How fast must an electron move so that its total energy isI 0% more than its rest mass

You are in an airplane cruising smoothly at 600 mph. What experiment, if any, could you do that would demonstrate that you are moving, while those on the ground are at rest?

Frame S' moves relative to frame S as shown in Figure Q27.2. a. A ball is at rest in frame S ' . What are the speed and direction of the ball in frame S? b. A ball is at rest in frame S. What are the speed and direction of the ball in frame S '?

a. Two balls move as shown in Figure Q27.3. What are the speed and direction of each ball in a reference frame that moves with ball I? b. What are the speed and direction of each ball in a reference frame that moves with ball 2?

A lighthouse beacon ale1ts ships to the danger of a rocky coastline. a. According to the lighthouse keeper, with what speed does the light leave the lighthouse? b. A boat is approaching the coastline at speed 0.5c. According to the captain, with what speed is the light from the beacon approaching her boat?

A lighthouse beacon ale1ts ships to the danger of a rocky coastline. a. According to the lighthouse keeper, with what speed does the light leave the lighthouse? b. A boat is approaching the coastline at speed 0.5c. According to the captain, with what speed is the light from the beacon approaching her boat?

At the instant that a clock standing next to you reads t = 1.0 ,s, you look at a second clock, 300 m away, and see that it reads I = 0 ,s. Are the two clocks synchronized? If not, which one is ahead?

Firecracker I is 300 m from you. Firecracker 2 is 600 m from you in the same direction. You see both explode at the same time. Define event I to be " firecracker I explodes" and event 2 to be "firecracker 2 explodes." Does event I occur before, after, or at the same time as event 2? Explain.

Firecrackers I and 2 are 600 m apart. You are standing exactly halfway between them. Your lab partner is 300 m on the other side of firecracker I. You see two flashes of light, from the two explosions, at exactly the same instant of time. Define event I to be " firecracker I explodes" and event 2 to be "firecracker 2 explodes." According to your lab partner, based on measurements he or she makes, does event I occur before, after, or at the same time as event 2? Explain.

Your clocks and calendars are synchronized with the clocks and calendars in a star system exactly I 0 ly from earth that is at rest relative to the earth. You receive a TV transmission from the star system that shows a date and time display. The date it shows is June 17, 2050. When you glance over at your own wall calendar, what date does it show?

Two trees are 600 m apart. You are standing exac tly halfway between them and your lab partner is at the base of tree I. Lightning strikes both trees. a. Your lab partner, based on measurements he makes, determines that the two lightning strikes were simultaneous. What did you see? Did you see the lightning hit tree I first, hit tree 2 first, or hit them both at the same instant of time? Explain. b. Lightning strikes the trees agai n. Tois time your lab partner sees both flashes of light at the same instant of time. What did you see? Did you see the li ghtning hit tree I first, hit tree 2 first, or hit them both at the same instant of time? Explain. c. In the scenario of part b, were the lightning strikes simultaneous? Explain. I I. Figure Q27. I I 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 ti me later, the fla shes from the two explosions arrive at Peggy at the same time. a. Were the explosions simultaneous in Peggy's reference frame? If not, which exploded first? Explain. b. Were the explosions simultaneous in Ryan's reference frame. If not, which exploded first? Explain.

In Figure Q27.12, clocks C1 and C2 in frame S are synchronized. Clock C' moves at speed v relative to frame S. Clocks C' and C1 read exactly the same as C' goes past. As C' passes C2, is the time shown on C' earlier, later, or the same as the time shown on C2? Explain.

In Figure Q27.12, clocks C1 and C2 in frame S are synchronized. Clock C' moves at speed v relative to frame S. Clocks C' and C1 read exactly the same as C' goes past. As C' passes C2, is the time shown on C' earlier, later, or the same as the time shown on C2? Explain.

A meter stick passes you at a speed of 0.5c. Explain clearly how you would measure the length of this fast-moving object.

You' re passing a car on the highway. You want to know how much time is required to completely pass the car, from no overlap between the cars to no overlap between the cars. Call your car A, the car you are passing B. a. Specify two events that can be given spacetime coordinates. In describing the events, refer to cars A and B and to their front bumpers and rear bumpers. b. T.n e ither reference frame, is there one clock that is present at both eveJJts? c. Who, if anyone, measures the proper lime between the events?

Your friend flies from Los Angeles to New York. He determines the distance using the tried-and-trued= vt. You and your assistants on the ground also measure the distance using meter sticks and surveying equipment. a. Who, if anyone, measures the proper lengtb? b. Who, if anyone, measures the shotter distance?

A I 00-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 al one instant of time? Explain.

Dan picks up a 15-m-long pole and begins running very fast, holding the pole horizontally and pointing in the direction he's running. He heads toward a barn that is 12 m long and has open doors at each end. Dan runs so fast that, to Farmer Brown standing by his barn, the ladder is only 5 m long. As soon as the pole is completely inside the barn, Farmer Brown closes both doors so that Dan and the pole are inside with both doors shut. Then, just before Dan reaches the far door, Farmer Brown opens both doors and Dan emerges, still moving at high speed. According to Dan, however, the barn is contracted to only 4 111 and the pole has its full 15 m length. Farmer Brown sees the pole completely inside the barn with both doors closed. What does Dan see happening?

The rocket speeds shown in Figure Q27 .18 are relative to the earth. Is the speed of A relative to B greater than less than, or equal to 0.8c?

Can a particle of mass m have total energy less than mc2? Explain.

In your chemistry classes, you have probably learned that, in a chemical reaction, the mass of the products is equal to the mass of the reactants. That is, the mass of the substances produced in a chemical reaction is equal to the mass of the substances consumed in the reaction. Is this absolutely true, or is there actually a small difference? Explain.

Lee and Leigh are twins. At their first birthday party, Lee is placed on a spaceship that travels away from the earth and back at a steady 0.866c. The spaceship eventually returns, landing in the swimming pool at Leigh's eleventh birthday party. When Lee emerges from the ship, it is discovered that A. He is still only I year old. B. He is 6 years old. C. He is also 11 years old. D. He is 21 years old.

A space cowboy wants to eject from his spacecraft 100,000 km after passing a space buoy, as seen by spectators at rest with respect to the buoy. To do this, the cowboy sets a timer on his craft that will start as he passes the buoy. He plans to cruise by the buoy at 0.300c. How much time should he allow between passing the buoy and ejecting? A. 1.0 I s B. 1.06 s C. I. I I s D. 1.33 s E. 1.58 s 23. I A lamp flas hes at the origin

A lamp flas hes at the origin. Then, I ,s later, a lamp flashes at a poi nt 150 111 from the origin. How fast, as a fraction of c, would an astronaut need to travel so that he measures the proper time between these two events? A. 0.35c B. 0.50c C. 0.62c D. 0.87c

Energy in the sun is produced by the fusion of four protons into a helium nucleus. The process involves several steps, but the net reaction is simply 4p ~ 4He + energy. Given this, you can say that A. One helium atom has more mass than four hydrogen atoms. B. One helium atom has less mass than four hydrogen atoms. C. One helium atom has the same mass as four hydrogen atoms.

A particle moving at speed 0.40c has momentum p0 . The speed of the particle is increased to 0.80c. Its momentum is now A. Less than 2p0 B. Exactly 2p0 C. Greater than 2p0.

A particle moving at speed 0.40c has kinetic energy K0 . The speed of the particle is increased to 0.80c. The kinetic energy is now A. Less than 4K0 B. Exactly 4K0 C. Greater than 4K0

The X-15 rocket-powered plane holds the record for the fastest speed ever attained by a manned aircraft, at 2020 mis. At this speed, by how much is the 15.5-m-long aircraft length contracted? Hint: Use the binomial approximation.

A rocket cruising past earth at 0.800c shoots a bullet out the b ack door, opposite the rocket's motion, at 0.900c relative to the back door, opposite the rocket's motion, at 0.900c relative to the rocket. What is the bullet's speed relative to the eaith?

A base on Planet X fires a missile toward an oncoming space fighter. The missile's speed according to the base is 0.85c. The space fighter measures the missile's speed as 0.96c. How fast is the space fighter travel ing relative to Planet X?

A solar flare blowing out from the sun at 0.90c is ove1taking a rocket as it flies away from the sun at 0.80c. Accordi ng to the crew on board, with what speed is the flare gaining on the rocket?

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 Newtonian momentum?

A 1.0 g particle has momentum 400,000 kg mis. What is the particle's speed?

Al what speed is a particle's momentum twice its Newtonian value?

Whal is the speed of a particle whose momentum is mc?

What are the kinetic energy, the rest energy, and the total energy of a 1.0 g partic le with a speed of 0.80c?

A quarter-pound hamburger with all the fixings has a mass of 200 g. The food energy of the hamburger (480 food calories) is 2MJ. a. What is the energy equivalent of the mass of the hamburger? b. By what factor does the energy equivalent exceed the food energy?

How fast must an electron move so that its total energy is I 0% more than its rest mass energy?

At what speed is a particle' s kinetic energy twice its rest energy?

A firecracker explodes at x = 0 m, t = 0 .s. A second explodes at x = 300 m, 1 = 2.0 . s. What is the proper time between these events?

You're standing on an asteroid when you see your best friend rocketing by in her new spaceship. As she goes by, you notice that the front and rear of her ship coincide exactly with the 400-m-diamete r of another nearby asteroid that is stationary with respect to you. However, you happen to know that your friend's spaceship measured 500 m long in the showroom. What is your fri end's speed relative to you?

subatomic particle moves through the laboratory at 0.90c. Laboratory experimenters measure its li fetime, from creation to annihilation, to be 2.3 ps ( I ps = I picosecond = 10-12 s). According to the particle, how long did it live?

You and Maria each own identical spaceships. As you fly past Maria, you measure her ship to be 90 m long and your own ship to be 100 m long. a. How long does Maria measure your ship to be? b. How fast is Maria moving relative to you?

A very fast-moving train car passes you, moving to the right at 0.50c. You measure its length to be 12 m. Your friend David flies past you to the right at a speed relative to you of 0.80c. How long does David measure the train car to be?

Two events in reference frame S occur I 0 .s apart at the same point in space. Frame S' travels at speed v = 0.90c relative to frame S. a. What is the time interval between the events in reference frame S'? b. What is the di stance between the events in frame S '?

A spaceship heads directly toward an asteroid at a relative speed of 0.75c. When it is 3.0 X 108 m from the asteroid, as measured in the asteroid's frame, the rocket fires a laser pulse at the asteroid. According to the rocket captain, what is the time interval between when the pulse hits the asteroid and when the rocket passes the asteroid, barely missing it?

Because of the earth's rotation, a person living on top of a mountain moves at a faster speed than someone at sea level. The mountain dweller's c locks thus run slowly compared to those at sea level. If the average life span of a hermit is 80 years, on average how much longer would a hermit dwelling on the top of a 3000-m-high mountain live compared to a sea-level hermit?

Two spaceships approach each other at speeds of 0.80c and 0.90c relative to the sun. When they are 5.0 X 109 m apart, as measured in the sun's reference frame, they each set their clocks to zero. By how much do the ir clocks differ at the instant they pass each other? Hint: First find how long it takes the spaceships to pass in the sun's reference frame.

You fly 5000 km across the United States on an airliner at 250 mis. 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? Hint: Use the binomial approximation.

A cube has a density of2000 kg/1113 while at rest in the laboraINT tory. What is the cube's density as measured by an experime nter in the laboratory as the c ube moves through the laboratory at 90% of the speed of light in a direction perpendicular to one of its faces?

A railroad car that is 20 m long when at rest passes Rachael, who is standing on the ground. She records that it takes 120 ns to go by. How fa st is the car moving, as a fraction of c?

A spaceship flies past an experimenter who measures its length to be one-half the length he had measured when the spaceship was at rest. An astronaut aboard the spaceship notes that his clock ticks at I-second intervals. What is the time between ticks as measured by the experimenter?

Marissa's spaceship approaches Joseph's at a speed of0.99c. As Marissa passes Joseph, they synchronize their clocks to both read t = 0 s. When Marissa's clock reads 100 s, she sends a light signal back to Joseph. According to his clock, when does he receive this signal?

At a speed of 0.90c, a spaceship travels to a star that is 9.0 ly distant. a. According to a scientist on earth, how long does the trip take? b. According to a scientist on the spaceship, how long does the trip take? c. According to the scientist on the spaceship, what is the distance traveled during the trip? d. At what speed do observers on the spaceship see the star approaching them?

In an attempt to reduce the extraordinarily long travel times INT 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 fas t that you age only 20 years during the round trip. a. How fast must the rocket travel relative to earth? b. How much energy is needed to accelerate the rocket to this speed? c. How many times larger is this energy than the total energy used by the United States in the year 2012, which was roughly 1.0 X I020 J?

A rocket traveling at 0.500c sets out for the nearest star, Alpha Centauri, which is 4.25 ly away from eaJth. lt 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 and (b) the rocket crew? (c) Which answers are the correct ones, those in part a or those in part b?

A distant quasar is found to be moving away from the eatth 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 measured by astronomers in the other galaxy?

Two rockets approach each other. Each is traveling at 0.75c in the earth's reference frame. What is the speed of one rocket relative to the other?

A railcar has a velocity of 0.5c relative to the ground. To another train traveling on the same track, the railcar's velocity is -0.2c. What is the velocity of the train relat.ive to the ground?

A military jet traveling at 1500 mis has engine trouble and the pilot must bail out. Her ejection seat shoots her forward at 300 mis relative to the jet. According to the Lorentz velocity transformation, by how much is her velocity relative to the ground less than the 1800 mis predicted by Gali lean relativity? Hint: Use the binomial approximation.

James, Daniella, and Tara all possess identical clocks. As Daniella passes James in her rocket, James observes that her clock runs at 80% the rate of his clock. As Tara passes in her rocket, in the same direction as Daniella, James observes that her clock runs at 70% the rate of his clock. At what rate, relative to her clock, does Daniella observe Tara's clock to run?

A space beacon on Planet Karma emits a pulse of light every second. Spaceman Trevor flies directly toward the beacon at a speed of0.95c. According to Trevor, what is the time between one pulse reaching his ship and the next? Hint: First find the time between pulses reaching the ship in Planet Karma's reference frame.

Two rockets, A and B, approach the earth from opposite directions at speed 0.800c. 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?

The highest-energy cosmic ray ever detected had an energy of about 3.0 x !020 eV. Assume that this cosmic ray was a proton. a. What was the proton 's speed as a fraction of c? b. If this proton started at the same t.ime and place as a photon traveling at the speed of light, how

What is the speed of an electron after being accelerated from rest through a 20 x !06 V potential difference?

What is the speed of a proton after being accelerated from rest through a 50 X I06 V potential difference?

The half-l ife of a muon at rest is 1.5 .s. 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 .s. a. What is the speed of the muons in the storage ring? b. What is the total energy of a muon in the storage ring? The mass of a muon is 207 times the mass of an electron.

What is the momentum of a particle with speed 0.95c and total energy 2.0 X 10-ro J?

What is the momentum of a particle whose total energy is four times its rest energy? Give your answer as a multiple ofmc.

What is the total energy, in MeV, of a. A proton traveling at 99.0% of the speed of light? b. An electron traveling at 99.0% of the speed of light?

What is the velocity, as a fraction of c, of a. A proton with 500 GeV total energy? b. An electron with 2.0 GeV total energy?

At what speed is the kinetic energy of a particle twice its Newtonian value?

The factor y appears in many relativistic expressions. A value y = 1.0 I implies that relati vity chaQges the Newtonian values by approximately I% and that relativistic effects can no longer be ignored. At what kinetic energy, in MeV, is y = 1.01 for (a) an electron, and (b) a proton?

The factor y appears in many relativistic expressions. A value y = 1.0 I implies that relati vity chaQges the Newtonian values by approximately I% and that relativistic effects can no longer be ignored. At what kinetic energy, in MeV, is y = 1.01 for (a) an electron, and (b) a proton?

A standard nuclear power plant generates 3.0 GW of thermal power from the fission of235U. Experiments show that, on average, 0. 19 u of mass is lost in each fi ssion of a 235U nuc leus. How many kilograms of 235U undergo fission each year in this power plant?

The sun radiates energy at the rate 3.8 X 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 X 1030 kg. a. How much mass does the sun lose each year? b. What percentage is this of the sun's total mass? c. Estimate the lifetime of the sun.

The radioactive element radium (Ra) decays by a process known as alpha decay, in which the nucleus emits a helium nucleus. (These high-speed helium nuclei were named alpha particles when radioactivity was first discovered, long before the identity of the particles was establi shed.) The reaction is 226Ra ~ 222Rn + 4He, where Rn is the element radon. The accurately measured atomic masses of the three atoms are 226.025, 222.017, and 4.003. How much energy is released in each decay? (The energy released in radioactive decay is what makes nuclear waste "hot.")

The nuclear reaction that powers the sun is the fu sion of four protons into a helium nucleus. The process involves several steps, but the net reaction is simply 4p-> 4He +energy. The mass of a helium nucleus is known to be 6.64 x I 0- 27 kg. a. How much energy is released in each fusion? b. What fraction of the initial rest mass energy is this energy?

When antimatter (which we'll leam more about in Chapter 30) Im interacts with an equal mass of ordinary matter, both matter and antimatter are converted completely into energy in the form of photons. In an antimatter-fueled spacesh ip, a staple of science fiction, the newly created photons are shot from the back of the ship, propelling it forward. Suppose such a ship has a mass of 2.0 X 106 kg, and carries a mass of fuel equal to I% of its mass, or 1.0 x I 04 kg of matter and an equal mass of antimatter. a. What is the final speed of the ship, assuming it starts from rest, if all energy released in the matter-antimatter annihilation is transformed into the kinetic energy of the ship? b. Not only do photons have energy, as you learned in Chapter 25, they also have momentum. Explain why, when energy and momentum conservation are both considered, the final speed of the ship will be less than you calculated in part a.

What is the half-life of a pion in the reference frame of the patient undergoing pion therapy? A. 1.8 x 10-io s B. 1.8 x 10-s s C. 1.8 X 10-7 s D. 1.8 x 10-6 s

According to the pion, what is the distance it travels from the accelerator to the medical bay? A. 0.30 m B. 3.0 m C. 30 m D. 3000 m

The proton collision that creates the pion also creates a gamma-ray photon traveling in the same direction as the pion. The photon will get to the medical bay first because it is moving faster. What is the speed of the photon in the pion's reference frame? A. 0.00005c B. 0.5c C. 0.99995c D. c

If the pion slows down to 0.99990c, about what percentage of its kinetic energy is lost? A. 0.03% B. 0.3% c. 3% D. 30%