Question: Why is the speed of sound in

> Parallel light of wavelength λ strikes a slit of width a at normal incidence. The light is viewed on a screen that is 1.0 m past the slits. In each case that follows, sketch the intensity on the screen as a function of x, the distance from the center of

> If gear A in Problem 73 has an initial frequency of 0.955 Hz and an angular acceleration of 3.0 rad/s2, how many rotations does each gear go through in 2.0 s?

> Sketch some magnetic field lines for two identical bar magnets in the given configuration. Be sure to show field lines inside the magnets as well as outside.

> A lid is put on a box that is 15 cm long, 13 cm wide, and 8.0 cm tall, and the box is then evacuated until its inner pressure is 0.80 × 105 Pa. How much force is required to lift the lid (a) at sea level; (b) in Denver, on a day when the atmospheric pr

> Sketch some magnetic field lines for two identical bar magnets in the given configuration. Be sure to show field lines inside the magnets as well as outside.

> A current I = 40.0 A flows through a strip of metal. An electromagnet is switched on so that there is a uniform magnetic field of magnitude 0.30 T directed into the page. How would you hook up a voltmeter to measure the Hall voltage? Show how the voltmet

> Crossed electric and magnetic fields are established over a certain region. The magnetic field is 0.635 T vertically downward. The electric field is 2.68 × 106 V/m horizontally east. An electron, traveling horizontally northward, experiences zero net for

> Show that the time for one revolution of a charged particle moving perpendicular to a uniform magnetic field is independent of its speed. (This is the principle on which the cyclotron operates.) In doing so, write an expression that gives the period T (t

> A sample containing sulfur (atomic mass 32 u), manganese (55 u), and an unknown element is analyzed in a mass spectrometer. As in Fig. 19.17(a), the ions move around half a circle before striking a photographic plate. The sulfur and manganese ions are se

> A 402 kg pile driver is raised 12 m above ground. (a) How much work must be done to raise the pile driver? (b) How much work does gravity do on the driver as it is raised? (c) The driver is now dropped. How much work does gravity do on the driver as i

> Peggy drives from Cornwall to Atkins Glen in 45 min. Cornwall is 73.6 km from Illium in a direction 25° west of south. Atkins Glen is 27.2 km from Illium in a direction 15° south of west. Using Illium as your origin, (a) draw the initial and final posit

> A battery charger delivers a current of 3.0 A for 4.0 h to a 12 V storage battery. What is the total charge that passes through the battery in that time?

> Radium-226 decays as /. If the / nucleus is at rest before the decay and the / nucleus is in its ground state, estimate the kinetic energy of the alpha particle. (Assume that the / nucleus takes away an insignificant fraction of the kinetic energy

> A boy of mass 60.0 kg is rescued from a hotel fire by leaping into a firefighters' net. The window from which he leapt was 8.0 m above the net. The firefighters lower their arms as he lands in the net so that he is brought to a complete stop in a time of

> A rectangular loop of wire, carrying current I1 = 2.0 mA, is next to a very long wire carrying a current I2 = 8.0 A. (a) What is the direction of the magnetic force on each of the four sides of the rectangle due to the long wire's magnetic field? (b) C

> A sample containing 12C, 16O, and an unknown isotope is analyzed in a mass spectrometer. As in Fig. 19.17(a), the ions move around a semicircle before striking a photographic plate. The 12C+ and 16O+ ions are separated by 2.250 cm on the plate, and the u

> After being accelerated through a potential difference of 5.0 kV, a singly charged 12C+ ion moves in a circle of radius 21 cm in the magnetic field of a mass spectrometer. What is the magnitude of the field?

> An electromagnetic flowmeter is used to measure blood flow rates during surgery. Blood containing Na+ ions flows due south through an artery with a diameter of 0.40 cm. The artery is in a downward magnetic field of 0.25 T and develops a Hall voltage of 0

> Naturally occurring carbon consists of two different isotopes (excluding 14C, which is present in only trace amounts). The most abundant isotope is 12C. When carbon is placed in a mass spectrometer, 12C+ ions moved in a circle of radius 15.0 cm, whereas

> In free fall, we assume the acceleration to be constant. Not only is air resistance ignored, but the gravitational field strength is assumed to be constant. From what height can an object fall to Earth's surface such that the gravitational field strength

> An alpha particle with a kinetic energy of 1.0 MeV is headed straight toward a gold nucleus. (a) Find the distance of closest approach between the centers of the alpha particle and gold nucleus. (Assume the gold nucleus remains stationary. Since its mas

> In one type of mass spectrometer, ions having the same velocity move through a uniform magnetic field. The spectrometer is being used to distinguish 12C+ and 14C+ ions. The 12C+ ions move in a circle of diameter 25 cm. (a) What is the diameter of the or

> Which of these unidentified nuclides are isotopes of each other?

> Calculate the mass density of nuclear matter.

> (a) Use Gauss’s law to prove that the electric field outside any spherically symmetrical charge distribution is the same as if all of the charge were concentrated into a point charge. (b) Now use Gauss’s law to prove that the electric field inside a sph

> Pascal’s principle: proof by contradiction. Points A and B are near each other at the same height in a fluid. Suppose PA > PB. (a) Can both vA and vB be zero? Explain. (b) Point C is just above point D in a static fluid. Suppose the pressure at C incre

> Sketch some magnetic field lines for two identical bar magnets in the given configuration. Be sure to show field lines inside the magnets as well as outside.

> A singly charged ion of unknown mass moves in a circle of radius 12.5 cm in a magnetic field of 1.2 T. The ion was accelerated through a potential difference of 7.0 kV before it entered the magnetic field. What is the mass of the ion?

> In a photoelectric experiment using sodium, when incident light of wavelength 570 nm and intensity 1.0 W/m2 is used, the measured stopping potential is 0.28 V. (a) What would the stopping potential be for incident light of wavelength 400.0 nm and intens

> Horizontally polarized light with intensity I0 passes through two ideal polarizers, one after the other. The transmission axes of the first and second polarizers are at angles θ1 and θ2, respectively, to the horizontal. Rank the intensities of the light

> A beam of α particles (helium nuclei) is used to treat a tumor located 10.0 cm inside a patient. To penetrate to the tumor, the α particles must be accelerated to a speed of 0.458c, where c is the speed of light. (Ignore relativistic effects.) The mass o

> Six protons move (at speed v) in magnetic fields (magnitude B) along circular paths. Rank them in order of the radius of their paths, greatest to smallest. (a) v = 6 × 106 m/s, B = 0.3 T (b) v = 3 × 106 m/s, B = 0.6 T (c) v = 3 × 106 m/s, B = 0.1 T (d)

> What is the electric force on the chloride ion in the lower right- hand corner in the diagram? Since the ions are in water, the “effective charge” on the chloride ions (Cl−) is −2 &A

> When two particles travel through a region of uniform magnetic field pointing out of the plane of the paper, they follow the trajectories shown. What are the signs of the charges of each particle?

> An electromagnetic flowmeter is used to measure blood flow rates during surgery. Blood containing ions (primarily Na+) flows through an artery with a diameter of 0.50 cm. The artery is in a magnetic field of 0.35 T and develops a Hall voltage of 0.60 mV

> A positron (q = +e) moves at 5.0 × 107 m/s in a magnetic field of magnitude 0.47 T. The magnetic force on the positron has magnitude 2.3 × 10−12 N. (a) What is the component of the positron's velocity perpendicular to the magnetic field? (b) What is th

> In a CRT, electrons moving at 1.8 × 107 m/s pass between the poles of an electromagnet where the magnetic field is 2.0 mT directed upward. (a) What is the radius of their circular path while in the magnetic field? (b) The time the electron

> If the pressure amplitude of a sound wave is doubled, what happens to the displacement amplitude, the intensity, and the intensity level?

> Find the electric potential energy for the following array of charges: charge q1 = +4.0 µC is located at (x, y) = (0.0, 0.0) m; charge q2 = +3.0 µC is located at (4.0, 3.0) m; and charge q3 = −1.0 µC is located at (0.0, 3.0) m.

> A certain electric device has the current-voltage (I-V) graph shown with Problem 30. What is the power dissipated at points 1 and 2?

> A cosmic ray muon with the same charge as an electron and a mass of 1.9 × 10−28 kg is moving toward the ground at an angle of 25° from the vertical with a speed of 7.0 × 107 m/s. As it crosses point

> A 100 g ball collides elastically with a 300 g ball that is at rest. If the 100 g ball was traveling in the positive x-direction at 5.00 m/s before the collision, what are the velocities of the two balls after the collision?

> A sample of gold, , decays radioactively with an initial rate of 1.00 × 1010 Bq into / . The half-life is 2.70 days. (a) What is the decay rate after 8.10 days? (b) What particle or particles are emitted during this decay process?

> Common sports injuries result in the tearing of tendons and ligaments due to overstretching. If the anterior cruciate ligament (ACL) in an athlete’s knee has a length of 1.0 cm, a breaking point of 190 MPa, and a Young’s modulus of 600 MPa, how far must

> (a) Show that the number of electron states in a sub-shell is 4â„“ + 2. [Hint: First, how many states are in each orbital? Second, how many orbitals are in each subshell?] (b) By summing the number of states in each of subshells, show th

> A variable inductor can be placed in series with a lightbulb to act as a dimmer. (a) What inductance would reduce the current through a 100 W lightbulb to 75% of its maximum value? Assume a 120 V rms, 60 Hz source. (b) Could a variable resistor be used

> The energy at which the fundamental forces are expected to unify is about 1019 GeV. Find the mass (in SI units) of a particle with rest energy 1019 GeV.

> At a certain point on Earth's surface in the southern hemisphere, the magnetic field has a magnitude of 5.0 × 10−5 T and points upward and toward the north at an angle of 55° above the horizontal. A cosmic ray muon with the same charge as an electron and

> A magnet produces a 0.30 T field between its poles, directed to the east. A dust particle with charge q = −8.0 × 10−18 C is moving straight down at 0.30 cm/s in this field. What is the magnitude and direction of the magnetic force on the dust particle?

> Find the magnetic force on the electron at point c.

> What is the potential energy if a third point charge q = −4.2 nC is placed at point c?

> A 3.0 kg object is initially moving northward at 15 m/s. Then a force of 15 N, toward the east, acts on it for 4.0 s. (a) At the end of the 4.0 s, what is the object's final velocity? (b) What is the change in momentum during the 4.0 s?

> Find the magnetic force on the electron at point b.

> Find the magnetic force on the electron at point a.

> The figure shows a simplified circuit diagram for an automobile. The equivalent resistor R represents the total electrical load due to spark plugs, lights, radio, fans, starter, rear window defroster, and the like in parallel. If R = 0.850 â„&

> Two blocks are connected by an ideal cord that passes over a frictionless pulley. If m1 = 3.6 kg and m2 = 9.2 kg, and block 2 is initially at rest 140 cm above the floor, how long does it take block 2 to reach the floor?

> Rank the electrons in order of the magnitude of the magnetic force on them, from greatest to least.

> A rocket engine can accelerate a rocket launched from rest vertically up with an acceleration of 20.0 m/s2. However, after 50.0 s of flight the engine fails. Ignore air resistance. (a) What is the rocket's altitude when the engine fails? (b) When does

> Consider the camera flash in Problem 96. If the flash really discharges according to Eq. (18-48), then it takes an infinite amount of time to discharge. When Problem 96 assumes that the capacitor discharges in 4.0 × 10−3 s, we mean that the capacitor has

> In Example 6.1, find the work done by the movers as they slide the chest up the ramp if the coefficient of friction between the chest and the ramp is 0.20.

> The average speed of blood in the aorta is 0.3 m/s, and the radius of the aorta is 1 cm. There are about 2 × 109 capillaries with an average radius of 6 μm. What is the approximate average speed of the blood flow in the capillaries?

> A parallel plate capacitor used in a flash for a camera must be able to store 32 J of energy when connected to 300 V. (Most electronic flashes actually use a 1.5 to 6.0 V battery, but increase the effective voltage using a dc-dc inverter.) (a) What shou

> Consider the circuit in the diagram. After the switch S has been closed for a long time, what are the current through the 12 Ω resistor and the voltage across the capacitor?

> In each of five situations, two point charges (Q1, Q2) are separated by a distance d. Rank them in order of the electric potential energy, from highest to lowest. (a) Q1 = 1 µC, Q2 = 2 µC, d = 1 m (b) Q1 = 2 µC, Q2 = −1 µC, d = 1 m (c) Q1 = 2 µC, Q2 = −4

> A naval aviator had to eject from her plane before it crashed at sea. She is rescued from the water by helicopter and dangles from a cable that is 45 m long while being carried back to the aircraft carrier. What is the period of her vibration as she swin

> A 20 µF capacitor is discharged through a 5.0 kΩ resistor. The initial charge on the capacitor is 200 µC. (a) Sketch a graph of the current through the resistor as a function of time. Label both axes with numbers and units. (b) What is the initial powe

> Using a mass spectrometer, the mass of the / ion is found to be 238.050 24 u. (a) Use this result to calculate the mass of the / nucleus. (b) Now find the binding energy of the / nucleus.

> A proton moves in a helical path at speed v = 4.0 × 107 m/s high above the atmosphere, where Earth's magnetic field has magnitude B = 1.0 × 10−6 T. The proton's velocity makes an angle of 25° with the magnetic field. (a) Find the radius of the helix. [H

> (a) In a charging RC circuit, how many time constants have elapsed when the capacitor has 99.0% of its final charge? (b) How many time constants have elapsed when the capacitor has 99.90% of its final charge? (c) How many time constants have elapsed wh

> An automobile traveling at a speed of 30.0 m/s applies its brakes and comes to a stop in 5.0 s. If the automobile has a mass of 1.0 × 103 kg, what is the average horizontal force exerted on it during braking? Assume the road is level.

> In the circuit, the initial energy stored in the capacitor is 25 J. At t = 0 the switch is closed. (a) Sketch a graph of the voltage across the resistor (VR) as a function of t. Label the vertical axis with key numerical value(s) and units. (b) At what

> (a) Light of wavelength 300 nm is incident on a metal that has a work function of 1.4 eV. What is the maximum speed of the emitted electrons? (b) If light of wavelength 800 nm is incident on a metal that has a work function of 1.6 eV, are any electrons

> Explain why the displacement of air elements at condensations and rarefactions is zero.

> A 1.5 hp motor operates on 120 V. Ignoring I2R losses, how much current does it draw?

> In the circuit, the capacitor is initially uncharged. At t = 0, switch S is closed. Find the currents I1 and I2 and voltages V1 and V2 (assuming V3 = 0) at points 1 and 2 at (a) t = 0 (i.e., just after the switch is closed) and at (b) t = 1.0 ms.

> To get to a concert in time, a harpsichordist has to drive 122 mi in 2.00 h. (a) If he drove at an average speed of 55.0 mi/h in a due west direction for the first 1.20 h, what must be his average speed if he drives 30.0° south of west for the remaining

> Five conducting spheres are charged as shown. All have the same magnitude net charge except E, whose net charge is zero. Which pairs are attracted to each other and which are repelled by each other when they are brought near each other, but well away fro

> In Fig. 3.39, two blocks are connected by a lightweight cord that does not stretch and that passes over an ideal pulley. (a) If m1 = 3.0 kg and m2 = 5.0 kg, what are the accelerations of each block? (b) What is the tension in the cord?

> Show that Eq. (26-23) reduces to the nonrelativistic relationship between momentum and kinetic energy, K ≈ p2/(2m), for K ≪ E0.

> In a defibrillator (see Example 17.12), a charged capacitor is connected to paddles that make electrical contact with the patient's skin. If gel is applied to the patient's chest to make a good connection between the paddles and the skin, the effective r

> (a) What is the position of the peak of the pulse shown in the figure at t = 3.00 s? (b) When does the peak of the pulse arrive at x = 4.00 m?

> In the circuit of Problem 88, at what time after switch S is closed is the voltage across the combination of three capacitors 50% of its final value?

> Consider the circuit shown with R1 = 25 Ω, R2 = 33 Ω, C1 = 12 µF, C2 = 23 µF, C3 = 46 µF, and V = 6.0 V. (a) Draw an equivalent circuit with one resistor and one capacitor an

> In the circuit, R = 30.0 kΩ and C = 0.10 µF. The capacitor is allowed to charge fully, and then the switch is changed from position a to position b. What will the voltage across the resistor be 8.4 ms later?

> In the Cornell Electron Storage Ring, electrons and positrons circulate in opposite directions with kinetic energies of 6.0 GeV each. When an electron collides with a positron and the two annihilate, one possible (though unlikely) outcome is the producti

> A wind turbine converts some of the kinetic energy of the wind into electric energy. Suppose that the blades of a small wind turbine have length L = 4.0 m. (a) When a 10 m/s (22 mi/h) wind blows head-on, what volume of air (in m3) passes through the cir

> In the circuit shown, assume the battery emf is 20.0 V, R = 1.00 MΩ, and C = 2.00 µF. The switch is closed at t = 0. At what time t will the voltage across the capacitor be 15.0 V?

> A tangent galvanometer is an instrument, developed in the nineteenth century, designed to measure current based on the deflection of a compass needle. A coil of wire in a vertical plane is aligned in the magnetic north-south direction. As illustrated, a

> An ammeter with a full-scale deflection for I = 10.0 A has an internal resistance of 24 Ω. We need to use this ammeter to measure currents up to 12.0 A. The lab instructor advises that we get a resistor and use it to protect the ammeter. (a) What size r

> Show that c2 = 931.494 MeV/u. [Hint: Start with the conversion factors to SI units for MeV and atomic mass units.]

> A 0.15 kg baseball traveling in a horizontal direction with a speed of 20 m/s hits a bat and is popped straight up with a speed of 15 m/s. (a) What is the change in momentum (magnitude and direction) of the baseball? (b) If the bat was in contact with

> Find the potential at the sodium ion, Na+, which is surrounded by two chloride ions, Cl−, and a calcium ion, Ca2+, in water as shown in the diagram. The effective charge of the positive sodium ion in water is 2.0 × 10&acirc

> Consider the circuit in the diagram. Given: I1 = 2.50 A /, / , R1 = 8.00 Ω, and R2 = 5.00 Ω. Find the values of I2, I3, and R3.

> Two cars, a Porsche Boxster convertible and a Toyota Scion xB, are traveling at constant speeds in the same direction, although the Boxster is 186 m behind the Scion. The speed of the Boxster is 24.4 m/s and the speed of the Scion is 18.6 m/s. Sketch gra

> Iodine is eliminated from the body through biological processes with an effective half-life of about 140 days. The radioactive half-life of iodine-131 is 8 days. Suppose some radioactive 131I nuclei are present in the body. Assuming that no new 131I nucl

> A BMW of mass 2.0 × 103 kg is traveling at 42 m/s. It approaches a 1.0 × 103 kg Volkswagen going 25 m/s in the same direction and strikes it in the rear. Neither driver applies the brakes. Ignore the relatively small frictional forces on the cars due to

> Transverse waves travel on five stretched strings with the following properties. Rank the strings according to the time it takes a transverse wave pulse to travel from one end to the other, from largest to smallest. (a) length L, total mass m, tension F

> Derive Eq. (12-5): (a) Starting with Eq. (12-4), substitute T = TC + 273.15. (b) Apply the binomial approximation to the square root (see Appendix A.9) and simplify.

> The longest “string” (a thick metal wire) on a particular piano is 2.0 m long and has a tension of 300.0 N. It vibrates with a fundamental frequency of 27.5 Hz. What is the total mass of the wire?

> A guitar's E-string has length 65 cm and is stretched to a tension of 82 N. It vibrates at a fundamental frequency of 329.63 Hz. Determine the mass per unit length of the string.