Solved: A starship voyages to a distant planet 10 ly away.

What is an inertial reference frame?

What is relativity about?

How does relativity affect time?

How does relativity affect space?

How does relativity affect mass and energy?

Does relativity have applications?

Which of these is an inertial reference frame (or a very good approximation)? a. Your bedroom b. A car rolling down a steep hill c. A train coasting along a level track d. A rocket being launched e. A roller coaster going over the top of a hill f. A sky diver falling at terminal speed

An airplane is flying at speed 200 m/s with respect to the ground. Sound wave 1 is approaching the plane from the front, sound wave 2 is catching up from behind. Both waves travel at 340 m/s relative to the ground. What is the speed of each wave relative to the

Ocean waves are approaching the beach at 10 m/s. A boat heading out to sea travels at 6 m/s. How fast are the waves moving in the boats reference frame? a. 16 m/s b. 10 m/s c. 6 m/s d. 4 m/s

Experimenter A in reference frame S stands at the origin looking in the positive x-direction. Experimenter B stands at x = 900 m looking in the negative x-direction. A firecracker explodes somewhere between them. Experimenter B sees the light flash at t = 3.0 ms. Experimenter A sees the light flash at t = 4.0 ms. What are the spacetime coordinates of the explosion?

A carpenter is working on a house two blocks away. You notice a slight delay between seeing the carpenters hammer hit the nail and hearing the blow. At what time does the event hammer hits nail occur? a. At the instant you hear the blow b. At the instant you see the hammer hit c. Very slightly before you see the hammer hit d. Very slightly after you see the hammer hit

An experimenter in reference frame S stands at the origin looking in the positive x-direction. At t = 3.0 ms she sees firecracker 1 explode at x = 600 m. A short time later, at t = 5.0 ms, she sees firecracker 2 explode at x = 1200 m. Are the two explosions simultaneous? If not, which firecracker exploded first?

A tree and a pole are 3000 m apart. Each is suddenly hit by a bolt of lightning. Mark, who is standing at rest midway between the two, sees the two lightning bolts at the same instant of time. Nancy is at rest under the tree. Define event 1 to be lightning strikes tree and event 2 to be lightning strikes pole. For Nancy, does event 1 occur before, after, or at the same time as event 2?

Saturn is 1.43 * 1012 m from the sun. A rocket travels along a line from the sun to Saturn at a constant speed of 0.9c relative to the solar system. How long does the journey take as measured by an experimenter on earth? As measured by an astronaut on the rocket?

A tree and a pole are 3000 m apart. Each is hit by a bolt of lightning. Mark, who is standing at rest midway between the two, sees the two lightning bolts at the same instant of time. Nancy is flying her rocket at v = 0.5c in the direction from the tree toward the pole. The lightning hits the tree just as she passes by it. Define event 1 to be lightning strikes tree and event 2 to be lightning strikes pole. For Nancy, does event 1 occur before, after, or at the same time as event 2?

In Example 36.4 a rocket traveled along a line from the sun to Saturn at a constant speed of 0.9c relative to the solar system. The Saturn-to-sun distance was given as 1.43 * 1012 m. What is the distance between the sun and Saturn in the rockets reference frame?

Molly flies her rocket past Nick at constant velocity v. Molly and Nick both measure the time it takes the rocket, from nose to tail, to pass Nick. Which of the following is true? a. Both Molly and Nick measure the same amount of time. b. Molly measures a shorter time interval than Nick. c. Nick measures a shorter time interval than Molly

A firecracker explodes at the origin of an inertial reference frame. Then, 2.0 ms later, a second firecracker explodes 300 m away. Astronauts in a passing rocket measure the distance between the explosions to be 200 m. According to the astronauts, how much time elapses between the two explosions?

Beth and Charles are at rest relative to each other. Anjay runs past at velocity v while holding a long pole parallel to his motion. Anjay, Beth, and Charles each measure the length of the pole at the instant Anjay passes Beth. Rank in order, from largest to smallest, the three lengths L A, LB, and LC

Peggy is standing in the center of a long, flat railroad car that has firecrackers tied to both ends. The car moves past Ryan, who is standing on the ground, with velocity v = 0.8c. Flashes from the exploding firecrackers reach him simultaneously 1.0 ms after the instant that Peggy passes him, and he later finds burn marks on the track 300 m to either side of where he had been standing. a. According to Ryan, what is the distance between the two explosions, and at what times do the explosions occur relative to the time that Peggy passes him? b. According to Peggy, what is the distance between the two explosions, and at what times do the explosions occur relative to the time that Ryan passes her?

An 8.0-m-long school bus drives past at 30 m/s. By how much is its length contracted?

An electron moves through the lab at 99% the speed of light. The lab reference frame is S and the electrons reference frame is S. In which reference frame is the electrons rest mass larger? a. In frame S, the lab frame b. In frame S, the electrons frame c. It is the same in both frames.

A rocket flies past the earth at 0.90c. As it goes by, the rocket fires a bullet in the forward direction at 0.95c with respect to the rocket. What is the bullets speed with respect to the earth?

Electrons in a particle accelerator reach a speed of 0.999c relative to the laboratory. One collision of an electron with a target produces a muon that moves forward with a speed of 0.95c relative to the laboratory. The muon mass is 1.90 * 10-28 kg. What is the muons momentum in the laboratory frame and in the frame of the electron beam?

Calculate the rest energy and the kinetic energy of (a) a 100 g ball moving with a speed of 100 m/s and (b) an electron with a speed of 0.999c.

The rockets of the Goths and the Huns are each 1000 m long in their rest frame. The rockets pass each other, virtually touching, at a relative speed of 0.8c. The Huns have a laser cannon at the rear of their rocket that fires a deadly laser beam perpendicular to the rockets motion. The captain of the Huns wants to send a threatening message to the Goths by firing a shot across their bow. He tells his first mate, The Goths rocket is length contracted to 600 m. Fire the laser cannon at the instant the tail of their rocket passes the nose of ours. The laser beam will cross 400 m in front of them. But things are different in the Goths reference frame. The Goth captain muses, The Huns rocket is length contracted to 600 m, 400 m shorter than our rocket. If they fire as the nose of their ship passes the tail of ours, the lethal laser beam will pass right through our side. The first mate on the Huns rocket fires as ordered. Does the laser beam blast the Goths or not?

FIGURE Q36.1 shows two balls. What are the speed and direction of each (a) in a reference frame that moves with ball 1 and (b) in a reference frame that moves with ball 2?

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 beam relative to Tom?

Firecracker A is 300 m from you. Firecracker B is 600 m from you in the same direction. You see both explode at the same time. Define event 1 to be firecracker A explodes and event 2 to be firecracker B explodes. Does event 1 occur before, after, or at the same time as event 2? Explain

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 2 to be firecracker B explodes. According to your lab partner, based on measurements he or she makes, does event 1 occur before, after, or at the same time as event 2? Explain

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 Peggys reference frame? If not, which exploded first? Explain. b. Were the explosions simultaneous in Ryans reference frame? If not, which exploded first? Explain

FIGURE Q36.6 shows a rocket traveling from left to right. At the instant it is halfway between two trees, lightning simultaneously (in the rockets 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 sitting on the ground halfway between the trees as the rocket passed overhead. According to the student, were the lightning strikes simultaneous? If not, which tree was hit first? Explain.

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, if anyone, measures the shorter flight time?

As the meter stick in FIGURE Q36.8 flies past you, you simultaneously measure the positions of both ends and determine that L 6 1 m. a. To an experimenter in frame S, the meter sticks frame, did you make your two measurements simultaneously? If not, which end did you measure first? Explain. b. Can experimenters in frame S give an explanation for why your measurement is less than 1 m?

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.

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? Exp

Event A occurs at spacetime coordinates 1300 m, 2 ms2. a. Event B occurs at spacetime coordinates 11200 m, 6 ms2. Could A possibly be the cause of B? Explain. b. Event C occurs at spacetime coordinates 12400 m, 8 ms2. Could A possibly be the cause of C? Explain.

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 relative to frame S? b. What is the position of the two explosions in frame S?

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?

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 papers speed relative to the ground if he throws the paper (a) forward, (b) backward, and (c) to the side?

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?

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 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?

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 1x, y, z2 = 130 m, 40 m, 0 m2 be preset?

Bjorn is standing at x = 600 m. Firecracker 1 explodes at the origin and firecracker 2 explodes at x = 900 m. The flashes from both explosions reach Bjorns eye at t = 3.0 ms. At what time did each firecracker explode?

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 Biancas eye at t = 3.0 ms. At what time does she see the flash from firecracker 2?

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 ms and the flash from bolt 1 at t = 50 ms. According to your assistant, were the lightning strikes simultaneous? If not, which occurred first, and what was the time difference between the two?

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 is the time difference between the two?

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 simultaneously? If not, which do you see first, and what is the time difference between the two?

A cosmic ray travels 60 km through the earths atmosphere in 400 ms, as measured by experimenters on the ground. How long does the journey take according to the cosmic ray?

At what speed, as a fraction of c, does a moving clock tick at half the rate of an identical clock at rest?

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 between the launch and the arrival of the first radio message from the astronaut saying that she has arrived?

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?

At what speed, as a fraction of c, would a round-trip astronaut lose 1 25 of the elapsed time shown on her watch?

At what speed, in m/s, would a moving clock lose 1.0 ns in 1.0 day according to experimenters on the ground? Hint: Use the binomial approximation

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? Hint: Use the binomial approximation.

Jill claims that her new rocket is 100 m long. As she flies past your house, you measure the rockets length and find that it is only 80 m. What is Jills speed, as a fraction of c?

At what speed, as a fraction of c, will a moving rod have a length 60% that of an identical rod at rest

A cube has a density of 2000 kg/m3 while at rest in the laboratory. What is the cubes 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?

A muon travels 60 km through the atmosphere at a speed of 0.9997c. According to the muon, how thick is the atmosphere?

Our Milky Way galaxy is 100,000 ly in diameter. A spaceship crossing the galaxy measures the galaxys diameter to be a mere 1.0 ly. a. What is the spacecrafts speed, as a fraction of c, relative to the galaxy? b. How long is the crossing time as measured in the galaxys reference frame?

A human hair is about 50 mm in diameter. At what speed, in m/s, would a meter stick shrink by a hair? Hint: Use the binomial approximation.

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 1x, t2 = 13.0 * 1010 m, 200 s2. What are the spacetime coordinates of the collision in earths reference frame?

An event has spacetime coordinates 1x, t2 = 11200 m, 2.0 ms2 in reference frame S. What are the events spacetime coordinates (a) in reference frame S that moves in the positive x-direction at 0.80c and (b) in reference frame S that moves in the negative x-direction at 0.80c?

In the earths 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 ms. 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 rockets reference frame? b. Are the events simultaneous in the rockets frame? If not, which occurs first?

A rocket cruising past earth at 0.80c shoots a bullet out the back door, opposite the rockets motion, at 0.90c relative to the rocket. What is the bullets speed, as a fraction of c, relative to the ear

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 laboratory experiment shoots an electron to the left at 0.90c. What is the electrons speed, as a fraction of c, relative to a proton moving to the right at 0.90c?

A proton is accelerated to 0.999c. a. What is the protons momentum? b. By what factor does the protons momentum exceed its Newtonian momentum?

A 1.0 g particle has momentum 400,000 kgm/s. What is the particles speed in m/s?

At what speed, as a fraction of c, is a particles momentum twice its Newtonian value?

What is the speed, as a fraction of c, of a particle whose momentum is mc?

A quarter-pound hamburger with all the fixings 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 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?

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?

At what speed, as a fraction of c, is a particles kinetic energy twice its rest energy?

At what speed, as a fraction of c, is a particles total energy twice its rest energy

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 complete annihilation. What is the ratio of the energy released in this star-antistar collision to the energy released in the supernova?

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 Higgswhich decays too quickly to be observed directlyis immediately transformed into two photons emitted back to back. Two photons, with momenta 3.31 * 10-17 kgm/s, were detected. What is the mass of the Higgs boson? Give your answer as a multiple of the proton mass. Hint: The relationship between energy and momentum applies to photons if you treat a photon as a massless particle.

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? Hint: c = 1 light hour per hour

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 simultaneous events for a passenger seated in the car? If not, which occurs first and by how much time? b. Are the bell and siren simultaneous events for a bicyclist waiting to cross the tracks? If not, which occurs first and by how much time?

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 distance between the two explosions is 120 ly. According to the aliens, what is the time between the explosions?

Two events in reference frame S occur 10 ms 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?

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 time has elapsed on the astronauts chronometers

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 dont, because they are accelerating), how long is the tube in the electrons reference frame?

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? Hint: The Doppler effect for light was covered in Chapter

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 that you age only 20 years during the round trip. a. How fast, as a fraction of c, must the rocket travel relative to earth? b. How much energy is needed to accelerate the rocket to this speed? c. Compare this amount of energy to the total energy used by the United States in the year 2015, which was roughly 1.0 * 1020 J.

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 0.90c. How much additional energy is needed to increase its speed by 1 m/s?

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 and (b) the rocket crew? (c) Which answers are the correct ones, those in part a or those in part b?

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 velocities v1 = 0.30c, v2 = 0.50c, and v3 = 0.70c. All three spaceships, each at the origin of its reference frame, happen to pass Delta as it explodes. a. What are the times of the two explosions as measured by scientists on each of the three spaceships? b. Does one spaceship find that the explosions are simultaneous? If so, which one? c. Does one spaceship find that Epsilon explodes before Delta? If so, which one? d. Do your answers to parts b and c violate the idea of causality? Explain

Two rockets approach each other. Each is traveling at 0.75c in the earths reference frame. What is the speed, as a fraction of c, of one rocket relative to the other?

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?

A rocket fires a projectile at a speed of 0.95c while traveling past the earth. An earthbound scientist measures the projectiles speed to be 0.90c. What was the rockets speed as a fraction of c?

Through what potential difference must an electron be accelerated, starting from rest, to acquire a speed of 0.99c?

What is the speed, in m/s, of a proton after being accelerated from rest through a 50 * 106 V potential difference?

The half-life of a muon at rest is 1.5 ms. 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 ms. 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 ring? The mass of a muon is 207 times the mass of an electron

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 zaxes. To find out if this is really true, consider two spray-paint nozzles attached to rods perpendicular to the x-axis. It has been confirmed that, when both rods are at rest, both nozzles are exactly 1 m above the base of the rod. One rod is placed in the S reference frame with its base on the x-axis; the other is placed in the S reference frame with its base on the x@axis. The rods then swoop past each other and, as FIGURE P36.60 shows, each paints a stripe across the other rod. We will use proof by contradiction. Assume that objects perpendicular to the motion are contracted. An experimenter in frame S finds that the S nozzle, as it goes past, is less than 1 m above the x-axis. The principle of relativity says that an experiment carried out in two different inertial reference frames will have the same outcome in both. a. Pursue this line of reasoning and show that you end up with a logical contradiction, two mutually incompatible situations. b. What can you conclude from this contradiction?

Derive the Lorentz transformations for t and t. Hint: See the comment following Equation 36.22

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. What is the particles speed, as a fraction of c, in the earths reference frame?

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 earths reference frame, calculate x, t, and the spacetime interval s for these events. b. In the rockets reference frame, calculate x, t, and the spacetime interval s for these events. c. Repeat your calculations of part a if the rocket is replaced with a laser beam

Lets 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 at a speed of c/2 and object C, of mass 2m, that, to conserve momentum, is shot to the right at a speed of c/4. Suppose this explosion is observed in reference frame S that is moving to the right at half the speed of light. a. Use the Lorentz velocity transformation to find the velocity and the Newtonian momentum of A in S. b. Use the Lorentz velocity transformation to find the velocities and the Newtonian momenta of B and C in S. c. What is the total final momentum in S? d. Newtonian momentum was conserved in frame S. Is it conserved in frame S?

a. What are the momentum and total energy of a proton with speed 0.99c? b. What is the protons momentum in a different reference frame in which E = 5.0 * 10-10 J?

At what speed, as a fraction of c, is the kinetic energy of a particle twice its Newtonian value?

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 much thermal energy does the plant generate in one year? b. What mass of uranium is transformed into energy in one year?

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 to propel the ship. After consuming all the fuel and reaching top speed, the spaceship flies past a space station that is stationary with respect to the planet from which the ship was launched. What is the length of the spaceship as measured by astronauts on the space station?

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 suns total mass? c. Fusion takes place in the core of a star, where the temperature and pressure are highest. A star like the sun can sustain fusion until it has transformed about 0.10% of its total mass into energy, then fusion ceases and the star slowly dies. Estimate the suns lifetime, giving your answer in billions of years

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 established.) The reaction is 226 Ra S 222 Rn + 4 He, where Rn is the element radon. The accurately measured atomic masses of the three atoms are 226.0254 u, 222.0176 u, and 4.0026 u. 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 fusion of four protons into a helium nucleus. The process involves several steps, but the net reaction is simply 4p S 4 He + energy. The mass of a proton, to four significant figures, is 1.673 * 10-27 kg, and the mass of a helium nucleus is known to be 6.644 * 10-27 kg. a. How much energy is released in each fusion? b. What fraction of the initial rest mass energy is this energy?

Consider the inelastic collision e- + e- S e- + e- + e- + e+ in which an electron-positron pair is produced in a head-on collision between two electrons moving in opposite directions at the same speed. This is similar to Figure 36.39, but both of the initial electrons are moving. a. What is the threshold kinetic energy? That is, what minimum kinetic energy must each electron have to allow this process to occur? b. What is the speed of an electron with this kinetic energy?

An electron moving to the right at 0.90c collides with a positron moving to the left at 0.90c. The two particles annihilate and produce two gamma-ray photons. What is the wavelength of the photons?

Two rockets are each 1000 m long in their rest frame. Rocket Orion, traveling at 0.80c relative to the earth, is overtaking rocket Sirius, which is poking along at a mere 0.60c. According to the crew on Sirius, how long does Orion take to completely pass? That is, how long is it from the instant the nose of Orion is at the tail of Sirius until the tail of Orion is at the nose of Sirius?

Some particle accelerators allow protons 1p+2 and antiprotons 1p-2 to circulate at equal speeds in opposite directions in a device called a storage ring. The particle beams cross each other at various points to cause p+ + p- collisions. In one collision, the outcome is p+ + p- S e+ + e- + g + g, where g represents a high-energy gamma-ray photon. The electron and positron are ejected from the collision at 0.9999995c and the gamma-ray photon wavelengths are found to be 1.0 * 10-6 nm. What were the proton and antiproton speeds, as a fraction of c, prior to the collision?

A ball of mass m traveling at a speed of 0.80c has a perfectly inelastic collision with an identical ball at rest. If Newtonian physics were correct for these speeds, momentum conservation would tell us that a ball of mass 2m departs the collision with a speed of 0.40c. Lets do a relativistic collision analysis to determine the mass and speed of the ball after the collision. a. What is gp, written as a fraction like a/b? b. What is the initial total momentum? Give your answer as a fraction times mc. c. What is the initial total energy? Give your answer as a fraction times mc2 . Dont forget that there are two balls. d. Because energy can be transformed into mass, and vice versa, you cannot assume that the final mass is 2m. Instead, let the final state of the system be an unknown mass M traveling at the unknown speed uf. You have two conservation laws. Find M and uf

A very fast pole vaulter lives in the country. One day, while practicing, he notices a 10.0-m-long barn with the doors open at both ends. He decides to run through the barn at 0.866c while carrying his 16.0-m-long pole. The farmer, who sees him coming, says, Aha! This guys pole is length contracted to 8.0 m. There will be a short interval of time when the pole is entirely inside the barn. If Im quick, I can simultaneously close both barn doors while the pole vaulter and his pole are inside. The pole vaulter, who sees the farmer beside the barn, thinks to himself, That farmer is crazy. The barn is length contracted and is only 5.0 m long. My 16.0-m-long pole cannot fit into a 5.0-m-long barn. If the farmer closes the doors just as the tip of my pole reaches the back door, the front door will break off the last 11.0 m of my pole. Can the farmer close the doors without breaking the pole? Show that, when properly analyzed, the farmer and the pole vaulter agree on the outcome. Your analysis should contain both quantitative calculations and written explanation