A thin film of oil (n = 1.50) is spread over a puddle of water (n = 1.33). In a region where the film looks red from directly above (λ = 630 nm), what is the minimum possible thickness of the film?
> Light of wavelength 589 nm incident on a pair of slits produces an interference pattern on a distant screen in which the separation between adjacent bright fringes at the center of the pattern is 0.530 cm. A second light source, when incident on the same
> Use a compass to make an accurate drawing of the wavefronts in a double-slit interference experiment similar to Fig. 25.17c. Place the slits 2.0 cm apart and let the wavelength of the incident wave be 1.0 cm. Using a straightedge, draw lines of construct
> The length of the auditory canal in humans averages about 2.5 cm. What are the lowest three standing wave frequencies for a pipe of this length open at one end? What effect might resonance have on the sensitivity of the ear at various frequencies? (Refer
> A Ping-Pong ball that has been dented during hard play can often be restored by placing it in hot water. Explain why this works.
> Block A, with a mass of 220 g, is traveling north on a frictionless surface with a speed of 5.0 m/s. Block B, with a mass of 300 g, travels west on the same surface until it collides with A. After the collision, the blocks move off together with a veloci
> Ramon has a coherent light source with wavelength 547 nm. He wishes to send light through a double slit with slit separation of 1.50 mm to a screen 90.0 cm away. What is the minimum width of the screen if Ramon wants to display five complete bright fring
> Light incident on a pair of slits produces an interference pattern on a screen 2.50 m from the slits. If the slit separation is 0.0150 cm and the distance between adjacent bright fringes in the pattern is 0.760 cm, what is the wavelength of the light? [H
> If the incline is frictionless, find the total work done on the sliding crate. The tension in the rope is 110.5 N.
> Michaela is planning a trip in Ireland from Killarney to Cork to visit Blarney Castle (see Example 3.2). She also wants to visit Mallow, which is located 39 km due east of Killarney and 22 km due north of Cork. Draw the displacement vectors for the trip
> Jim rides his skateboard down a ramp that is in the shape of a quarter circle with a radius of 5.00 m. At the bottom of the ramp, Jim is moving at 9.00 m/s. Jim and his skateboard have a mass of 65.0 kg. How much work is done by friction as the skateboar
> The electric field between plates (A) is zero. As the beam exits the space between plates (B), it has been deflected 2.0 mm downward (Δy = −2.0 mm). What is the electric field between plates (B)?
> While passing a slower car on the highway, you accelerate uniformly from 17.4 m/s to 27.3 m/s in a time of 10.0 s. (a) How far do you travel during this time? (b) What is your acceleration magnitude?
> In a fixed-target experiment, high-energy charged particles from an accelerator are smashed into a stationary target. By contrast, in a colliding beam experiment, two beams of particles are accelerated to high energies; particles moving in opposite direc
> Two coherent EM waves have intensities of I0 and 0.28I0. What is the resulting intensity when they interfere constructively?
> The mass of an aluminum atom is 27.0 u. What is the mass of one mole of aluminum atoms? (No calculation required!)
> In a double-slit interference experiment, the wavelength is 475 nm, the slit separation is 0.120 mm, and the screen is 36.8 cm away from the slits. What is the linear distance between adjacent maxima on the screen? [Hint: Assume the small-angle approxim
> Show that the interference fringes in a double-slit experiment are equally spaced on a distant screen near the center of the interference pattern. [Hint: Use the small-angle approximation for θ.]
> A cue stick hits a cue ball with an average force of 24 N for a duration of 0.028 s. If the mass of the ball is 0.16 kg, how fast is it moving after being struck?
> Light of 650 nm is incident on two slits. A maximum is seen at an angle of 4.10° and the next minimum at 4.78°. What is the order m of the maximum and what is the distance d between the slits?
> Repeat Problem 25 assuming that n1 < n2 < n3.
> The particle moves along a straight line from a to b.
> A thin film is viewed both in reflected and transmitted light at normal incidence. The figure shows the strongest two rays for each. Show that if rays 1 and 2 interfere constructively, then rays 3 and 4 must interfere destructively, and if rays 1 and 2 i
> A lens is placed on a flat plate of glass to test whether its surface is spherical. See the following figure. Show that the radius rm of the mth dark ring should be where R is the radius of curvature of the lens surface facing the plate and the wavelengt
> In a certain region of space, there is a uniform electric field / V/m to the east and a uniform magnetic field / to the west. (a) What is the electromagnetic force on an electron moving north at 1.0 × 107 m/s? (b) With the electric and magnetic fi
> What are the four lowest standing wave frequencies for an organ pipe that is 4.80 m long and closed at one end?
> Dynamite is being used to blast through rock to build a road. After one explosion, the masses and kinetic energies of several fragments of rock thrown up into the air are: (a) 8 kg, 400 J (b) 2 kg, 1600 J (c) 4 kg, 1600 J (d) 16 kg, 100 J (e) 1 kg, 1600
> Two optically flat plates of glass are separated at one end by a wire of diameter 0.200 mm; at the other end they touch. Thus, the air gap between the plates has a thickness ranging from 0 to 0.200 mm. The plates are 15.0 cm long and are illuminated from
> A typical sneeze expels material at a maximum speed of 44 m/s. Suppose the material begins inside the nose at rest, 2.0 cm from the nostrils. It has a constant acceleration for the first 0.25 cm and then moves at constant velocity for the remainder of th
> A guitar string has a fundamental frequency f. The player presses on a fret, reducing the vibrating part of the string to 5/6 of its original length. Ignoring the very small change in tension, by what factor does the fundamental frequency change?
> Two equal charges (Q = +1.00 nC) are situated at the diagonal corners A and B of a square of side 1.0 m. What is the magnitude of the electric field at point D?
> A circular loop of wire moves in one of three directions near a long, straight current-carrying wire. For each case, find the direction of the current in the loop, the direction of the magnetic force on the loop, and the direction of the magnetic force o
> See Problem 21. This time the glass plates are immersed in clear oil with an index of refraction of 1.50. (a) What is the minimum distance between the two glass plates for one of the dark regions? (b) What is the minimum distance between the two glass
> The formula for the speed of transverse waves on a spring is the same as for a string. (a) A spring is stretched to a length much greater than its relaxed length. Explain why the tension in the spring is approximately proportional to the length. (b) A
> At a science museum, Marlow looks down into a display case and sees two pieces of very flat glass lying on top of each other with light and dark regions on the glass. The exhibit states that monochromatic light with a wavelength of 550 nm is incident on
> The intensity of reflection of various wavelengths of light projected onto the eye can be used to determine the thickness of the tear film that coats the cornea. The tear film and cornea have indices of refraction 1.360 and 1.376, respectively. When whit
> Belinda needs to find the CM of a sculpture she has made so that it will hang in a gallery correctly. The sculpture is all in one plane and consists of various shaped uniform objects with masses and sizes as shown. Where is the CM of this sculpture? Assu
> It is believed that a large electric fish known as Torpedo occidentalis uses electricity to shock its victims. A typical fish can deliver a potential difference of 0.20 kV for a duration of 1.5 ms. This pulse delivers charge at a rate of 18 C/s. (a) Wha
> In an amusement park maze with all the walls covered with mirrors, Pilar sees Hernando's reflection from a series of three mirrors. If the reflected angle from mirror 3 is 55° for the mirror arrangement shown in the figure, what is the angle of incidence
> Two coherent EM waves have amplitudes of E0 and 0.67E0. What is the resulting amplitude when they interfere destructively?
> A soap film has an index of refraction n = 1.35. The film is viewed in transmitted light. (a) At a spot where the film thickness is 910.0 nm, which wavelengths are weakest in the transmitted light? (b) Which wavelengths are strongest in the transmitted
> A soap film has an index of refraction n = 1.35. The film is viewed in reflected light. (a) At a spot where the film thickness is 910.0 nm, which wavelengths are missing in the reflected light? (b) Which wavelengths are strongest in the reflected light
> When does the string first look completely flat for t > 0?
> A camera lens (n = 1.50) is coated with a thin film of magnesium fluoride (n = 1.38) of thickness 90.0 nm. What wavelength in the visible spectrum is most strongly transmitted through the film?
> A transparent film (n = 1.3) is deposited on a glass lens (n = 1.5) to form a nonreflective coating. What is the minimum thickness that would minimize reflection of light with wavelength 500.0 nm in air?
> Rank points A–E in order of the potential, from highest to lowest.
> Kim says that she was less than 10 ft away from the president when she took a picture of him with her 50 mm focal length camera lens. The picture shows the upper half of the president's body (3.0 ft of his total height). On the negative of the film, this
> Kyle is climbing a sailboat mast and is 5.00 m above the surface of the ocean, while his friend Rob is scuba diving below the boat. Kyle shouts to someone on another boat and Rob hears him shout 0.0210 s later. The ocean temperature is 25°C and the air i
> Suppose we have two tanks, one containing helium gas and the other nitrogen gas. The two gases are at the same temperature and pressure. Which has the higher number density (or are they equal)? Which has the higher mass density (or are they equal)?
> A thin film of oil (n = 1.50) of thickness 0.40 µm is spread over a puddle of water (n = 1.33). For which wavelength in the visible spectrum do you expect constructive interference for reflection at normal incidence?
> In Problem 111, the wire that goes through the top corner of the triangle has a linear mass density of 0.150 g/m. What current in this wire would make it “hover” above the other two? [Hint: The sum of the magnetic and gravitational forces on the wire is
> (a) In Practice Problem 7.11, find the momentum change of the ball of mass m1 during the collision. Give your answer in x- and y- component form; express the components in terms of m1 and vi. (b) Repeat for the ball of mass m2. How are the momentum chan
> A camera lens (n = 1.50) is coated with a thin layer of magnesium fluoride (n = 1.38). The purpose of the coating is to allow all the light to be transmitted by canceling out reflected light. What is the minimum thickness of the coating necessary to canc
> The positions of three particles, written as (x, y) coordinates, are: particle 1 (mass 4.0 kg) at (4.0 m, 0 m); particle 2 (mass 6.0 kg) at (2.0 m, 4.0 m); particle 3 (mass 3.0 kg) at (−1.0 m, −2.0 m). What is the location of the CM?
> A Michelson interferometer is set up using white light. The arms are adjusted so that a bright white spot appears on the screen (constructive interference for all wavelengths). A slab of glass (n = 1.46) is inserted into one of the arms. To return to the
> Use the definition that 1 mol of 12C (carbon-12) atoms has a mass of exactly 12 g, along with Avogadro's number, to derive the conversion between atomic mass units and kg.
> 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
