A police car’s radar gun emits microwaves with a frequency of f1 = 7.50 GHz. The beam reflects from a speeding car, which is moving toward the police car at 48.0 m/s with respect to the police car. The speeder’s radar detector detects the microwave at a frequency f2. (a) Which is larger, f1 or f2? (b) Find the frequency difference f2 − f1.
> By rewriting each unit in terms of kilograms, meters, seconds, and coulombs, show that 1 N/C = 1 V/m.
> Suppose a transparent vessel 30.0 cm long is placed in one arm of a Michelson interferometer, as in Example 25.2. The vessel initially contains air at 0°C and 1.00 atm. With light of vacuum wavelength 633 nm, the mirrors are arranged so that a bright spo
> Explain why it would be impossible to uniquely define the temperature of an object if the zeroth law of thermodynamics were violated.
> A Michelson interferometer is adjusted so that a bright fringe appears on the screen. As one of the mirrors is moved 25.8 µm, 92 bright fringes are counted on the screen. What is the wavelength of the light used in the interferometer?
> Two coherent EM waves have amplitudes of E0 and 0.48E0. What is the resulting amplitude when they interfere constructively?
> In the circuit shown, an emf of 150 V is connected across a resistance network. What is the current through R2? Each of the resistors has a value of 10 Ω.
> Verify the locations and sizes of the images formed by the two lenses in Fig. 24.2 using the lens equation and the following data: f1 = +4.00 cm, f2 = −2.00 cm, s = 8.00 cm (where s is the distance between the lenses), p1 = +6.00 cm, and h1 = 2.00 mm. (N
> The leg bone (femur) breaks under a compressive force of about 5 × 104 N for a human and 10 × 104 N for a horse. The human femur has a compressive strength of 160 MPa, whereas the horse femur has a compressive strength of 140 MPa. What is the effective c
> (a) What is the focal length of a magnifying glass that gives an angular magnification of 8.0 when the image is at infinity? (b) How far must the object be from the lens?
> The intensity of solar radiation that falls on a detector on Earth is 1.00 kW/m2. The detector is a square that measures 5.00 m on a side and the normal to its surface makes an angle of 30.0 with respect to the Sun’s radiation. How long will it take for
> An insect that is 5.00 mm long is placed 10.0 cm from a simple magnifier with a focal length of 12.0 cm. (a) What is the position of the image? (b) What is the size of the image? (c) Is the image upright or inverted? (d) Is the image real or virtual?
> Five converging lenses are used as simple magnifiers. In each case, the focal length f and the distance between the lens and the object p are given. Rank them in order of the angular magnification, greatest to least. (a) f = 15 cm, p = 15 cm; (b) f = 15
> A sailboat sails from Marblehead Harbor directly east for 45 nautical miles, then 60° south of east for 20.0 nautical miles, east for 30.0 nautical miles, 30° east of north for 10.0 nautical miles, and finally west for 62 nautical miles. At that time the
> In a plate glass factory, sheets of glass move along a conveyor belt at a speed of 15.0 cm/s. An automatic cutting tool descends at preset intervals to cut the glass to size. Since the assembly belt must keep moving at constant speed, the cutter is set t
> Is it possible for a skin diver to dive to any depth as long as his snorkel tube is sufficiently long? (A snorkel is a face mask with a breathing tube that sticks above the surface of the water.)
> Veronique is nearsighted; she cannot see clearly anything more than 6.00 m away without her contacts. One day she doesn't wear her contacts; rather, she wears an old pair of glasses prescribed when she could see clearly up to 8.00 m away. Assume the glas
> (a) One of the fastest land animals of North America is the pronghorn antelope. (a) If a pronghorn antelope accelerates from rest in a straight line with a constant acceleration of 1.7 m/s2, how much time does it take for the antelope to reach a speed of
> The positions of three objects, written as (x, y) coordinates, are: (1.0 m, 1.0 m), (2.0 m, 3.0 m), and (3.0 m, 1.0 m). The objects have equal masses. If one of the objects is moved 12 cm in the positive x- direction, by how much does the CM move?
> In the ac generator of Fig. 20.6, the emf produced is ℰ(t) = ωBA sin ωt. If the generator is connected to a load of resistance R, then the current that flows is (a) Find the magnetic forces on sides 2 and 4 at the i
> Suppose the distance from the lens to the retina is 18 mm. (a) What must the refractive power of the lens be when looking at distant objects? (b) What must the refractive power of the lens be when looking at an object 20.0 cm from the eye? (c) Suppose
> A nearsighted man cannot clearly see objects more than 2.0 m away. The distance from the lens to the retina is 2.0 cm, and the eye's power of accommodation is 4.0 D (in other words, the refractive power of the lens increases by a maximum of 4.0 D when ac
> A penny is at the bottom of a bowl brim full of water. When you look at the water surface from the side, with your eyes at the water level, the penny appears to be just barely under the surface and a horizontal distance of 3.0 cm from the edge of the bow
> A guitar string has a fundamental frequency f. The tension in the string is increased by 1.0%. Ignoring the very small stretch of the string, how does the fundamental frequency change?
> (a) If Harry has a near point of 1.5 m, what focal length contact lenses does he require? (b) What is the refractive power of these lenses?
> Anne's retina is 1.8 cm from the lens. The nearest object she can see clearly without corrective lenses is 2.0 m away. (a) Sketch a ray diagram to show (qualitatively) what happens when she tries to look at something closer than 2.0 m without corrective
> Six sound waves have pressure amplitudes p0 and frequencies f as given. Rank them in order of the displacement amplitude, largest to smallest. (a) p0 = 0.05 Pa, f = 400 Hz (b) p0 = 0.01 Pa, f = 400 Hz (c) p0 = 0.01 Pa, f = 2000 Hz (d) p0 = 0.05 Pa, f = 8
> An RLC series circuit has L = 0.300 H and C = 6.00 µF. The source has a peak voltage of 440 V. (a) What is the angular resonant frequency? (b) When the source is set at the resonant frequency, the peak current in the circuit is 0.560 A. What is the resi
> The uncorrected far point of Colin's eye is 2.0 m. What refractive power contact lens enables him to clearly distinguish objects at large distances?
> If Michaela needs to wear reading glasses with refractive power of +3.0 D, what is her uncorrected near point? Ignore the distance between the glasses and the eye.
> Calculate the frequency of an EM wave with a wavelength the size of (a) the thickness of a piece of paper (60 µm), (b) a 91 m long soccer field, (c) the diameter of Earth, and (d) the distance from Earth to the Sun.
> (a) In Fig. 3.27, what is the instantaneous acceleration of the sports car of Example 3.7 at the time of 14 s from the start? (b) What is the frictional force on the car at this instant, in terms of the weight W? (c) What is the displacement of the car
> Suppose that the lens in a particular eye has a focal length that can vary between 1.85 cm and 2.00 cm, but the distance from the lens to the retina is only 1.90 cm. (a) Is this eye nearsighted or farsighted? Explain. (b) What range of distances can th
> Joe is told by his ophthalmologist that he requires glasses with a refractive power of −4.50 D to correct his vision. His previous prescription was −4.00 D. (a) Is Joe nearsighted or farsighted? (b) When Joe is not wearing his glasses, how far away can
> In an action movie, the hero dangles his archenemy over the edge of a cliff. The archenemy's mass is 68 kg and his center of mass is 44 cm horizontally past the edge of the cliff. The hero's center of mass is 15 cm horizontally from the edge of the cliff
> Two long insulated wires lie in the same horizontal plane. A current of 20.0 A flows toward the north in wire A and a current of 10.0 A flows toward the east in wire B. What are the magnitude and direction of the magnetic field at a point that is 5.00 cm
> A grinding wheel, with a mass of 20.0 kg and a radius of 22.4 cm, is a uniform cylindrical disk. (a) Find the rotational inertia of the wheel about its central axis. (b) When the grinding wheel's motor is turned off, friction causes the wheel to slow f
> A shooting star is a meteoroid that burns up when it reaches Earth’s atmosphere. Many of these meteoroids are quite small. Calculate the kinetic energy of a meteoroid of mass 5.0 g moving at a speed of 48 km/s and compare it to the kinetic energy of a 11
> One can estimate the size of the blind spot on the retina by treating the eye as a camera obscura. Suppose your friend Julie's eye can be approximated as a sphere of diameter 2.5 cm. She notices that a 3.5 cm diameter ball held 40 cm from her pupil can j
> A 35.0 nC charge is placed at the origin and a 55.0 nC charge is placed on the +x-axis, 2.20 cm from the origin. (a) What is the electric potential at a point halfway between these two objects? (b) What is the electric potential at a point on the +x-ax
> The distance from the lens of a particular eye to the retina is 1.75 cm. What is the focal length of the lens when the eye produces a clear image of an object 25.0 cm away?
> (a) What is the resistance of the heater element in a 1500 W hair dryer that plugs into a 120 V outlet? (b) What is the current through the hair dryer when it is turned on? (c) At a cost of $0.10 per kW· h, how much does it cost to run the hair dryer f
> Use the result of Problem 58 to show that in any elastic head-on collision between two objects, the relative speed of the two is the same before and after the collision. [Hint: Look at the collision in its CM frame—the reference frame in which the CM is
> If the distance from the lens to the retina is 2.00 cm, show that the focal length of the lens must vary between 1.85 cm and 2.00 cm to see objects from 25.0 cm to infinity.
> A person on a safari wants to take a photograph of a hippopotamus from a distance of 75.0 m. The animal is 4.00 m long, and its image is to be 1.20 cm long on the camera's image sensor. (a) What focal length lens should be used? (b) What would be the s
> Esperanza uses a camera with a lens of focal length 50.0 mm to take a photo of her son Carlos, who is 1.2 m tall and standing 3.0 m away. (a) What must be the distance between the lens and the camera's sensor to get a sharp picture? (b) What is the magn
> The peak force on a runner’s foot during a race is found to be vertical and three times his weight. What is the peak force on the foot of a runner whose mass is 85 kg?
> A statue is 6.6 m from the opening of a pinhole camera, and the screen is 2.8 m from the pinhole. (a) Is the image erect or inverted? (b) What is the magnification of the image? (c) To get a brighter image, we enlarge the pinhole to let more light thro
> A photoelectric effect experiment is performed with tungsten. The work function for tungsten is 4.5 eV. (a) If ultraviolet light of wavelength 0.20 µm is incident on the tungsten, calculate the stopping potential. (b) If the stopping potential is turne
> A camera uses a 200.0 mm focal length telephoto lens to take pictures from a distance of infinity to as close as 2.0 m. What are the minimum and maximum distances from the lens to the sensor?
> (a) In the diagram, what are the potentials at points b and c? Let V = 0 at infinity. (b) What is the change in electric potential energy if a third charge q3 = +2.00 nC is moved from point b to point c? (If you have done Problem 15, compare your answer
> A beam of electrons is accelerated across a potential of 15 kV before passing through two slits. The electrons form an interference pattern on a screen 2.5 m in front of the slits. The first-order maximum is 8.3 mm from the central maximum. What is the d
> Show that if two thin lenses are close together (s, the distance between the lenses, is negligibly small), the two lenses can be replaced by a single equivalent lens with focal length feq. Find the value of feq in terms of f1 and f2.
> Women often experience back pain when they are pregnant. Suppose a woman's mass before pregnancy is 68 kg and her center of mass when standing is located directly above the hips. By the thirty- fourth week of pregnancy, she has gained 8.0 kg (the combine
> A 75.0 kg skier starts from rest and slides down a 32.0 m frictionless slope that is inclined at an angle of 15.0° with the horizontal. Ignore air resistance. Calculate the work done by gravity on the skier and the work done by the normal force on the sk
> A sound wave with a frequency of 400.0 Hz is incident upon a set of stairs. The reflected waves from the vertical surfaces of adjacent steps interfere destructively. What is the minimum tread depth of a step for this to occur?
> Jamila has a set of reading glasses with focal length +0.50 m. (a) Are the lenses converging or diverging? (b) An object is placed 40.0 cm in front of one of the lenses. Where is the image formed? (c) What is the size of the image relative to the size
> In order to read his book, Stephen uses a pair of reading glasses. When he holds the book at a distance of 25 cm from his eyes, the glasses form an upright image a distance of 52 cm from his eyes. (a) Is this a converging or diverging lens? (b) What is
> An underground explosion sends out both transverse (S waves) and longitudinal (P waves) mechanical wave pulses (seismic waves) through Earth's crust. Suppose the speed of transverse waves is 8.0 km/s and that of longitudinal waves is 10.0 km/s. On one oc
> A light ray reflects from a plane mirror as shown in the figure. What is the angle of deviation δ?
> A relay race is run along a straight-line track of length 300.0 m running south to north. The first runner starts at the south end of the track and passes the baton to a teammate at the north end of the track. The second runner races back to the start li
> A standard “35 mm” slide measures 24.0 mm by 36.0 mm. Suppose a slide projector produces a 60.0 cm by 90.0 cm image of the slide on a screen. The focal length of the lens is 12.0 cm. (a) What is the distance between the slide and the screen? (b) If the
> (a) In the diagram, what are the potentials at points a and b? Let V = 0 at infinity. (b) What is the change in electric potential energy if a third charge q3 = +2.00 nC is moved from point a to point b? (If you have done Problem 14, compare your answer
> An early cyclotron at Cornell University was used from the 1930s to the 1950s to accelerate protons, which would then bombard various nuclei. The cyclotron used a large electromagnet with an iron yoke to produce a uniform magnetic field of 1.3 T over a r
> A loop of wire is connected to a battery and a variable resistor as shown. Two other loops of wire, B and C, are placed inside the large loop and outside the large loop, respectively. As the resistance in the variable resistor is increased, are there cur
> The projector in a movie theater has a lens with a focal length of 29.5 cm. It projects an image of the 70.0 mm wide film onto a screen that is 38.0 m from the projector. (a) How wide is the image on the screen? (b) What kind of lens is used in the pro
> An object that is 6.00 cm tall is placed 40.0 cm in front of a diverging lens. The magnitude of the focal length of the lens is 20.0 cm. Find the image position and size. Is the image real or virtual? Upright or inverted?
> Sketch a ray diagram to show that if an object is placed less than the focal length from a converging lens, the image is virtual and upright.
> Choose two rays in Fig. 23.7 and use them to prove that the angle of incidence is equal to the angle of reflection. [Hint: Choose a wavefront at two different times, one before reflection and one after. The time for light to travel from one wavefront to
> A stereo system whose amplifier can produce 60 W per channel is replaced by one rated 120 W per channel. Would you expect the new stereo to be able to play twice as loudly as the old one? Explain.
> (a) Find the number of water molecules in 1.00 L of water. (b) What fraction of the liter’s volume is occupied by water nuclei?
> The filament of an incandescent lightbulb is made of tungsten. At room temperature of 20.0°C the filament has a resistance of 10.0 Ω. (a) What is the power dissipated in the lightbulb immediately after it is connected to a 120 V emf (when the filament is
> Verify that the SI unit of impulse is the same as the SI unit of momentum.
> Two plane mirrors form a 70.0° angle as shown. For what angle θ is the final ray horizontal?
> (a) Find the equivalent resistance between terminals A and B to replace all of the resistors in the diagram. (b) What current flows through the emf? (c) What is the current through the 4.00 Ω resistor at the bottom?
> Two metal spheres of the same radius R are given charges of equal magnitude and opposite sign. No other charges are nearby. Sketch the electric field lines when the center-to-center distance between the spheres is approximately 3R.
> In a thunderstorm, charge is separated through a complicated mechanism that is ultimately powered by the Sun. A simplified model of the charge in a thundercloud represents the positive charge accumulated at the top and the negative charge at the bottom a
> A spaceship traveling 12.3 km/s relative to Earth sends out an EM pulse with a wavelength of 850.00 nm (as measured by the source). The pulse is reflected from another spaceship that is moving toward the first spaceship at a speed of 24.6 km/s relative t
> A spherical wave (from a point source) reflects from a planar surface. Draw a ray diagram and sketch some wavefronts for the reflected wave.
> At a marine animal park, Alison is looking through a glass window and watching dolphins swim underwater. If the dolphin is swimming directly toward her at 15 m/s, how fast does the dolphin appear to be moving?
> What is the purpose of the gel that is spread over the skin before an ultrasonic imaging procedure? [Hint: The speed of sound in the gel is similar to the speed in the body, while the speed in air is much slower. What happens to a wave at an abrupt chang
> Light travels in a medium with index n1 toward a boundary with another material of index n2 < n1. (a) Which is larger, the critical angle or Brewster's angle? Does the answer depend on the values of n1 and n2 (other than assuming n2 < n1)? (b) What can
> (a) Sunlight reflected from the still surface of a lake is totally polarized when the incident light is at what angle with respect to the horizontal? (b) In what direction is the reflected light polarized? (c) Is any light incident at this angle transm
> Some glasses used for viewing 3D movies are polarized, one lens having a vertical transmission axis and the other horizontal. While standing in line on a winter afternoon for a 3D movie and looking through his glasses at the road surface, Maurice notices
> A 6.0 kg object is at rest on a frictionless surface when it is struck head-on by a 2.0 kg object moving at 10 m/s. If the collision is elastic, what is the speed of the 6.0 kg object after the collision? [Hint: You will need two equations.]
> In an experiment to measure the index of refraction of human skin, it was found that if a beam of unpolarized light was shone on a skin sample from air at an incident angle of 54.7°, the reflected light was completely polarized. What is the index of refr
> What is the index of refraction of the core of an optical fiber if the cladding has n = 1.20 and the critical angle at the core-cladding boundary is 45.0°?
> (a) Find the potential at points a and b in the following diagram for charges Q1 = +2.50 nC and Q2 = −2.50 nC. (b) How much work must be done by an external agent to bring a point charge q from infinity to point b?
> Sketch the shape of the string at t = 1.6 s.
> Light rays from the Sun, which is at an angle of 35° above the western horizon, strike the still surface of a pond. (a) What is the angle of incidence of the Sun's rays on the pond? (b) What is the angle of reflection of the rays that leave the pond su
> Sketch the shape of the string at t = 2.2 s.
> The intensity of sunlight that reaches Earth's atmosphere is 1400 W/m2. What is the intensity of the sunlight that reaches Jupiter? Jupiter is 5.2 times as far from the Sun as Earth. [Hint: Treat the Sun as an isotropic source of light waves.]
> A motor scooter travels east at a speed of 12 m/s. The driver then reverses direction and heads west at 15 m/s. What is the change in velocity of the scooter? Give magnitude and direction.
> Compare the orbital radii of the He+ and H atoms for levels of equal energy (not the same value of n). Can you draw a general conclusion from your results?
> The radioactive decay of 238U produces alpha particles with a kinetic energy of 4.17 MeV. (a) At what speed do these alpha particles move? (b) Put yourself in the place of Rutherford and Geiger. You know that alpha particles are positively charged (fro
> (a) Using the result of Problem 26, calculate the numerical aperture of a fiber-optic cable whose cladding and core have indices of refraction 1.40 and 1.62, respectively. (b) Light enters the fiber from a balloon of saline solution (n = 1.35), which is
> A useful measure of the quality of a fiber-optic cable such as those used in endoscopes and other medical equipment is the numerical aperture. The larger the numerical aperture, the more light will be carried by the fiber. If light is incident on the fib
> The figure shows some light rays reflected from a small defect in the glass toward the surface of the glass. (a) If θc = 40.00°, what is the index of refraction of the glass? (b) Is there any point above the glass at which a vie
> Is there a critical angle for a light ray coming from a medium with an index of refraction 1.2 and incident on a medium that has an index of refraction 1.4? If so, what is the critical angle that allows total internal reflection in the first medium?
> (a) Find the electric potential at points a and b for charges of +4.2 nC and −6.4 nC located as shown in the following figure. (b) What is the potential difference ΔV for a trip from b to a? (c) How much work must be done
> The prism in the figure is made of crown glass. Its index of refraction ranges from 1.517 for the longest visible wavelengths to 1.538 for the shortest. Find the range of refraction angles for the light transmitted into air through the right side of the
