Repeat Problem 25 assuming that n1 < n2 < n3.
> Why does a helium weather balloon expand as it rises into the air? Assume the temperature remains constant.
> A transverse wave on a string has amplitude 4.0 mm, angular frequency 600 rad/s, and wavenumber 6.0 rad/m. (a) What is the maximum transverse speed of a point on the string? (b) What is the average transverse speed of a point on the string? [Hint: How
> A futuristic train moving in a straight line with a uniform speed of 0.80c passes a series of communications towers. The spacing between the towers, according to an observer on the ground, is 3.0 km. A passenger on the train uses an accurate stopwatch to
> The light-second is a unit of distance; 1 light-second is the distance that light travels in 1 second. (a) Find the conversion between light-seconds and meters: 1 light-second = ? m. (b) What is the speed of light in units of light-seconds per second?
> Fill in the missing algebraic steps in the derivation of the time dilation equation [Eq. (26-4)].
> An engineer in a train moving toward the station with a velocity v = 0.60c lights a signal flare as he reaches a marker 1.0 km from the station (according to a scale laid out on the ground). By how much time, on the station-master's clock, does the arriv
> A 2.00 µF capacitor is charged using a 5.00 V battery, and a 3.00 µF capacitor is charged using a 10.0 V battery. (a) What is the total energy stored in the two capacitors? (b) The batteries are disconnected, and the two capacitors are connected togeth
> A steep cliff west of Lydia's home reflects a 1020 kHz radio signal from a station that is 74 km due east of her home. If there is destructive interference, what is the minimum distance of the cliff from her home? Assume there is a 180° phase shift when
> A sports car traveling along a straight line increases its speed from 20.0 mi/h to 60.0 mi/h. (a) What is the ratio of the final to the initial magnitude of its momentum? (b) What is the ratio of the final to the initial kinetic energy?
> A skier with a mass of 63 kg starts from rest and skis down an icy (frictionless) slope that has a length of 50 m at an angle of 32° with respect to the horizontal. At the bottom of the slope, the path levels out and becomes horizontal, the snow becomes
> An experiment similar to Example 25.1 is performed; the power at the receiver as a function of x is shown in the figure. (a) Approximately what is the wavelength of the microwaves? (b) If the amplitude of the wave entering the detector at the first max
> The current in a 0.080 H solenoid increases from 20.0 mA to 160.0 mA in 7.0 s. Find the average emf in the solenoid during that time interval.
> An unmarked police car starts from rest just as a speeding car passes at a speed of v. If the police car speeds up with a constant acceleration of a, what is the speed of the police car when it catches up to the speeder, who does not realize she is being
> The particle moves along a straight line from b to a.
> The circuit shown has a source voltage of 440 V rms, resistance R = 250 Ω, inductance L = 0.800 H, and capacitance C = 2.22 µF. (a) Find the angular frequency ω0 for resonance in this circuit. (b) Draw a phasor diagr
> A spider’s web can undergo SHM when a fly lands on it and displaces the web. For simplicity, assume that a web is described by Hooke’s law (even though really it deforms permanently when displaced). If the web is initially horizontal and a fly landing on
> When Albert turns on his small desk lamp, the light falling on his book has intensity I0. When this is not quite enough, he turns the small lamp off and turns on a high-intensity lamp so that the light on his book has intensity 4I0. What is the intensity
> Four coherent EM waves have intensities of I0, 0.80I0, 0.60I0, and 0.40I0. The second is 180° out of phase with the first; the third and fourth are in phase with the first. What is the intensity of the superposition of the four?
> Four coherent EM waves are all in phase. Individually, they have intensities of I0, 0.80I0, 0.60I0, and 0.40I0. What is the intensity of the superposition of the four?
> Two coherent EM waves have intensities of I0 and 0.60I0. What is the resulting intensity when they interfere destructively?
> A grating has exactly 8000 slits uniformly spaced over 2.54 cm and is illuminated by light from a mercury vapor discharge lamp. What is the expected angle for the third-order maximum of the green line (λ = 546 nm)?
> A nurse applies a force of 4.40 N to the piston of a syringe. The piston has an area of 5.00 × 10−5 m2. What is the pressure increase in the fluid within the syringe?
> A spaceship resting on Earth has a length of 35.2 m. As it departs on a trip to another planet, it has a length of 30.5 m as measured by the Earthbound observers. The Earthbound observers also notice that one of the astronauts on the spaceship exercises
> You are given a slide with two slits cut into it and asked how far apart the slits are. You shine white light on the slide and notice the first-order color spectrum that is created on a screen 3.40 m away. On the screen, the red light with a wavelength o
> What potential difference must be applied to an x-ray tube to produce x-rays with a minimum wavelength of 45.0 pm?
> Starting from rest, a horse pulls a 250 kg cart for a distance of 1.5 km. It reaches a speed of 0.38 m/s by the time it has walked 50.0 m and then walks at constant speed. The frictional force on the rolling cart is a constant 260 N. Each gram of oats th
> An engine pulls a train of 20 freight cars, each having a mass of 5.0 × 104 kg, with a constant force. The cars move from rest to a speed of 4.0 m/s in 20.0 s on a straight track. Neglecting friction, what is the force with which the tenth car pulls the
> A double slit is illuminated with monochromatic light of wavelength 600.0 nm. The m = 0 and m = 1 bright fringes are separated by 3.0 mm on a screen 40.0 cm away from the slits. What is the separation between the slits? [Hint: Is the small-angle approxim
> A system consists of three particles with these masses and velocities: mass 3.0 kg, moving north at 3.0 m/s; mass 4.0 kg, moving south at 5.0 m/s; and mass 7.0 kg, moving north at 2.0 m/s. What is the total momentum of the system?
> Light from a helium-neon laser (632.8 nm) is incident on a pair of slits. In the interference pattern on a screen 1.5 m from the slits, the bright fringes are separated by 1.35 cm. What is the slit separation? [Hint: Is the small-angle approximation just
> 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?
> 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?
> 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?
> 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.)
