a) Find the angle labeled θ1. (b) Calculate the critical angle between the glass and ai

> An electric baseboard heater can convert 100% of the electric energy used into heat that flows into the house. Since a gas furnace might be located in a basement and sends exhaust gases up the chimney, the heat flow into the living space is less than 100

> (a) Imagine drawing a circle on the surface of a metal plate. When the temperature increases, what happens to the size of the circle? (b) Instead of drawing a circle, suppose you cut out the circle and then put it back inside the hole in the plate. What

> In a hydraulic lift, the radii of the pistons are 2.50 cm and 10.0 cm. A car weighing W = 10.0 kN is to be lifted by the force of the large piston. (a) What force Fa must be applied to the small piston? (b) When the small piston is pushed in by 10.0 cm

> A photon of wavelength 0.148 00 nm, traveling due east, is scattered by an electron initially at rest. The wavelength of the scattered photon is 0.149 00 nm, and it moves at an angle θ north of east. (a) Find θ. (b) What is the south component of the el

> Explain why the molar specific heat at constant volume is not the same as the molar specific heat at constant pressure for gases. Why is the distinction between constant volume and constant pressure usually insignificant for the specific heats of liquids

> Verify that / has dimensions of energy.

> The wiring circuit for a typical room is shown schematically. (a) Of the six locations for a circuit breaker indicated by A, B, C, D, E, and F, which one would best protect the wiring against a short circuit in any one of the three appliances? Explain.

> A train of mass 55 200 kg is traveling along a straight, level track at 26.8 m/s. Suddenly the engineer sees a truck stalled on the tracks 184 m ahead. If the maximum possible braking force has magnitude 84.0 kN, can the train be stopped in time?

> You are walking to class with a backpack full of books. As you walk at constant speed on flat ground, does the force exerted on the backpack by your back and shoulders do any work? If so, is it positive or negative? Answer the same questions in two other

> The resistance of a conductor is 19.8 Ω at 15.0°C and 25.0 Ω at 85.0°C. What is the temperature coefficient of resistance of the material?

> Massimo, a machinist, is cutting threads for a bolt on a lathe. He wants the bolt to have 18 threads per inch. If the cutting tool moves parallel to the axis of the would-be bolt at a linear velocity of 0.080 in./s, what must the rotational speed of the

> After a day at the beach, a child brings home a bucket containing some saltwater. Eventually the water evaporates, leaving behind a few salt crystals. The molecular order of the salt crystals is greater than the order of the dissolved salt sloshing aroun

> A new dormitory is being built at a college in North Carolina. To save costs, it is proposed to not include air conditioning ducts and vents. A member of the board overseeing the construction says that stand- alone air conditioning units can be supplied

> In the railroad freight yard, an empty freight car of mass m rolls along a straight level track at 1.0 m/s and collides with an initially stationary, fully loaded boxcar of mass 4.0m. The two cars couple together on collision. (a) What is the speed of t

> What is the ground-state electron configuration of a K+ ion?

> Two point charges (+10.0 nC and −10.0 nC) are located 8.00 cm apart. (a) What is the change in electric potential energy when a third point charge of −4.2 nC is moved from point c to point b? (b) How much work would

> Two point charges are located on a coordinate system as follows: Q1 = −4.5 µC at x = 1.00 cm and y = 1.00 cm and Q2 = 6.0 µC at x = 3.00 cm and y = 1.00 cm. (a) What is the electric field at point P located at

> A starship takes 3.0 days to travel between two distant space stations according to its own clocks. Instruments on one of the space stations indicate that the trip took 4.0 days. How fast did the starship travel relative to that space station?

> Chronic exposure to loud noises can be damaging to one's hearing. This can be a problem in occupations in which heavy machinery is used. If a machine produces sound with an intensity level of 100.0 dB, what would its intensity level have to be to reduce

> Three point charges are located at the corners of a right triangle as shown in the figure. How much work does it take for an external force to move the charges apart until they are very far away from one another?

> To understand Rayleigh's criterion as applied to the pupil of the eye, notice that rays do not pass straight through the center of the lens system (cornea + lens) of the eye except at normal incidence because the indices of refraction on the two sides of

> A particle traveling at a speed of 6.50 × 106 m/s has the uncertainty in its position given by its de Broglie wavelength. What is the minimum uncertainty in the speed of the particle?

> An external magnetic field is parallel to the central axis of a 50 turn coil of radius 5.0 cm. During an interval of 160 ms, the field changes from 0.20 T in one direction to 0.30 T in the opposite direction. The resistance of the coil is 82 Q. What is t

> A warm pitcher of lemonade is put into an ice chest. Describe what happens to the entropies of lemonade and ice as heat flows from the lemonade to the ice within the chest.

> Can a heat engine be made to operate without creating any “thermal pollution,” that is, without making its cold reservoir get warmer in the long run? The net work output must be greater than zero.

> A magnetic dipole antenna has its axis aligned with the vertical. The antenna sends out radio waves. If you are due south of the antenna, what is the polarization state of the radio waves that reach you?

> An x-ray diffraction experiment using 16 keV x-rays is repeated using electrons instead of x-rays. What should the kinetic energy of the electrons be in order to produce a diffraction pattern with maxima at the same angles as the x-rays (using the same c

> An 81 kg student who has just studied matter waves is concerned that he may be diffracted as he walks through a doorway that is 81 cm across and 12 cm thick. (a) If the wavelength of the student must be about the same size as the doorway to exhibit diff

> A cylindrical disk has volume 8.97 × 10−3 m3 and mass 8.16 kg. The disk is floating on the surface of some water with its flat surfaces horizontal. The area of each flat surface is 0.640 m2. (a) What is the specific gravity of the disk? (b) How far belo

> The mass density of diamond (a crystalline form of carbon) is 3500 kg/m3. How many carbon atoms per cubic centimeter are there?

> A toy car with a mass of 120 g moves to the right with a speed of 0.75 m/s. A small child drops a 30.0 g piece of clay onto the car. The clay sticks to the car and the car continues to the right. What is the change in speed of the car? Consider the frict

> A solar cell provides an emf of 0.45 V. (a) If the cell supplies a constant current of 18.0 mA for 9.0 h, how much electric energy does it supply? (b) What is the power—the rate at which it supplies electric energy?

> A voltmeter with a resistance of 670 kΩ is used to measure the voltage across the 83.0 kΩ resistor in the figure with Problems 79 and 80. What is the voltmeter reading?