At What Speed, V, Must The Painting Move Parallel To Its Width If It Is To Appear To Be Square?

Mastering Physics Solutions Chapter 29 Relativity

Mastering Physics Solutions

Affiliate 29 Relativity Q.1CQ
Some distant galaxies are moving abroad from us at speeds greater than 0.5c. What is the speed of the light received on Earth from these galaxies? Explicate.
Solution:
According to second postulate of special theory of relativity the speed of light (c) is same in all inertial frames of references in vacuum. And so light from these galaxies received on the earth moves with the speed as is truthful for all light in a vacuum.

Chapter 29 Relativity Q.1P
CE Predict/Explain You lot are in spaceship, traveling directly away from the Moon with a speed of 0.9c A low-cal signal is sent in your direction from the surface of the Moon. (a) As the indicate passes your transport, exercise y'all mensurate its speed to exist greater than, among the following:

• the speed you measure will be greater then 0.1c in fact, information technology will be c, since all observers in inertial frames measure the same speed of low-cal
• Yous will measure a speed less than 0.1c because of time dilation, which causes clocks to run wearisome.
• When you mensurate a speed you detect if exist betwixt c and 0.9c.

Solution:

• As the signal passes our ship, we will mensurate speed of the point greater than 0.1c
• Answer (I) The speed you measure volition be greater than 0.1c; in fact, it will be c, since all observers in inertial frames measures the same speed of lite.

Chapter 29 Relativity Q.2CQ
The speed of lite in glass is less than c. Why is this non a violation of the 2nd postulate of relativity?
Solution:
We know according to 2d postulate of special theory of relativity, the speed (c) of calorie-free is aforementioned in all inertial frames of references, and speed of light in vacuum is c. Here c is the speed of lite in vacuum only. In all other media other than vacuum the speed of light is less than c. And then the speed of low-cal in drinking glass is less than c.

Affiliate 29 Relativity Q.2P
Albert is piloting his spaceship, heading eastward with a speed of 0.90c. Albert's ship sends a lite beam in the frontward (due east-ward) direction, which travels abroad from his ship at a speed c. Meanwhile, Isaac is piloting his ship in the westward direction, also at 0.90c, toward Albert's ship. With what speed does Isaac encounter?
Solution:
According to second postulate of special theory of relativity, the speed of calorie-free in vacuum, , is same in all inertial frames of reference, independent of the motion of the source or the receiver. The speed of Albert's lite beam observed by Isaac is c

Chapter 29 Relativity Q.3CQ
How would velocities add if the speed of light were infinitely large? Justify your reply past considering Equation 29–4.
Solution:

Affiliate 29 Relativity Q.3P
CE A street performer tosses a ball direct upward into the air (effect ane) and then catches it in his mouth (event ii). For each of the following observers, state whether the time they measure betwixt these two events is the proper time or the dilated time: (a) the street performer; (b) a stationary observer on the other side of the street; (c) a person sitting at abode watching the performance on Television receiver; (d) a person observing the operation from a moving motorcar.
Solution:
The definition of proper fourth dimension is the time deviation between the two events which occur at the aforementioned location past given observer or particular observer. Here in the given problem, the two events are a street performer tosses a ball direct up into the air (event i) so catches it in his mouth (upshot 2). Now we have to make up one's mind for the post-obit observers, whether the time they measured between these two events is the proper time or dilated time.

• (a) Hither the street performer is in the rest frame of reference. With respect to this street performer these two events occur at the same location. And then he measures the fourth dimension betwixt these two events is proper time
• (b) The stationary observer on the other side of the street is likewise in the balance frame. With respect to him these two events occur at the same location. And so he measures the time betwixt these two events is proper fourth dimension
• (c) The person sitting at habitation watching the operation on TV is in the balance frame. With respect to him these two events occur at the same location. And so he measures the time departure between these two events is proper fourth dimension
• (d) A person moving in the car observed these 2 events are situated at different locations. So with respect to him, he measures the time between these two events is dilated time

Chapter 29 Relativity Q.4CQ
Describe some of the everyday consequences that would follow if the speed of light were 35 mi/h.
Solution:
If the speed of light is 35 mi/h so we experience relativistic effects like

•  A person in movement would age slowly than a person who stays at domicile due to fourth dimension dilation.
•  The length of a car in move seems to be shorter due to length contraction.
•  No object can movement faster than light.

Even if the engine of your car is very powerful and even if you try to accelerate it, your auto will not be able to motion faster than 35 mi/h

Chapter 29 Relativity Q.4P
СE Predict/Explain A clock in a moving rocket is observed to run boring, (a) If the rocket reverses direction, does the clock run slow, fast, or at its normal rate? (b) Cull the all-time explanation from amid the following:

• The clock will run slow, just as before. The rate of the clock depends simply on relative speed, not on management of motion.
• When the rocket reverses direction the rate of the clock reverses besides, and this makes it run fast.
• Reversing the direction of the rocket undoes the the time dilation upshot, and and so the clock volition now run at its normal rate.

Solution:

• The clock volition notwithstanding run slow as before.
• Respond (I)

The clock will run boring, merely as before. The rate of the clock depends only on relative speed, non on direction of motion.

Chapter 29 Relativity Q.5CQ
When we view a afar galaxy, we notice that the lite coming from it has a longer wavelength (it is "red-shifted") than the respective light here on Globe. Is this consequent with the postulate that all observers measure the aforementioned speed of calorie-free? Explain.
Solution:
Aye
Here the light rays are coming from the distant milky way. In spite of not taking the wavelength of the light rays coming from the milky way, all these light rays move with the same speed in vacuum. These calorie-free rays accept longer wavelength and the frequency of this "red shifted" lite will exist affected, this is because nosotros know the formula. v = λf From this formula the wavelength () and frequency (f) of the calorie-free rays are inversely proportional to each other. From this relation the longer wavelength implies a smaller frequency.

Affiliate 29 Relativity Q.5P
СE Predict/Explain Suppose you are a traveling salesman for SSC, the Spacely Sprockets Company. You travel on a spaceship that reaches speeds nigh the speed of light, and you are paid by the hour, (a) When y'all return to Earth after a sales trip, would you prefer to be paid according to the clock at Spacely Sprockets universal headquarters on Globe, according to the clock on the spaceship in which yous travel, or would your pay be the same in either case? (b) Choose the best caption from amidst the following:

• You want to be paid according to the clock on Earth, because the clock on the spaceship runs dull when it approaches the speed of light.
• Collect your pay co-ordinate to the clock on the spaceship considering according to you lot the clock on Earth has run slow.
• Your pay would be the aforementioned in either case because motion is relative, and all mertial observers will concur on the amount of fourth dimension that has elapsed.

Solution:

• I would like to be paid according to the clock at Spacely Sprockets universal Headquarters on earth.
• Answer (I) Yous want to be paid according to the clock on earth, because the clock on the space transport runs ho-hum when information technology approaches the speed of low-cal.

Chapter 29 Relativity Q.6CQ
According to the theory of relativity, the maximum speed foi whatsoever particle is the speed of light. Is there a like restriction on the maximum free energy of a particle? Is in that location a maximum momentum? Explain.
Solution:

Chapter 29 Relativity Q.6P
A neon sign in front of a café flashes on and off in one case every 4.1 southward, every bit measured past the caput cook. How much time elapses between flashes of the sign as measured by an astronaut in a spaceship moving toward Earth With a speed of 0.84c?
Solution:

Chapter 29 Relativity Q.7CQ
Give an argument that shows that аn object of finite mass cannot be accelerated from remainder to a speed greater than the speed of lite in a vacuum.
Solution:

Chapter 29 Relativity Q.7P
A lighthouse sweeps its axle of light around in a circumvolve one time every 7.5 s. To an observer in a spaceship moving, away from Earth, the beam of lite completes one total circle every 15 s. What is the speed of the spaceship relative to Earth?
Solution:

Chapter 29 Relativity Q.8P
Refer to Case 29–1. How much does Benny historic period if he travels to Vega with a speed of 0.9995c?
Solution:

Chapter 29 Relativity Q.9P
As a spaceship flies past with speed 5, you observe that one.0000 south elapses on the ship's clock in the same time that 1.0000 min elapses on Earth. How fast is the ship traveling, relative to the World? (Express your answer as a fraction of the speed of lite.)
Solution:

Affiliate 29 Relativity Q.10P
Donovan Bailey set a world record for the 100-yard nuance on July 27, 1996. If observers on a spaceship moving with a speed of 0.7705c relative to Earth saw Donovan Bailey'due south run and measured his time to be 15.44 s, find the time that was recorded on Earth.
Solution:

Chapter 29 Relativity Q.11P
Find the average altitude (in the Earth's frame of reference) covered by the muons in Example 29–2 if their speed relative to World is 0.750c.
Solution:

Chapter 29 Relativity Q.12P
The Pi Meson An elementary particle called a pi meson (or pion for short) has an average lifetime of 2.half-dozen × 10–8 due south when at residue. If a pion moves with a speed of 0.99c relative to Globe, detect (a) the average lifetime of the pion as measured past an observer on Earth and (b) the average distance traveled by the pion as measured by the same observer, (c) How far would the pion have traveled relative to World if relativistic time dilation did not occur?
Solution:

Chapter 29 Relativity Q.13P
The Σ– Particle The Σ– is an exotic particle that has a lifetime (when at residue) of 0.15 ns. How fast would it have to travel in guild for its lifetime, as measured by laboratory clocks, to exist 0.25 ns?
Solution:

Chapter 29 Relativity Q.14P
IP (a) Is it possible for you to travel far plenty and fast enough then that when you return from a trip, you lot are younger than your stay-at-domicile sis, who was born 5.0 y later y'all? (b) Suppose yous fly on a rocket with a speed 5 = 0.99c for one y, according to the send'south clocks and calendars. How much fourth dimension elapses on Earth during your one-y trip? (c) If y'all were 22 y old when you left home and your sister was 17, what are your ages when yous return?
Solution:

Chapter 29 Relativity Q.15P
The radar antenna on a navy ship rotates with an angular speed of 0.29 rad/s. What is the angular speed of the antenna as measured by an observer moving away from the antenna with a speed of 0.82c?
Solution:

Chapter 29 Relativity Q.16P
An observer moving toward Earth with a speed of 0.95c notices that it takes 5.0 min for a person to fill her machine with gas. Suppose, instead, that the observer had been moving away from Earth with a speed of 0.80c. How much fourth dimension would the observer have measured for the motorcar to be filled in this case?
Solution:

Chapter 29 Relativity Q.17P
IP An astronaut moving with a speed of 0.65c relative to Earth measures her heart charge per unit to be 72 beats per infinitesimal, (a) When an World-based observer measures the astronaut's heart rate, is the consequence greater than, less than, or equal to 72 beats per minute? Explain. (b) Calculate the astronaut's heart rate equally measured on Earth.
Solution:

Chapter 29 Relativity Q.18P
BIO Newly sprouted sunflowers can grow at the rate of 0.30 in. per day. One such sunflower is left on Earth, and an identical one is placed on a spacecraft that is traveling away from World with a speed of 0.94c. How tall is the sunflower on the spacecraft when a person on Earth says his is 2.0 in. high?
Solution:

Chapter 29 Relativity Q.19P
An astronaut travels to Mars with a speed of 8350 thousand/due south. Afterward a month (thirty.0 d) of travel, as measured by clocks on Earth, how much difference is there between the Earth clock and the spaceship clock? Give your answer in seconds.
Solution:

Chapter 29 Relativity Q.20P
Every bit measured in Earth's frame of reference, two planets are 424,000 km apart. A spaceship flies from ane planet to the other with a abiding velocity, and the clocks on the ship bear witness that the trip lasts only 1.00 s. How fast is the ship traveling?
Solution:

Chapter 29 Relativity Q.21P
Captain Jean-Luc is piloting the USS Enterprise XXIII at a abiding speed v = 0.825c. As the Enterprise passes the planet Vulcan, he notices that Ms sentinel and the Vulcan clocks both read ane:00 p.m. At 3:00 p.m., according to his watch, the Enterprise passes the planet Endor. If the Vulcan and Endor clocks are synchronized with each other, what fourth dimension exercise the Endor clocks read when the Enterprise passes by?
Solution:

Chapter 29 Relativity Q.22P
IP A plane flies with a constant velocity of 222 m/s. The clocks on the plane show that information technology takes exactly ii.00 h to travel a sure altitude, (a) According to ground-based clocks, will the flight accept slightly more or slightly less than 2.00 h? (b) Calculate how much longer or shorter than 2.00 h this flying will last, according to clocks on the ground.
Solution:

Chapter 29 Relativity Q.23P
CE Tf the universal speed of lite in a vacuum were larger than 3.00 Ten 108 m/s, would the effects of length contraction be greater or less than they are now? Explain.
Solution:

Affiliate 29 Relativity Q.24P
How fast does a 250-m spaceship motility relative to an observer who measures the ship's length to be 150 m?
Solution:

Chapter 29 Relativity Q.25P
Suppose the speed of low-cal in a vacuum were only 25.0 mi/h. Find the length of a wheel being ridden at a speed of 20.0 mi/h as measured past an observer sitting on a park bench, given that its proper length is 1.89 m.
Solution:

Chapter 29 Relativity Q.26P
A rectangular painting is 124 cm broad and fourscore.5 cm high, every bit indicated in Figure 29–29. At what speed, v, must the painting move parallel to its width if information technology is to appear to be square?

Solution:

Chapter 29 Relativity Q.27P
The Linac portion of the Fermilab Tevatron contains a loftier-vacuum tube that is 64 g long, through which protons travel with an average speed five = 0.65c. How long is the Linac tube, every bit measured in the proton's frame of reference?
Solution:

Chapter 29 Relativity Q.28P
A cubical box is 0.75 chiliad on a side, (a) What are the dimensions of the box as measured by an observer moving with a speed of 0.88c parallel to one of the edges of the box? (b) What is the volume of the box, as measured by this observer?
Solution:

Chapter 29 Relativity Q.29P
When parked, your car is v.0 m long. Unfortunately, your garage is only four.0 m long, (a) How fast would your car have to be moving for an observer on the ground to find your motorcar shorter than your garage? (b) When you are driving at this speed, how long is your garage, as measured in tire auto'southward frame of reference?
Solution:

Chapter 29 Relativity Q.30P
An astronaut travels to a distant star with a speed of 0.55c relative to Earth. From the astronaut'south betoken of view, the star is 7.5 ly from Earth. On the return trip, the astronaut travels with a speed of 0.89c relative to World. What is the distance covered on the return trip, as measured past the astronaut? Give your answer in light-years.
Solution:

Chapter 29 Relativity Q.31P
IP Laboratory measurements show that an electron traveled 3.50 cm in a time of 0.200 ns. (a) In the rest frame of the electron, did the lab travel a distance greater than or less than 3.l cm? Explain, (b) What is the electron's speed? (c) In the electron's frame of reference, how far did the laboratory travel?
Solution:

Chapter 29 Relativity Q.32P
You and a friend travel through space in identical spaceships. Your friend informs you that he has made some length measurements and that his send is 150 g long but that yours is only 120 m long. From your point of view, (a) how long is your friend's send, (b) how long is your send, and (c) what is the speed of your friend's send relative to yours?
Solution:

Chapter 29 Relativity Q.33P
A ladder 5.0 m long leans against a wall inside a spaceship. From the signal of view of a person on the ship, the base of operations of the ladder is 3.0 thou from the wall, and the top of the ladder is 4.0 chiliad higher up the floor. The spaceship moves past the World with a speed of 0.90c in a direction parallel to the flooring of the ship. Find the angle the ladder makes with the flooring as seen by an observer on World.
Solution:

Chapter 29 Relativity Q.34P
When traveling past an observer with a relative speed 5, a rocket is measured to be 9.00 g long. When the rocket moves with a relative speed 2v, its length is measured to be 5.00 chiliad. (a) What is the speed v? (b) What is the proper length of the rocket?
Solution:

Chapter 29 Relativity Q.35P
IP The starships Picard and La Forge are traveling in the same direction toward the Andromeda galaxy. The Picard moves with a speed of 0.90c relative to the La Forge. A person on the La Forge measures the length of the ii ships and finds the aforementioned value, (a) Tf a person on the Picard also measures the lengths of the two ships, which of the following is observed : (i) the Picard is longer; (two) the La Forge is longer; or (iii) both ships take the same length? Explain, (b) Calculate the ratio of the proper length of the Picard to the proper length of the La Forge.
Solution:

Affiliate 29 Relativity Q.36P
A spaceship moving toward Earth with a speed of 0.90c launches a probe in the forward direction with a speed of 0.10c relative to the send. Find the speed of the probe relative to Globe.
Solution:

Chapter 29 Relativity Q.37P
Suppose the probe in Problem 36 is launched in the opposite direction to the motion of the spaceship. Observe the speed of the probe relative to Earth in this example.
Solution:

Chapter 29 Relativity Q.38P
A spaceship moving relative to an observer with a speed of 0.70c shines a beam of light in the frontward direction, directly toward the observer. Use Equation 29–4 to calculate the speed of the beam of light relative to the observer.
Solution:

Affiliate 29 Relativity Q.39P
Suppose the speed of light is 35 mi/h. A paper girl riding a bicycle at 22 mi/h throws a rolled-up newspaper in the frontward direction, as shown in Effigy 29–30. If the paper is thrown with a speed of 19 mi /h relative to the bike, what is its speed, v, with respect to the footing?
FIGURE 29–30

Solution:

Affiliate 29 Relativity Q.40P
2 asteroids head straight for Earth from the same direction. Their speeds relative to Earth are 0.80c for asteroid 1 and 0.60c for asteroid 2. Observe the speed of asteroid 1 relative to asteroid 2.
Solution:

Affiliate 29 Relativity Q.41P
Two rocket ships approach Earth from reverse directions, each with a speed of 0.8c relative to Earth. What is the speed of i ship relative to the other?
Solution:

Chapter 29 Relativity Q.42P
A spaceship and an asteroid are moving in the same direction away from Earth with speeds of 0.77c and 0.41c, respectively. What is the relative speed between the spaceship and the asteroid?
Solution:

Affiliate 29 Relativity Q.43P
An electron moves to the right in a laboratory accelerator with a speed of 0.84c. A second electron in a unlike accelerator moves to the left with a speed of 0.43c relative to the commencement electron. Detect the speed of the second electron relative to the lab.
Solution:

Chapter 29 Relativity Q.44P
IP 2 rocket ships are racing toward Earth, as shown in Effigy 29–31. Ship A is in the lead, budgeted the Earth at 0.80c and separating from ship В with a relative speed of 0.50c. (a) As seen from Earth, what is the speed, v, of Ship B? (b) If ship A increases its speed by 0.10c relative to the Earth, does the relative speed betwixt ship A and ship В increase by 0.10c, by more than 0.10c, or past less than 0.10c? Explain, (c) Detect the relative speed between ships A and В for the situation described in office (b).

Solution:

Affiliate 29 Relativity Q.45P
IP An inventor has proposed a device that will accelerate objects to speeds greater than c. He proposes to place the object to exist accelerated on a conveyor belt whose speed is 0.80c. Next, the entire system is to be placed on a second conveyor belt that also has a speed of 0.80c, thus producing a concluding speed of 1.6c.
(a) Construction details aside, should you invest in this scheme?
(b) What is the actual speed of the object relative to the ground?
Solution:

Affiliate 29 Relativity Q.46P
A 4.5 × 106-kg spaceship moves away from World with a speed of 0.75c. What is the magnitude of the send's (a) classical and (b) relativistic momentum?
Solution:

Chapter 29 Relativity Q.47P
An asteroid with a mass of 8.2 × 1011 kg is observed to have a relativistic momentum of magnitude 7.74 × 1020 kg • 1000/s. What is the speed of the asteroid relative to the observer?
Solution:

Affiliate 29 Relativity Q.48P
An object has a relativistic momentum that is 7.5 times greater than its classical momentum. What is its speed?
Solution:

Chapter 29 Relativity Q.49P
A football game player with a mass of 88 kg and a speed of 2.0 thou/s collides caput-on with a actor from the opposing squad whose mass is 120 kg. The players stick together and are at residue later on the collision. Find the speed of the second player, assuming the speed of light is 3.0 m/s.
Solution:

Chapter 29 Relativity Q.50P
In the previous problem, suppose the speed of the 2nd player is ane.two k/s. What is the speed of the players after the standoff?
Solution:

Chapter 29 Relativity Q.51P
A space probe with a rest mass of 8.two × 107 kg and a speed of 0.50c smashes into an asteroid at rest and becomes embedded within it. If the speed of the probe-asteroid system is 0.26c afterward the standoff, what is the residue mass of the asteroid?
Solution:

Chapter 29 Relativity Q.52P
At what speed does the classical momentum, p = mv, requite an error, when compared with the relativistic momentum, of (a) 1.00% and (b)'5.00%?
Solution:

Chapter 29 Relativity Q.53P
A proton has 1836 times the residuum mass of an electron. At what speed will an electron have the same momentum every bit a proton moving at 0.0100c?
Solution:

Chapter 29 Relativity Q.54P
СE Particles A through D have the following residue energies and total energies:

Rank these particles in social club of increasing (a) rest mass, (b) kinetic free energy, and (c) speed. Betoken ties where advisable.
Solution:

Chapter 29 Relativity Q.55P
Find the work that must exist done on a proton to advance it from balance to a speed of 0.90c.
Solution:

Chapter 29 Relativity Q.56P
If a neutron moves with a speed of 0.99c, what are its (a) total energy, (b) residuum free energy, and (c) kinetic energy?
Solution:

Affiliate 29 Relativity Q.57P
A leap with a force constant of 584 Northward/k is compressed a altitude of 39 cm. Find the resulting increase in the jump's mass.
Solution:

Chapter 29 Relativity Q.58P
When a certain capacitor is charged, its mass increases past 8.3 × x−sixteen kg. How much energy is stored in the capacitor?
Solution:

Chapter 29 Relativity Q.59P
What minimum energy must a gamma ray have to create an electron-antielectron pair?
Solution:

Affiliate 29 Relativity Q.60P
When a proton encounters an antiproton, the ii particles demolish each other, producing two gamma rays. Assuming the particles were at rest when they annihilated, notice the energy of each of the two gamma rays produced. (Note: Tire residual energies of an antiproton and a proton are identical.)
Solution:

Chapter 29 Relativity Q.61P
A rocket with a mass of 2.7 × 106 kg has a relativistic kinetic free energy of 2.7 × 1023 J. How fast is the rocket moving?
Solution:

Affiliate 29 Relativity Q.62P
A rocket with a mass of 2.7 × 106 kg has a relativistic kinetic free energy of 2.vii × 1023 J. How fast is the rocket moving?
Solution:

Affiliate 29 Relativity Q.63P
A nuclear power plant produces an average of 1.0 × 103 MW of power during a year of performance. Find the corresponding change in mass of reactor fuel, assuming all of the free energy released past the fuel can be converted directly to electrical energy. (In a practical reactor, just a relatively small fraction of the energy can be converted to electricity.)
Solution:

Chapter 29 Relativity Q.64P
A helium atom has a rest mass of mHe = 4.002603 u. When disassembled into its constituent particles (2 protons, two neutrons, 2 electrons), the well-separated individual particles have the following masses: mp = 1.007276 u, mn = ane.008665 u, me = 0.000549 u. How much piece of work is required to completely detach a helium atom? (Notation: 1 u of mass has a rest free energy of 931.49 MeV.)
Solution:

Chapter 29 Relativity Q.65P

Solution:

Chapter 29 Relativity Q.66P
A proton has 1836 times the rest mass of an electron. At what speed volition an electron accept the same kinetic free energy as a proton moving at 0.0250c?
Solution:

Chapter 29 Relativity Q.67P
IP Consider a baseball with a rest mass of 0.145 kg. (a) How much work is required to increase the speed of the baseball from 25.0 m/south to 35.0 thou/s? (b) Is the work required to increase the speed of the baseball game from 200,000,025 m/s to 200,000,035 m/s greater than, less than, or the same equally the corporeality found in part (a)? Explain, (c) Calculate the work required for the increase in speed indicated in part (b).
Solution:

Chapter 29 Relativity Q.68P
IP A particle has a kinetic energy equal to its rest energy, (a) What is the speed of this particle? (b) If the kinetic energy of this particle is doubled, does its speed increment by a more than, less than, or exactly a factor of two? Explicate. (c) Calculate the speed of a particle whose kinetic energy is twice its balance free energy.
Solution:

Chapter 29 Relativity Q.69P
A lump of putty with a mass of 0.240 kg and a speed of 0.980c collides head-on and sticks to an identical lump of putty moving with the aforementioned speed. Afterwards the standoff the organization is at rest. What is the mass of the system afterward the collision?
Solution:

Chapter 29 Relativity Q.70P
Notice the radius to which the Sunday must exist compressed for information technology to become a black hole.
Solution:

Chapter 29 Relativity Q.71P
The Blackness Hole in the Center of the Milky way Recent measurements show that the black hole at the center of the Milky Manner galaxy, which is believed to coincide with the powerful radio source Sagittarius A*, is 2.6 million times more massive than the Sunday; that is, Chiliad = 5.2 × 1036 kg. (a) What is the maximum radius of this black pigsty? (b) Find the acceleration of gravity at the Schwarzschild radius of this black pigsty, using the expression for R given in Equation 29–10. (c) How does your answer to part (b) change if the mass of the black hole is doubled? Explicate.
Solution:

Chapter 29 Relativity Q.72GP
CE Two observers are moving relative to one another. Which of the post-obit quantities volition they ever measure to have the same value: (a) their relative speed; (b) the time betwixt 2 events; (c) the length of an object; (d) the speed of light in a vacuum; (e) the speed of a third observer?
Solution:
Hither two observers are moving relative to one some other so they measure that they take the aforementioned speed relative to one some other. Besides according to the 2nd postulate of special theory of relativity the speed of lite is c in vacuum in all inertial frames of references. And so the two observers will always measure
(a) The relative speed and
(d) The speed of calorie-free in vacuum have the same value, the remaining are the time between 2 events, length of an object and speed of a 3rd observer are different for different observers.

Chapter 29 Relativity Q.73GP
CE You lot are standing next to a rails as an aeroplane kinds, (a) If you lot and the pilot find a clock in the cockpit, which of you measures the proper time? (b) If you and the pilot discover a large clock on the control belfry, which of you lot measures the proper fourth dimension? (c) Which of you measures the proper length of the airplane? (d) Which of you measures the proper length of the runway?
Solution:
(a) The pilot will measure the right proper time of the cockpit clock considering the he is in rest frame of reference with respect to the clock. Then airplane pilot volition notice correct proper fourth dimension in the clock which is in erect pit.
(b) You measure the right proper fourth dimension in the large clock on the control belfry, because you are in the rest frame of reference with respect to the clock on the control belfry.
(c) The pilot measures the correct proper length of the aero plane. Because airplane pilot is in the rest frame of reference with respect to the aero plane.
(d) Yous measure the correct proper length of the runway considering you are in the rest frame with respect to the runway.

Chapter 29 Relativity Q.74GP
CE Which clock runs slower relative to a clock on the North Pole: clock on an airplane flying from New York to Los Angeles, or clock two on an airplane flight from Los Angeles to New York? Assume each plane has the same speed relative to the surface of the Globe. Explain.
Solution:
Clock 2 on an plane flight from Los Angeles to New York runs slower than clock 1 on an plane flying from New York to Los Angeles because its speed relative to the axis of the spinning earth is greater than the speed of other airplane.
Hither the airplane which has the clock 2 has greater speed because the direction of motion of this airplane is in the aforementioned direction of the centrality of the spinning earth.

Chapter 29 Relativity Q.75GP
CE An apple drops from the bough of a tree to the ground. Is the mass of the apple tree virtually the top of its fall greater than, less than, or the same as its mass later on it has landed? Explain.
Solution:
Let h be the tiptop of apple tree in the bender of a tree from the basis.
If the apple tree is at the near top of its fall, i.e. at greater height h then t the earth- apple organization has more than gravitational potential energy. Hence this increased free energy is equivalent to the increased mass according to the Einstein's mass-energy equivalence relation. Eastward = k\({ c }^{ ii }\)
So the mass of the apple tree virtually the acme of its fall is greater

Chapter 29 Relativity Q.76GP
CE Predict/Explicate Consider two apple pies that are identical in every respect, except that pie ane is piping hot and pie ii is at room temperature, (a) If identical forces are applied to the two pies, is the dispatch of pie ane greater than, less than, or equal to the dispatch of pie 2? (b) Choose the best explanation from amid the following:

• The acceleration of pie 1 is greater because the fact that information technology is hot means information technology has the greater free energy.
• The fact that pie 1 is hot means information technology behaves as if it has more mass than pie 2, and therefore it has a smaller acceleration.
• The pies take the aforementioned dispatch regardless of their temperature considering they accept identical balance masses.

Solution:
a) Dispatch of pie 1 is less than pie 2
(b) Hither pie1 is hotter than the pie2. That means the pie one has more free energy than the pie 2. Therefore the pie1 is more massive than the pie ii.
So when we apply aforementioned force to the two pies, the massive pie will take less dispatch. Therefore acceleration of pie i is less than the acceleration of pie 2. Therefore option 2 is correct.

Chapter 29 Relativity Q.77GP
CE Is the mass of a warm cup of tea greater than, less than, or the same every bit the mass of the same cup of tea when it has cooled? Explain.
Solution:
The Einstein's mass – energy equivalence relationship E = m\({ c }^{ 2 }\)
From this formula nosotros can say that the energy (Eastward) and mass (m) of a particle are directly proportional to each other. The warm cup of tea has more than energy than the same cup of tea when it has cooled. So by using the above relation the mass of warm cup of tea is greater than the mass of the aforementioned cup of tea when it has cooled.

Affiliate 29 Relativity Q.78GP
CE Predict/Explain An uncharged capacitor is charged past moving some electrons from i plate of the capacitor to the other plate, (a) Is the mass of the charged capacitor greater than, less than, or the same as the mass of the uncharged capacitor? (b) Choose the all-time caption from among the following:

• The charged capacitor has more mass considering it is storing energy within it, just similar a compressed jump.
• The charged capacitor has less mass because some of its mass now appears every bit the energy of the electrical field between its plates.
• The capacitor has the same mass whether information technology is charged or not because charging it simply involves moving electrons from i plate to the other without irresolute the total number of electrons.

Solution:
(a) Mass of charged capacitor is greater than the mass of uncharged capacitor.
(b) Pick I is right
The charged capacitor has more mass because it is storing energy inside it, just like a compressed spring.

Chapter 29 Relativity Q.79GP
Cosmic Rays Protons in catholic rays accept been observed with kinetic energies equally big as 1.0 × 1020 eV. (a) How fast are these protons moving? Give your answer as a fraction of the speed of light, (b) Evidence that the kinetic energy of a unmarried i of these protons is much greater than the kinetic energy of a 15-mg emmet walking with a speed of viii.8 mm/s.
Solution:

Chapter 29 Relativity Q.80GP
An apple falls from a tree, landing on the basis 3.7 chiliad below. How long is the apple tree in the air, as measured past an observer moving toward Earth with a speed of 0.89c?
Solution:

Affiliate 29 Relativity Q.81GP
What is the momentum of a proton with i.l × 103 MeV of kinetic energy? (Notation: The rest energy of a proton is 938 MeV.)
Solution:

Chapter 29 Relativity Q.82GP
IP A container holding ii.00 moles of an ideal monatomic gas is heated at constant volume until the temperature of the gas increases by 112 F°. (a) Does the mass of the gas increase, decrease, or stay the same? Explain, (b) Calculate the change in mass of the gas, if whatsoever.
Solution:

Chapter 29 Relativity Q.83GP
Al4C nucleus, initially at residuum, emits a beta particle. The beta particle is an electron with 156 keV of kinetic free energy, (a) What is the speed of the beta particle? (b) What is the momentum of the beta particle? (c) What is the momentum of the nucleus after information technology emits the beta particle? (d) What is the speed of the nucleus after information technology emits the beta particle?
Solution:

Chapter 29 Relativity Q.84GP
A clock at rest has a rectangular shape, with a width of 24 cm and a height of 12 cm. When this clock moves parallel to its width with a certain speed v its width and height are the same. Relative to a clock at residuum, how long does it accept for the moving clock to accelerate by 1.0 s?
Solution:

Chapter 29 Relativity Q.85GP
A starship moving toward Earth with a speed of 0.75c launches a shuttle craft in the forrard direction. Tire shuttle, which has a proper length of 12.v m, is only 6.25 one thousand long as viewed from Earth. What is the speed of the shuttle relative to the starship?
Solution:

Chapter 29 Relativity Q.86GP
When a particle of charge q and momentum p enters a uniform magnetic field at correct angles it follows a circular path of radius R = p/qB, as shown in Figure 29–32. What radius does this expression predict for a proton traveling with a speed 5 = 0.99c through a magnetic field В = 0.20 T if you employ (a) the nonrelativistic momentum (p = mv) or (b) the relativistic momentum
Solution:

Chapter 29 Relativity Q.87GP
IP A starship moving abroad from Earth with a speed of 0.75c launches a shuttle arts and crafts in the reverse management, that is, toward World. (a) If the speed of the shuttle relative to the starship is 0.40c, and its proper length is 13 grand, how long is the shuttle as measured by an observer on World? (b) If the shuttle had been launched in the forward management instead, would its length equally measured past an observer on Earth exist greater than, less than, or the same as the length found in part (a)? Explicate. (c) Calculate the length for the case described in function (b).
Solution:

Chapter 29 Relativity Q.88GP
A 2.5-chiliad titanium rod in a moving spacecraft is at an bending of 45° with respect to the direction of motion. The craft moves directly toward Earth at 0.98c. As viewed from Earth, (a) how long is the rod and (b) what bending does the rod make with the direction of motion?
Solution:

Chapter 29 Relativity Q.89GP
Electrons are accelerated from rest through a potential difference of 276,000 V. What is the concluding speed predicted (a) classically and (b) relativistically?
Solution:

Chapter 29 Relativity Q.90GP
IP In Conceptual Checkpoint 29-ii we considered an astronaut at rest on an inclined bed within a moving spaceship. From the point of view of observer i, on board the ship, the astronaut has a length L0 and is inclined at an bending θ0 in a higher place the floor. Observer ii sees the spaceship moving to the right with a speed v.

Suppose a pion (a subatomic particle) is observed to have a kinetic energy G = 35.0 MeV and a momentum p = 5.61 × 1020 kg3 m/s = 105 MeV/c. What is the rest free energy of the pion? Requite your respond in MeV.
Solution:

Chapter 29 Relativity Q.91GP
A pocket-size star of mass thou orbits a supermassive blackness hole of mass M. (a) Find the orbital speed of the star if its orbital radius is 2R, where R is the Schwarzschild radius (Equation 29–ten). (b) Repeat part (a) for an orbital radius equal to R.
Solution:

Affiliate 29 Relativity Q.92GP
IP Consider a "relativistic air track" on which ii identical air carts undergo a completely inelastic collision. One cart is initially at rest; the other has an initial speed of 0.650c. (a) In classical physics, the speed of the carts after the standoff would be 0.325c. Exercise y'all look the terminal speed in this relativistic collision to be greater than or less than 0.325c? Explain, (b) Use relativistic momentum conservation to find the speed of the carts after they collide and stick together.
Solution:

Affiliate 29 Relativity Q.93GP
IP In Conceptual Checkpoint 29-ii we considered an astronaut at residuum on an inclined bed within a moving spaceship. From the indicate of view of observer 1, on board the ship, the astronaut has a length L0 and is inclined at an angle θ0 in a higher place the flooring. Observer 2 sees the spaceship moving to the right with a speed v.

Solution:

Affiliate 29 Relativity Q.94GP
A pulsar is a complanate, rotating star that sends out a narrow beam of radiation, like the light from a lighthouse. With each revolution, we meet a brief, intense pulse of radiations from the pulsar. Suppose a pulsar is receding directly abroad from Earth with a speed of 0.800c, and the starship Endeavor is sent out toward the pulsar with a speed of 0.950c relative to Earth. If an observer or Earth finds that 153 pulses are emitted by the pulsar every second, at what charge per unit does an observer on the Attempt see pulses emitted?
Solution:

Chapter 29 Relativity Q.95GP
Prove that the total energy of an object is related to its momentum by the relation E2 = p2c2 + (m0c2)2.
Solution:

Affiliate 29 Relativity Q.96GP
Prove that if 0<v1<с and 02<с are two velocities pointing in the same direction, the relativistic sum of these velocities, v, is greater than v1 and greater than v2 but less than c. In detail, bear witness that this is true even if v1 and v2 are greater than 0.5c.
Solution:

Chapter 29 Relativity Q.97GP
Show that an object with momentum p and rest mass m0 has a speed given by

Solution:

Chapter 29 Relativity Q.98GP
Decay of the ∑− Particle When at balance, the ∑− particle has a lifetime of 0.fifteen ns before it decays into a neutron and a pion. One detail particle is observed to travel iii.0 cm in the lab before decaying. What was its speed?
Solution:

Chapter 29 Relativity Q.99PP
Find the speed of an electron accelerated through a voltage of 25.0 kV—ignoring relativity. Express your reply as a fraction times the speed of light. (Speeds over about 0.1c are generally regarded every bit relativistic.)
A. 0.221c
B. 0.281c
C. 0.312c
D. 0.781c
Solution:

Affiliate 29 Relativity Q.100PP
When relativistic effects are included, do you await the speed of the electrons to be greater than, less than, or the same as the result found in the previous problem?
Solution:
When the relativistic effects are induced then the speed of the electrons will exist less than the speed we establish in problem 99.

Chapter 29 Relativity Q.101PP
Discover the speed of the electrons in Problem 99, this time using a correct relativistic adding. As before, express your answer as a fraction times the speed of calorie-free.
A. 0.301c
B. 0.312c
C. 0.412c
D. 0.953c
Solution:

Affiliate 29 Relativity Q.102PP
Suppose the accelerating voltage in Trouble 99 is increased past a cistron of 10. What is the correct relativistic speed of an electron in this case?
A. 0.205c
B. 0.672c
C. 0.740c
D. 0.862c
Solution:

Chapter 29 Relativity Q.103IP
Referring to Case 29?4 The Picard approaches star- base Faraway Point with a speed of 0.806c, and the La Forge approaches the starbase with a speed of 0.906c. Suppose the Picard at present launches a probe toward tire starbase. (a) What velocity must the probe have relative to the Picard if it is to be at balance relative to the la Forge? (b) Win at velocity must the probe have relative to the Picard if its velocity relative to the La Forge is to exist 0.100c? (c) For the situation described in part (b), what is the velocity of the probe relative to the Faraway Point starbase?
Solution:

Chapter 29 Relativity Q.104IP
Referring to Example 29-4 Faraway Betoken starbase launches a probe toward the approaching starships. The probe has a velocity relative to the Picard of −0.906c. The Picard approaches starbase Faraway Bespeak with a speed of 0.806c, and the La Forge approaches the starbase with a speed of 0.906c. (a) What is the velocity of the probe relative to the La Forge? (b) What is the velocity of the probe relative to Faraway Point starbase?
Solution:

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