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Physics for Scientists and Engineers A Strategic Approach with Modern Physics 4th edition Randall D. Knight - Solutions

The sun radiates energy at the rate 3.8 × 1026 W. The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is 2.0 × 1030 kg.a. How much mass does the sun lose each year?b. What percent is this of the sun’s total mass?c. Fusion takes
Many science fiction spaceships are powered by antimatter reactors. Suppose a 20-m-long spaceship, with a mass of 15,000 kg when empty, carries 2000 kg of fuel: 1000 kg each of matter and antimatter. The matter and antimatter are slowly combined, and the energy of their total annihilation is used
A typical nuclear power plant generates electricity at the rate of 1000 MW. The efficiency of transforming thermal energy into electrical energy is 1/3 and the plant runs at full capacity for 80% of the year. (Nuclear power plants are down about 20% of the time for maintenance and refueling.)a. How
At what speed, as a fraction of c, is the kinetic energy of a particle twice its Newtonian value?
a. What are the momentum and total energy of a proton with speed 0.99c?b. What is the proton’s momentum in a different reference frame in which E' = 5.0 × 10-10 J?
Let’s examine whether or not the law of conservation of momentum is true in all reference frames if we use the Newtonian definition of momentum: px = mux. Consider an object A of mass 3m at rest in reference frame S. Object A explodes into two pieces: object B, of mass m, that is shot to the left
A rocket is fired from the earth to the moon at a speed of 0.990c. Let two events be “rocket leaves earth” and “rocket hits moon.”a. In the earth’s reference frame, calculate Δx, Δt, and the spacetime interval s for these events.b. In the rocket’s reference frame, calculate Δx',
a. Derive a velocity transformation equation for uy and u'y. Assume that the reference frames are in the standard orientation with motion parallel to the x- and x'-axes.b. A rocket passes the earth at 0.80c. As it goes by, it launches a projectile at 0.60c perpendicular to the direction of motion.
Derive the Lorentz transformations for t and t'.
This chapter has assumed that lengths perpendicular to the direction of motion are not affected by the motion. That is, motion in the x-direction does not cause length contraction along the y- or z-axes. To find out if this is really true, consider two spray-paint nozzles attached to rods
The half-life of a muon at rest is 1.5 μs. Muons that have been accelerated to a very high speed and are then held in a circular storage ring have a half-life of 7.5 μs.a. What is the speed, as a fraction of c, of the muons in the storage ring?b. What is the total energy of a muon in the storage
What is the speed, in m/s, of a proton after being accelerated from rest through a 50 × 106 V potential difference?
Through what potential difference must an electron be accelerated, starting from rest, to acquire a speed of 0.99c?
A rocket fires a projectile at a speed of 0.95c while traveling past the earth. An earthbound scientist measures the projectile’s speed to be 0.90c. What was the rocket’s speed as a fraction of c?
Two rockets, A and B, approach the earth from opposite directions at speed 0.80c. The length of each rocket measured in its rest frame is 100 m. What is the length of rocket A as measured by the crew of rocket B?
Two rockets approach each other. Each is traveling at 0.75c in the earth’s reference frame. What is the speed, as a fraction of c, of one rocket relative to the other?
The star Delta goes supernova. One year later and 2.0 ly away, as measured by astronomers in the galaxy, star Epsilon explodes. Let the explosion of Delta be at xD = 0 and tD = 0. The explosions are observed by three spaceships cruising through the galaxy in the direction from Delta to Epsilon at
A rocket traveling at 0.50c sets out for the nearest star, Alpha Centauri, which is 4.3 ly away from earth. It will return to earth immediately after reaching Alpha Centauri. What distance will the rocket travel and how long will the journey last according to(a) Stay-at-home earthlings?(b) The
The quantity dE/dv, the rate of increase of energy with speed, is the amount of additional energy a moving object needs per 1 m/s increase in speed.a. A 25,000 kg truck is traveling at 30 m/s. How much additional energy is needed to increase its speed by 1 m/s?b. A 25,000 kg rocket is traveling at
In an attempt to reduce the extraordinarily long travel times for voyaging to distant stars, some people have suggested traveling at close to the speed of light. Suppose you wish to visit the red giant star Betelgeuse, which is 430 ly away, and that you want your 20,000 kg rocket to move so fast
On a futuristic highway, a 15-m-long rocket travels so fast that a red stoplight, with a wavelength of 700 nm, appears to the pilot to be a green light with a wavelength of 520 nm. What is the length of the rocket to an observer standing at the intersection as the rocket speeds through?
The Stanford Linear Accelerator (SLAC) accelerates electrons to v = 0.99999997c in a 3.2-km-long tube. If they travel the length of the tube at full speed (they don’t, because they are accelerating), how long is the tube in the electrons’ reference frame?
A starship voyages to a distant planet 10 ly away. The explorers stay 1 year, return at the same speed, and arrive back on earth 26 years, as measured on earth, after they left. Assume that the time needed to accelerate and decelerate is negligible.a. What is the speed of the starship?b. How much
Two events in reference frame S occur 10 μs apart at the same point in space. The distance between the two events is 2400 m in reference frame S'.a. What is the time interval between the events in reference frame S'?b. What is the velocity of S' relative to S?
The star Alpha goes supernova. Ten years later and 100 ly away, as measured by astronomers in the galaxy, star Beta explodes.a. Is it possible that the explosion of Alpha is in any way responsible for the explosion of Beta? Explain.b. An alien spacecraft passing through the galaxy finds that the
A 30-m-long rocket train car is traveling from Los Angeles to New York at 0.50c when a light at the center of the car flashes. When the light reaches the front of the car, it immediately rings a bell. Light reaching the back of the car immediately sounds a siren.a. Are the bell and siren
The diameter of the solar system is 10 light hours. A spaceship crosses the solar system in 15 hours, as measured on earth. How long, in hours, does the passage take according to passengers on the spaceship?
One of the important ways in which the Higgs boson was detected at the Large Hadron Collider was by observing a type of decay in which the Higgs—which decays too quickly to be observed directly—is immediately transformed into two photons emitted back to back. Two photons, with momenta 3.31 ×
A modest supernova (the explosion of a massive star at the end of its life cycle) releases 1.5 × 1044 J of energy in a few seconds. This is enough to outshine the entire galaxy in which it occurs. Suppose a star with the mass of our sun collides with an antimatter star of equal mass, causing
At what speed, as a fraction of c, is a particle’s total energy twice its rest energy?
At what speed, as a fraction of c, is a particle’s kinetic energy twice its rest energy?
At what speed, as a fraction of c, must an electron move so that its total energy is 10% more than its rest mass energy?
What are the rest energy, the kinetic energy, and the total energy of a 1.0 g particle with a speed of 0.80c?
A quarter-pound hamburger with all the fixiazzngs has a mass of 200 g. The food energy of the hamburger (480 food calories) is 2 MJ.a. What is the energy equivalent of the mass of the hamburger?b. By what factor does the energy equivalent exceed the food aenergy?
What is the speed, as a fraction of c, of a particle whose momentum is mc?
At what speed, as a fraction of c, is a particle’s momentum twice its Newtonian value?
A 1.0 g particle has momentum 400,000 kg m/s. What is the particle’s speed in m/s?
A proton is accelerated to 0.999c.a. What is the proton’s momentum?b. By what factor does the proton’s momentum exceed its aNewtonian momentum?
A laboratory experiment shoots an electron to the left at 0.90c. What is the electron’s speed, as a fraction of c, relative to a proton moving to the right at 0.90c?
A distant quasar is found to be moving away from the earth at 0.80c. A galaxy closer to the earth and along the same line of sight is moving away from us at 0.20c. What is the recessional speed of the quasar, as a fraction of c, as measured by astronomers in the other galaxy?
A rocket cruising past earth at 0.80c shoots a bullet out the back door, opposite the rocket’s motion, at 0.90c relative to the rocket. What is the bullet’s speed, as a fraction of c, relative to the earth?
In the earth’s reference frame, a tree is at the origin and a pole is at x = 30 km. Lightning strikes both the tree and the pole at t = 10 μs. The lightning strikes are observed by a rocket traveling in the x-direction at 0.50c.a. What are the spacetime coordinates for these two events in the
An event has spacetime coordinates (x, t) = (1200 m, 2.0 μs) in reference frame S. What are the event’s spacetime coordinates(a) In reference frame S' that moves in the positive x direction at 0.80c.(b) In reference frame S" that moves in the negative x-direction at 0.80c?
A rocket travels in the x-direction at speed 0.60c with respect to the earth. An experimenter on the rocket observes a collision between two comets and determines that the spacetime coordinates of the collision are (x', t') = (3.0 × 1010 m, 200 s). What are the spacetime coordinates of the
A human hair is about 50 μm in diameter. At what speed, in m/s, would a meter stick “shrink by a hair”?
Our Milky Way galaxy is 100,000 ly in diameter. A spaceship crossing the galaxy measures the galaxy’s diameter to be a mere 1.0 ly. a. What is the spacecraft’s speed, as a fraction of c, relative to the galaxy?b. How long is the crossing time as measured in the galaxy’s reference frame?
A muon travels 60 km through the atmosphere at a speed of 0.9997c. According to the muon, how thick is the atmosphere?
A cube has a density of 2000 kg/m3 while at rest in the laboratory. What is the cube’s density as measured by an experimenter in the laboratory as the cube moves through the laboratory at 90% of the speed of light in a direction perpendicular to one of its faces?
At what speed, as a fraction of c, will a moving rod have a length 60% that of an identical rod at rest?
You fly 5000 km across the United States on an airliner at 250 m/s. You return two days later at the same speed.a. Have you aged more or less than your friends at home?b. By how much?
At what speed, in m/s, would a moving clock lose 1.0 ns in 1.0 day according to experimenters on the ground?
At what speed, as a fraction of c, would a round-trip astronaut “lose” 1/25 of the elapsed time shown on her watch?
a. At what speed, as a fraction of c, must a rocket travel on a journey to and from a distant star so that the astronauts age 10 years while the Mission Control workers on earth age 120 years?b. As measured by Mission Control, how far away is the distant star?
An astronaut travels to a star system 4.5 ly away at a speed of 0.90c. Assume that the time needed to accelerate and decelerate is negligible.a. How long does the journey take according to Mission Control on earth?b. How long does the journey take according to the astronaut?c. How much time elapses
At what speed, as a fraction of c, does a moving clock tick at half the rate of an identical clock at rest?
A cosmic ray travels 60 km through the earth’s atmosphere in 400 μs, as measured by experimenters on the ground. How long does the journey take according to the cosmic ray?
You are flying your personal rocketcraft at 0.90c from Star A toward Star B. The distance between the stars, in the stars’ reference frame, is 1.0 ly. Both stars happen to explode simultaneously in your reference frame at the instant you are exactly halfway between them. Do you see the flashes
Event A occurs at spacetime coordinates (300 m, 2 μs).a. Event B occurs at spacetime coordinates (1200 m, 6 μs). Could A possibly be the cause of B? Explain.b. Event C occurs at spacetime coordinates (2400 m, 8 μs). Could A possibly be the cause of C? Explain.
You are standing at x = 9.0 km. Lightning bolt 1 strikes at x = 0 km and lightning bolt 2 strikes at x = 12.0 km. Both flashes reach your eye at the same time. Your assistant is standing at x = 3.0 km. Does your assistant see the flashes at the same time? If not, which does she see first, and what
Particle A has half the mass and twice the speed of particle B. Is the momentum pA less than, greater than, or equal to pB? Explain.
You are standing at x = 9.0 km and your assistant is standing at x = 3.0 km. Lightning bolt 1 strikes at x = 0 km and lightning bolt 2 strikes at x = 12.0 km. You see the flash from bolt 2 at t = 10 μs and the flash from bolt 1 at t = 50 μs. According to your assistant, were the lightning strikes
A 100-m-long train is heading for an 80-m-long tunnel. If the train moves sufficiently fast, is it possible, according to experimenters on the ground, for the entire train to be inside the tunnel at one instant of time? Explain.
Bianca is standing at x = 600 m. Firecracker 1, at the origin, and firecracker 2, at x = 900 m, explode simultaneously. The flash from firecracker 1 reaches Bianca’s eye at t = 3.0 μs. At what time does she see the flash from firecracker 2?
As the meter stick in FIGURE Q36.8 flies past you, you simultaneously measure the positions of both ends and determine that L < 1 m. a. To an experimenter in frame S', the meter stick??s frame, did you make your two measurements simultaneously? If not, which end did you measure first?
Your friend flies from Los Angeles to New York. She carries an accurate stopwatch with her to measure the flight time. You and your assistants on the ground also measure the flight time.a. Identify the two events associated with this measurement.b. Who, if anyone, measures the proper time?c. Who,
Your job is to synchronize the clocks in a reference frame. You are going to do so by flashing a light at the origin at t = 0 s. To what time should the clock at (x, y, z) = (30 m, 40 m, 0 m) be preset?
FIGURE Q36.6 shows a rocket traveling from left to right. At the instant it is halfway between two trees, lightning simultaneously (in the rocket??s frame) hits both trees. a. Do the light flashes reach the rocket pilot simultaneously? If not, which reaches her first? Explain.b. A student was
A starship blasts past the earth at 2.0 × 108 m/s. Just after passing the earth, it fires a laser beam out the back of the starship. With what speed does the laser beam approach the earth?
FIGURE Q36.5 shows Peggy standing at the center of her railroad car as it passes Ryan on the ground. Firecrackers attached to the ends of the car explode. A short time later, the flashes from the two explosions arrive at Peggy at the same time. a. Were the explosions simultaneous in Peggy??s
An out-of-control alien spacecraft is diving into a star at a speed of 1.0 × 108 m/s. At what speed, relative to the spacecraft, is the starlight approaching?
A baseball pitcher can throw a ball with a speed of 40 m/s. He is in the back of a pickup truck that is driving away from you. He throws the ball in your direction, and it floats toward you at a lazy 10 m/s. What is the speed of the truck?
Firecrackers A and B are 600 m apart. You are standing exactly halfway between them. Your lab partner is 300 m on the other side of firecracker A. You see two flashes of light, from the two explosions, at exactly the same instant of time. Define event 1 to be “firecracker A explodes” and event
A newspaper delivery boy is riding his bicycle down the street at 5.0 m/s. He can throw a paper at a speed of 8.0 m/s. What is the paper’s speed relative to the ground if he throws the paper(a) Forward, (b) Backward,(c) To the side?
At t = 1.0 s, a firecracker explodes at x = 10 m in reference frame S. Four seconds later, a second firecracker explodes at x = 20 m. Reference frame S' moves in the x-direction at a speed of 5.0 m/s. What are the positions and times of these two events in frame S'?
Teenagers Sam and Tom are playing chicken in their rockets. As FIGURE Q36.2 shows, an experimenter on earth sees that each is traveling at 0.95c as he approaches the other. Sam fires a laser beam toward Tom. a. What is the speed of the laser beam relative to Sam?b. What is the speed of the laser
A firecracker explodes in reference frame S at t = 1.0 s. A second firecracker explodes at the same position at t = 3.0 s. In reference frame S', which moves in the x-direction at speed v, the first explosion is detected at x' = 4.0 m and the second at x' = -4.0 m.a. What is the speed of frame S'
FIGURE Q36.1 shows two balls. What are the speed and direction of each (a) In a reference frame that moves with ball 1. (b) In a reference frame that moves with ball 2? 6 m/s 3 m/s FIGURE Q36.1
FIGURE CP35.50 shows a simple zoom lens in which the magnitudes of both focal lengths are f. If the spacing d < f, the image of the converging lens falls on the right side of the diverging lens. Our procedure of letting the image of the first lens act as the object of the second lens will
The lens shown in FIGURE CP35.49 is called an achromatic doublet, meaning that it has no chromatic aberration. The left side is flat, and all other surfaces have radii of curvature R. a. For parallel light rays coming from the left, show that the effective focal length of this two-lens system is f
Your task in physics laboratory is to make a microscope from two lenses. One lens has a focal length of 2.0 cm, the other 1.0 cm. You plan to use the more powerful lens as the objective, and you want the eyepiece to be 16 cm from the objective.a. For viewing with a relaxed eye, how far should the
Alpha Centauri, the nearest star to our solar system, is 4.3 light years away. Assume that Alpha Centauri has a planet with an advanced civilization. Professor Dhg, at the planet’s Astronomical Institute, wants to build a telescope with which he can find out whether any planets are orbiting our
The Hubble Space Telescope has a mirror diameter of 2.4 m. Suppose the telescope is used to photograph stars near the center of our galaxy, 30,000 light years away, using red light with a wavelength of 650 nm.a. What’s the distance (in km) between two stars that are marginally resolved? The
The resolution of a digital camera is limited by two factors: diffraction by the lens, a limit of any optical system, and the fact that the sensor is divided into discrete pixels. Consider a typical point-and-shoot camera that has a 20 μm-focal-length lens and a sensor with 2.5-μm-wide pixels.a.
Once dark adapted, the pupil of your eye is approximately 7 mm in diameter. The headlights of an oncoming car are 120 cm apart. If the lens of your eye is diffraction limited, at what distance are the two headlights marginally resolved? Assume a wavelength of 600 nm and that the index of refraction
High-power lasers are used to cut and weld materials by focusing the laser beam to a very small spot. This is like using a magnifying lens to focus the sun’s light to a small spot that can burn things. As an engineer, you have designed a laser cutting device in which the material to be cut is
A beam of white light enters a transparent material. Wavelengths for which the index of refraction is n are refracted at angle θ2. Wavelengths for which the index of refraction is n + δn, where δn << n, are refracted at angle θ2 + δu.a. Show that the angular separation of the two
White light is incident onto a 30? prism at the 40? angle shown in FIGURE P35.41. Violet light emerges perpendicular to the rear face of the prism. The index of refraction of violet light in this glass is 2.0% larger than the index of refraction of red light. At what angle ϕ does red light emerge
Modern microscopes are more likely to use a camera than human viewing. This is accomplished by replacing the eyepiece inFigure 35.14with a photo-ocular that focuses the image of the objective to a real image on the sensor of a digital camera. A typical sensor is 22.5 Î¼m wide and
A microscope with a tube length of 180 mm achieves a total magnification of 800× with a 40× objective and a 20× eyepiece. The microscope is focused for viewing with a relaxed eye. How far is the sample from the objective lens?
Marooned on a desert island and with a lot of time on your hands, you decide to disassemble your glasses to make a crude telescope with which you can scan the horizon for rescuers. Luckily you’re farsighted, and, like most people, your two eyes have different lens prescriptions. Your left eye
You’ve been asked to build a telescope from a 2.0× magnifying lens and a 5.0× magnifying lens.a. What is the maximum magnification you can achieve?b. Which lens should be used as the objective? Explain.c. What will be the length of your telescope
Mars (6800 km diameter) is viewed through a telescope on a night when it is 1.1 × 108 km from the earth. Its angular size as seen through the eyepiece is 0.50°, the same size as the full moon seen by the naked eye. If the eyepiece focal length is 25 mm, how long is the telescope?
The objective lens of a telescope is a symmetric glass lens with 100 cm radii of curvature. The eyepiece lens is also a symmetric glass lens. What are the radii of curvature of the eyepiece lens if the telescope’s magnification is 20×?
The cornea, a boundary between the air and the aqueous humor, has a 3.0 cm focal length when acting alone. What is its radius of curvature?
Yang can focus on objects 150 cm away with a relaxed eye. With full accommodation, she can focus on objects 20 cm away. After her eyesight is corrected for distance vision, what will her near point be while wearing her glasses?
A 15-cm-focal-length converging lens is 20 cm to the right of a 7.0-cm-focal-length converging lens. A 1.0-cm-tall object is distance L to the left of the first lens.a. For what value of L is the final image of this two-lens system halfway between the two lenses?b. What are the height and
A 1.0-cm-tall object is 110 cm from a screen. A diverging lens with focal length -20 cm is 20 cm in front of the object. What are the focal length and distance from the screen of a second lens that will produce a well-focused, 2.0-cm-tall image on the screen?
In FIGURE P35.30, what are the position, height, and orientation of the final image? Give the position as a distance to the right or left of the lens. fi = 10 cm f=-30 cm 1.0 cm. 5.0 cm 5.0 cm FIGURE P35.30
A common optical instrument in a laser laboratory is a beam expander. One type of beam expander is shown in FIGURE P35.29. The parallel rays of a laser beam of width w1enter from the left. a. For what lens spacing d does a parallel laser beam exit from the right?b. What is the width w2 of the
A common optical instrument in a laser laboratory is a beam expander. One type of beam expander is shown in FIGURE P35.28. The parallel rays of a laser beam of width w1enter from the left. a. For what lens spacing d does a parallel laser beam exit from the right?b. What is the width w2 of the

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