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college physics with an integrated approach

College Physics With An Integrated Approach To Forces And Kinematics 5th Edition Alan Giambattista - Solutions

Fill in the missing algebraic steps in the derivation of the time dilation equation [Eq. (26-4)] ΔΙ = 1 1 - 1²/² Δύο
By what factor is the momentum of a particle moving at 0.60c greater than the momentum of the same particle moving at 0.30c?
A particle is initially moving at 0.60c. If its momentum increases by a factor of 2.0, what is its speed?
The International Space Station (ISS) has a mass of 4.5 × 105 kg and orbits Earth at a speed of 7.7 km/s. By what percentage does the approximate momentum of the ISS calculated nonrelativistically differ from the relativistic momentum?
A spaceship of mass m is traveling away from Earth at speed v. Its momentum has magnitude 2.5mv. (a) Find v. (b) An astronaut on the spaceship has a watch that ticks once every second. How often does the watch tick as measured by an Earth observer?
An electron accelerator used in a hospital for cancer treatment produces a beam of electrons with kinetic energy 25 MeV. (a) What is the speed of the electrons produced by this accelerator? (b) If the end of the electron accelerator is placed 15 cm from the patient, how long, in the
A typical hospital accelerator built for proton beam therapy accelerates protons from rest by passing them through an electric potential difference of magnitude 75 MV. Find the speed of these protons.
PET scans involve the use of positron-emitting isotopes like carbon-11 and fluorine-18. These isotopes can be produced at hospital-based accelerators that first accelerate deuterons (hydrogen-2 nuclei) and then direct the deuterons onto a solid or gaseous target. Suppose a deuteron (rest energy
An experimental form of cancer therapy involves the use of a beam of highly ionized carbon atoms with a charge of +6e (all six electrons have been removed). The mass of the ions is 11.172 GeV/c2. If the accelerator is 7.50 m long and the ions are accelerated through a 125 MV potential difference,
Derive the energy-momentum relationStart by squaring the definition of total energy (E = K + E0) and then use the relativistic expressions for momentum and kinetic energy [Eqs. (26-15) and (26-18)]. E² = E + (pc)²
Starting with the energy-momentum relation and the definition of total energy, show that (pc)2 = K2 + 2KE0 [Eq. (26-23)]. E² = E + (pc)²
Show that Eq. (26-23) reduces to the nonrelativistic relationship between momentum and kinetic energy, K ≈ p2/(2m), for K ≪ E0. (pc)² = K² + 2KE0
Show that each of these statements implies that v ≪ c, which means that v can be considered a nonrelativistic speed: (a) γ − 1 ≪ 1 [Eq. (26-26)]; (b) K ≪ mc2 [Eq. (26-27)]; (c) p ≪ mc [Eq. (26-28)]; (d) K ≈ p2/(2m). Y-1 < 1 K
Two atomic clocks are synchronized. One is put aboard a spaceship that leaves Earth at t = 0 at a speed of 0.750c. (a) When the spaceship has been traveling for 48.0 h (according to the atomic clock on board), it sends a radio signal back to Earth. When would the signal be received on Earth,
Octavio, traveling at a speed of 0.60c, passes Tracy and her barn. Tracy, who is at rest with respect to her barn, says that the barn is 16 m long in the direction in which Octavio is traveling, 4.5 m high, and 12 m deep. (a) What does Tracy say is the volume of her barn? (b) What volume
A neutron (mass 939.565 MeV/c2) disintegrates into a proton (mass 938.272 MeV/c2), an electron (mass 0.5110 MeV/c2), and an antineutrino (mass negligibly small). What is the sum of the kinetic energies of the particles produced, if the neutron was at rest?
A starship is traveling at a speed of 0.78c toward Earth when it experiences a major malfunction and the crew is forced to evacuate. An escape pod that is 12.0 m long with respect to its passengers is ejected from the starship and sent toward Earth at a speed of 0.63c with respect to the starship.
According to the special theory of relativity, no object that has mass can travel faster than the speed of light. Yoo Jin says she knows something that moves faster than the speed of light. She tells you to consider a rotating beacon on Earth with a powerful laser that can send a beam to the
A biology professor notices a speck on a student's lab report and pulls out her magnifying lens to investigate. Holding the lens close to her eye, she is surprised to find Pelomyxa palustris, the largest known species of amoeba. (a) When observed without magnification at her near point of 28
A simple magnifier gives the maximum angular magnification when it forms a virtual image at the near point of the eye instead of at infinity. For simplicity, assume that the magnifier is right up against the eye, so that distances from the magnifier are approximately the same as distances from the
Five microscopes all have 16 cm tube lengths. Given the focal lengths of the eyepiece and objective, rank them in order of the magnifying power |M|, greatest to smallest. (a) fe = 1.5 cm, fo = 1.5 cm; (b) fe = 2.0 cm, fo = 2.0 cm; (c) fe = 1.5 cm, fo = 1.0 cm; (d) fe = 2.0 cm,
The eyepiece of a microscope has a focal length of 1.25 cm, and the objective lens focal length is 1.44 cm. (a) If the tube length is 18.0 cm, what is the angular magnification of the microscope? (b) What objective focal length would be required to double this magnification?
Jordan is building a compound microscope using an eyepiece with a focal length of 7.50 cm and an objective with a focal length of 1.500 cm. He will place the specimen a distance of 1.600 cm from the objective. (a) How far apart should Jordan place the lenses? (b) What will be the angular
To study the physical features of Hydra viridis, a student uses a compound microscope with a magnifying power of 425. (a) If the eyepiece has focal length 1.9 cm and the tube length is 19.2 cm, what focal length does the objective have? Assume a near point of 25 cm. (b) If the objective
A biologist observes a Paramecium with a microscope whose eyepiece and objective have focal lengths 2.25 cm and 1.10 cm, respectively. The specimen is 1.18 cm from the objective lens, and the final image is located at infinity. (a) What is the distance between the lenses? (b) What is the
Five telescopes all have the same magnifying power. Given the focal length of the objective, rank them in order of the focal length of the eyepiece, greatest to smallest. (a) fo = 80 cm; (b) fo = 60 cm; (c) fo =100 cm; (d) fo = 50 cm; (e) fo = 120 cm.A telescope mirror has
(a) If you were stranded on an island with a pair of 3.5 D reading glasses, could you make a useful telescope? If so, what would be the length of the telescope and what would be the angular magnification?(b) Answer the same questions if you also had a pair of 1.3 D reading glasses.
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 part of his body is 18 mm high. How close
The eyepiece of a Galilean telescope is a diverging lens. The focal points Fo and F′e coincide. In one such telescope, the lenses are a distance d = 32 cm apart and the focal length of the objective is 36 cm. A rhinoceros is viewed from a large distance. (a) What is the focal length of the
Good lenses used in cameras and other optical devices are actually compound lenses made of several lenses put together to minimize aberrations. Suppose a converging lens with a focal length of 4.00 cm is placed right next to a diverging lens with focal length of −20.0 cm. An object is placed 2.50
A slide projector has a projection lens of 10.0 cm focal length, and the screen is located 2.5 m from the projector. (a) What is the distance between the slide and the projection lens? (b) What is the magnification of the image? (c) How wide is the image of a slide of width 36 mm on
A cub scout makes a microscope by placing two converging lenses of +18 D at opposite ends of a 28 cm long tube.(a) What is the tube length of the microscope? (b) What is the angular magnification? (c) How far should an object be placed from the objective lens?
A convex lens of refractive power +12 D is used as a magnifier to examine a wildflower. What is the angular magnification if the final image is at (a) Infinity or (b) The near point of 25 cm?
Two converging lenses, separated by a distance of 50.0 cm, are used in combination. The first lens, located to the left, has a focal length of 15.0 cm. The second lens, located to the right, has a focal length of 12.0 cm. An object, 3.00 cm high, is placed at a distance of 20.0 cm in front of the
Two lenses, separated by a distance of 21.0 cm, are used in combination. The first lens has a focal length of +30.0 cm; the second has a focal length of −15.0 cm. An object, 2.0 mm long, is placed 1.8 cm before the first lens. (a) What are the intermediate and final image distances relative
A camera has a telephoto lens of 240 mm focal length. The lens can be moved in and out a distance of 16 mm from the image sensor by rotating the lens barrel. If the lens can focus objects at infinity, what is the closest object distance for which the camera can give a sharp image?
Two lenses, of focal lengths 3.0 cm and 30.0 cm, are used to build a small telescope. (a) Which lens should be the objective? (b) What is the angular magnification?What is the distance between the intermediate image (formed by the eyepiece) and the objective lens?
The image sensor of a camera measures 24 mm by 36 mm. The focal length of the camera lens is 50.0 mm. A picture is taken of a person 182 cm tall. What is the minimum distance from the camera for the person to stand so that the image fits on the sensor? Give two answers, one for each orientation of
A converging lens with a focal length of 5.500 cm is placed 8.00 cm to the left of a diverging lens with a focal length of −4.20 cm. An object that is 1.0 cm tall is placed 9.000 cm to the left of the converging lens. (a) Where is the final image formed? (b) How tall is the final
An object is placed between a concave mirror with a radius of curvature of 18.0 cm and a diverging lens with a focal length of magnitude 12.5 cm. The object is 15.0 cm from the mirror and 20.0 cm from the lens. Looking through the lens, you see two images. Image 1 is formed by light rays that
An object is located at x = 0. At x = 2.50 cm is a converging lens with a focal length of 2.00 cm, at x = 16.5 cm is an unknown lens, and at x = 19.8 cm is another converging lens with focal length 4.00 cm. An upright image is formed at x = 39.8 cm. For each lens, the object distance exceeds the
Use the thin-lens equation to show that the transverse magnification due to the objective of a microscope is mo = −L/fo.
A concave mirror has radius of curvature R. A ray of light parallel to and a distance away from the optical axis is incident on the mirror. (a) Use the law of reflection to find the distance from the vertex to the point where the reflected ray crosses the optical axis. (b) How far is this
(a) What is the angular size of the Moon as viewed from Earth's surface? See Appendix B for necessary information. (b) Elysha is gazing at a full Moon at night. The diameter of her pupil is 7.0 mm and the diameter of her eye is 2.0 cm. What is the diameter of the image of the Moon on her
If the figure shows the wavefronts for a double-slit interference experiment with light, at which of the labeled points is the intensity zero? The wavefronts represent wave crests only (not crests and troughs).(a) A only(b) B only(c) C only(d) A and B(e) B and C(f) A and C(g) A, B, and C
If the figure shows the surface water waves in a ripple tank with two coherent sources, at which of the labeled points would a bit of floating cork bob up and down with greater amplitude than at neighboring points? A. S₁ Co B S₂
Two coherent EM waves have amplitudes of E0 and 0.48E0. What is the resulting amplitude when they interfere constructively? pattern. What is the wavelength of the second source?
In a double-slit experiment, light rays from the two slits that reach the second maximum on one side of the central maximum travel distances that differ by (a) (b) 2λ λ (c) 1/2 (d) 2/4
Two coherent EM waves have amplitudes of E0 and 0.67E0. What is the resulting amplitude when they interfere destructively?
Two coherent EM waves have intensities of I0 and 0.28I0. What is the resulting intensity when they interfere constructively?
A Michelson interferometer is set up for microwaves. Initially the reflectors are placed so that the detector reads a maximum. When one of the reflectors is moved 12 cm, the needle swings to minimum and back to maximum six times. What is the wavelength of the microwaves?(a) 0.5 cm(b) 1 cm(c) 2
In a double-slit experiment with coherent light, the intensity of the light reaching the center of the screen from one slit alone is I0 and the intensity of the light reaching the center from the other slit alone is 9I0. When both slits are open, what is the intensity of the light at the
Two coherent EM waves have intensities of I0 and 0.60I0. What is the resulting intensity when they interfere destructively?
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?
Which of these actions will improve the resolution of a microscope? (a) Increase the wavelength of the light (b) decrease the wavelength of the light(c) Increase the diameter of the lenses(d) Decrease the diameter of the lenses(e) Both (b) and (c)(f) Both (b) and (d)(g) Both (a) and
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?
Coherent light of a single frequency passes through a double slit, with slit separation d, to produce a pattern of maxima and minima on a screen a distance D from the slits. What would cause the separation between adjacent minima on the screen to decrease?(a) Decrease the frequency of the incident
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 of light falling on the book when Albert
Two narrow slits, of width a, separated by a distance d, are illuminated by light with a wavelength of 660 nm. The resulting interference pattern is labeled (1) in the figure. The same light source is then used to illuminate another group of slits and produces pattern (2). The second slit
The figure shows the interference pattern obtained in a double-slit experiment. Which letter indicates a third-order maximum? Central bright fringe (a)(b) (c) (d) (e)
The intensity pattern in the diagram is due to (a) Two slits.(b) A single slit.(c) A grating.(d) A circular aperture. Relative intensity -10 -5 0 0 (degrees) 5 حمام 10
The f-stop of a camera lens is defined as the ratio of the focal length of lens to the diameter of the aperture. A large f-stop therefore means a small aperture. If diffraction is the only consideration, would you use the largest or the smallest f-stop to get the sharpest image?
Describe what happens to a single-slit diffraction pattern as the width of the slit is slowly decreased.
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 white light is incident on the cornea, strong
Why don't you see an interference pattern on your desk when you have light from two different lamps illuminating the surface?
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 glass plates and that the plates are
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 plates for one of the light
The antenna on a wireless router radiates microwaves at a frequency of 5.0 GHz. What is the maximum length of the antenna if it is not to exceed half of a wavelength?
(a) In what part of the EM spectrum is the laser pulse? (b) How long (in centimeters) is a single pulse of the laser in air? (c) How many wavelengths fit in one pulse?A laser used in LASIK eye surgery produces 55 pulses per second. The wavelength is 193 nm (in air), and each pulse lasts
(a) What is the total energy of a single pulse? (b) What is the intensity during a pulse?A laser used in LASIK eye surgery produces 55 pulses per second. The wavelength is 193 nm (in air), and each pulse lasts 10.0 ps. The average power emitted by the laser is 120.0 mW and the beam diameter is
A 2.0 mW laser pointer has a beam diameter of 1.5 mm. When it is accidentally pointed at a person’s eye, the beam is focused to a spot of diameter 20.0 μm on the retina and the retina is exposed for 80 ms. (a) What is the intensity of the laser beam? (b) What is the intensity of light
To increase the amount of light collected by the objective lens of a microscope, a technique known as oil immersion microscopy is used. To replace the air between the objective lens and the thin slip of glass (n = 1.51) covering the specimen, a drop of oil with the same index of refraction as the
Suppose you are facing due north at sunrise. Sunlight is reflected by a store's display window as shown. Is the reflected light partially polarized? If so, in what direction? Store's display window Observer Sunlight from the sunrise
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 viewer would not be able to see the defect? Explain.
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 refraction of this skin sample?
Starting with Fig. 23.39, perform all the algebraic steps to obtain the mirror equation in the form of Eq. (23-22). h AI CI | I B th' F 1 | I P -9- -R- V
A point source of light is in front of a plane mirror. (a) Show that all the reflected rays, when extended back behind the mirror, intersect in a single point.(b) Show that the image point lies on a line through the object and perpendicular to the mirror, and that the object and image
(a) For a converging lens with a focal length of 3.50 cm, find the object distance that will result in an inverted image with an image distance of 5.00 cm. Use a ray diagram to verify your calculations. (b) Is the image real or virtual? (c) What is the magnification?
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 projector?(c) Is the image on the screen
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 screen is moved farther from the
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 the magnification of the lens? (c)
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 of the object? (d) Is the
A 5.0 cm tall object is placed 50.0 cm from a lens with focal length −20.0 cm. (a) How tall is the image? (b) Is the image upright or inverted?
Samantha puts her face 32.0 cm from a makeup mirror and notices that her image is magnified by 1.80 times. (a) What kind of mirror is this? (b) Where is her face relative to the radius of curvature or focal length? (c) What is the radius of curvature of the mirror?
Draw a ray diagram and locate the image for the object shown in the figure. 2F Object F Converging lens F H 2F
In many cars the passenger's side mirror says: “Objects in the mirror are closer than they appear.” (a) Does this mirror form real or virtual images? (b) Since the image is diminished in size, is the mirror concave or convex? Why? (c) Show that the image must actually be closer
An object of height 5.00 cm is placed 20.0 cm from a converging lens of focal length 15.0 cm. Draw a ray diagram to find the height and position of the image.
A ray of light in air is incident on benzene contained in a shallow tank made of crown glass, making an angle of 60.0° with the surface. What is the angle of refraction of the light ray (measured from the normal) when it enters the glass at the bottom of the tank? Glass- 60.0% Air Benzene
Show that the deviation angle δ for a ray striking a thin converging lens at a distance d from the principal axis is given by δ = d/f. Therefore, a ray is bent through an angle δ that is proportional to d and does not depend on the angle of the incident ray (as long as it is paraxial).
(a) Sunlight reflected from the smooth ice surface of a frozen 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) What is the direction of the magnetic field of the reflected
The compound microscope is made from two lenses. Which statement is true concerning the operation of the compound microscope?(a) Both lenses form real images.(b) Both lenses form virtual images.(c) The lens closest to the object forms a virtual image; the other lens forms a real image.(d) The lens
Which of these statements best explains why a telescope enables us to see details of a distant object such as the Moon or a planet more clearly?(a) The image formed by the telescope is larger than the object.(b) The image formed by the telescope subtends a larger angle at the eye than the object
What are the three lowest angular speeds for which the wheel in Fizeau’s apparatus (see Fig. 22.11) allows the reflected light to pass through to the observer? Assume the distance between the notched wheel and the mirror is 8.6 km and that there are 5 notches in the wheel.
You are trying to communicate with a spaceship that is traveling at 1.2 × 108 m/s away from Earth. If you send a message at a frequency of 55 kHz, to what frequency should the astronauts on the ship tune to receive your message?
A microwave oven can heat 350 g of water from 25.0°C to 100.0°C in 2.00 min. (a) At what rate is energy absorbed by the water? (b) These microwaves pass through a waveguide of cross-sectional area 88.0 cm2. What is the average intensity of the microwaves in the waveguide? (c) What
You are standing 1.2 m from a heat lamp that draws an rms current of 12.5 A when connected to 120 V rms. (a) Assuming that the energy of the heat lamp is radiated uniformly in a hemispherical pattern, what is the intensity of the light on your face? (b) If you stand in front of the heat
During a laboratory experiment with an object placed in front of a concave mirror, the image distance q is determined for several different values of object distance p. How might the focal length f of the mirror be determined from a graph of the data? (a) Plot q versus p; slope = f (b) Plot q
The image of a slide formed by a slide projector is correctly described by which of the listed terms?(a) Real, upright, enlarged(b) Real, inverted, diminished(c) Virtual, inverted, enlarged(d) Virtual, upright, diminished(e) Real, upright, diminished(f) Real, inverted, enlarged(g) Virtual,
Which statements are true? The rays in a plane wave are1. Parallel to the wavefronts.2. Perpendicular to the wavefronts.3. Directed radially outward from a central point.4. Parallel to one another.(a) 1, 2, 3, 4(b) 1, 4(c) 2, 3(d) 2, 4
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 surface? (c) In what direction

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