1 The Nature Of Light 2 Geometric Optics And Image Formation 3 Interference 4 Diffraction 5 Relativity 6 Photons And Matter Waves 7 Quantum Mechanics 8 Atomic Structure 9 Condensed Matter Physics 10 Nuclear Physics 11 Particle Physics And Cosmology Chapter5: Relativity
Chapter Questions Section: Chapter Questions
Problem 5.1CYU: Check Your Understanding Explain how special relativity differs from general relativity. Problem 5.2CYU: Check Your Understanding What is if v=0.650c? Problem 5.3CYU: Check Your Understanding a. A particle travels at 1.90108m/sand lives 2.10108swhen at rest relative... Problem 5.4CYU: Check Your Understanding A particle is traveling through Earth’s atmosphere at a speed of 0.750c. To... Problem 5.5CYU: Check Your Understanding Shaw that if a time increment dt elapses for an observer who sees the... Problem 5.6CYU: Check Your Understanding Distances along a direction perpendicular to the relative motion of the two... Problem 5.7CYU: Check Your Understanding Suppose a space probe moves away from Earth at a speed 0.350c. It sends a... Problem 5.8CYU: Check Your Understanding What is the momentum of an electron traveling at a speed 0.985c? The rest... Problem 5.9CYU: Check Your Understanding What is the kinetic energy of an electron if its speed is 0.992c? Problem 1CQ: Which of Einstein’s postulates of special relativity includes a concept that does not ?t with the... Problem 2CQ: Is Earth an inertial frame of reference? Is the sun? Justify your response. Problem 3CQ: When you are flying in a commercial jet, it may appear to you that the airplane is stationary and... Problem 4CQ: (a) Does motion affect the rate of a clock as measured by an observer moving with it? (b) Does... Problem 5CQ: To whom does the elapsed time for a process seem to be longer, an observer moving relative to the... Problem 6CQ: (a) How could you travel far into the future of Earth without aging significantly? (b) Could this... Problem 7CQ: To whom does an object seem greater in length, an observer moving with the object or an observer... Problem 8CQ: Relativistic effects such as time dilation and length contraction are present for cars and... Problem 9CQ: Suppose an astronaut is moving relative to Earth at a significant fraction of the speed of light.... Problem 10CQ: Explain the meaning of the terms "red shift" and ' 'blue shift" as they relate to the relativistic... Problem 11CQ: What happens to the relativistic Doppler effect when relative velocity is zero? Is this the expected... Problem 12CQ: Is the relativistic Doppler effect consistent with the classical Doppler effect in the that is... Problem 13CQ: All galaxies farther away than about exhibit a red shift in their emitted light that is proportional... Problem 14CQ: How does modern relativity modify the law of conservation of momentum? Problem 15CQ: Is it possible for an external force to be acting on a system and relativistic momentum to be... Problem 16CQ: How are the classical laws of conservation of energy and conservation of mass modified by modern... Problem 17CQ: What happens to the mass of water in a pot when it cools, assuming no molecules escape or are added?... Problem 18CQ: Consider a thought experiment. You place an expanded balloon of air on weighing scales outside in... Problem 19CQ: The mass of the fuel in a nuclear reactor decreases by an observable amount as it puts out energy.... Problem 20CQ: We know that the velocity of an object with mass has an upper limit of c. Is there an upper limit on... Problem 21CQ: Given the fact that light travels at c, can it have mass? Explain. Problem 22CQ: If you use an Earth based telescope to project a laser beam onto the moon, you can move the spot... Problem 23P: What is if (b) If Problem 24P: What is if If Problem 25P: Particles called mesons are produced by accelerator beams. If these particles travel at and live... Problem 26P: Suppose a particle called a kaon is created by cosmic radiation striking the atmosphere. It moves by... Problem 27P: A neutral meson is a particle that can be created by accelerator beams. If one such particle lives... Problem 28P: A neutron lives 900 s when at rest relative to a observer. How fast is the neutron moving relative... Problem 29P: If relativistic effects are to be less than then must be less than 1.01. At what relative velocity... Problem 30P: If relativistic effects are to be less than then must be less than 1.03. At what relative velocity... Problem 31P: A spaceship, 200 m long as. seen on board, moves by the Earth at 0.970c. What is its length as... Problem 32P: How fast would a 6.0 m-long sports car have to be going past you in order for it to appear only 5.5... Problem 33P: (a) How far does the muon in Example 5.3 travel according to the earthbound observer? (b) How far... Problem 34P: (a) How long would the mum] in Example 5.3 have lived as observed on Earth if its velocity was.... Problem 35P: Unreasonable Results A spaceship is heading directly toward Earth at a velocity of 0.800c. The... Problem 36P: Describe the following physical occurrences as events, that is, in the form (x, y, z, t): (a) A... Problem 37P: Describe what happens to the angle and therefore to the transformed axes in Figure 5.17, as the... Problem 38P: Describe the shape of the world line on a space-time diagram of (a) an object that remains at rest... Problem 39P: A man standing still at a train station watches two boys throwing a baseball in a moving train.... Problem 40P: When observed from the sun at a particular instant, Earth and Mars appear to move in opposite... Problem 41P: A man is running on a straight road perpendicular to a train track and away from the track at a... Problem 42P: A man is running on a straight road that makes with the train track. The man is running in the... Problem 43P: In a frame at rest with respect to the billiard table, a billiard ball of mass m moving with speed v... Problem 44P: In a frame at rest with respect to the billiard table, two billiard balls of same mass m are moving... Problem 45P: In a frame S, two events are observed: event 1: a pion is created at rest at the origin and event 2:... Problem 46P: If two spaceships are heading directly toward each other at 0.800c, at what speed must a canister be... Problem 47P: Two planets are on a collision course, heading directly toward each other at 0.250c. A spaceship... Problem 48P: When a missile is shot from one spaceship toward another, it leaves the first at 0.950c and... Problem 49P: What is the relative velocity of two spaceships if one fires a missile at the other at 0.750c and... Problem 50P: Prove that for any relative velocity v between two observers, a beam of light sent from one to the... Problem 51P: Show that for any relative velocity v between two observers, a beam of light projected by one... Problem 52P: A highway patrol officer uses a device that measures the speed of vehicles by bouncing radar off... Problem 53P: Find the momentum of a helium nucleus having a mass of that is moving at 0.200c. Problem 54P: What is the momentum of an electron travelling at 0.98c? Problem 55P: (a) Find the momentum of a asteroid heading towards Earth at 30.0 km/s. (b) Find the ratio of this... Problem 56P: (a) What is the momentum of a 2000-kg satellite orbiting at 4.00 km/s? (b) Find the ratio of this... Problem 57P: What is the velocity of an electron that has a momentum of 3.04×10-21?kg·m/s? Note that you must... Problem 58P: Find the velocity of a proton that has a momentum of Problem 59P: What is the rest energy of an electron, given its mass is Give your answer in joules and MeV. Problem 60P: Find the rest energy in joules and MeV of a proton, given its mass Problem 61P: If the rest energies of a proton and a neutron (the two constituents of nuclei) are 938.3 and 939.6... Problem 62P: The Big Bang that began the universe is estimated to have released of energy. How many stars could... Problem 63P: A supernova explosion of a star produces of energy. (a) How many kilograms of mass are converted to... Problem 64P: (a) Using data from Potential Energy Of a System... Problem 65P: Using data from Potential Energy of a System... Problem 66P: There is approximately of energy available from fusion of hydrogen in the world's oceans. (a) If of... Problem 67P: A muon has a rest mass energy of 105.7 MeV, and it decays into an electron and a massless particle.... Problem 68P: A meson is a particle that decays into a muon and a massless particle. The meson has a rest mass... Problem 69P: (a) Calculate the relativistic kinetic energy of a 1000-kg car moving at 30.0 m/s if the speed of... Problem 70P: Alpha decay is nuclear decay in which a helium nucleus is emitted. If the helium nucleus has a mass... Problem 71P: (a) Beta decay is nuclear decay in which an electron is emitted. If the electron is given 0.750 MeV... Problem 72AP: (a) At what relative velocity is (b) At what relative velocity is Problem 73AP: (a) At what relative velocity is (b) At what relative velocity is Problem 74AP: Unreasonable Results (a) Find the value of required for the following situation. An earthbound... Problem 75AP: (a) How long does it take the astronaut in Example 5.5 to travel 4.30 ly at 0.99944c (as measured by... Problem 76AP: (a) How fast would an athlete need to be running for a race to look 100 yd long? (b) Is the answer... Problem 77AP: (a) Find the value of for the following situation. An astronaut measures the length of his spaceship... Problem 78AP: A clock in a spaceship tuns one-tenth the rate at which an identical clock on Earth runs. What is... Problem 79AP: An astronaut has a heartbeat rate of 66 beats per minute as measured during his physical exam on... Problem 80AP: A spaceship (A) is moving at speed c/2 with to another spaceship (B). Observers in A and B set their... Problem 81AP: Same two observers as in the preceding exercise, but now we look at two events occurring in... Problem 82AP: Same two observers as in the preceding exercises. A rod of length 1 m is laid out on the x-axis in... Problem 83AP: An observer at origin of inertial frame S sees a flashbulb go off at and at time At what time and... Problem 84AP: An observer sees two events 1.5108s apart at a separation of 800 m. How fast must a second observer... Problem 85AP: An observer standing by the railroad tracks sees two bolts of lightning strike the ends of a... Problem 86AP: Two astronomical events are observed from Earth to occur at a time of 1 s apart and a distance... Problem 87AP: Two astronomical events are observed to occur at a time of 0.30 s apart and a distance separation of... Problem 88AP: A spacecraft starts from being at rest at the origin and accelerates at a constant rate g, as seen... Problem 89AP: (a) All but the closest galaxies are receding from our own Milky Way Galaxy. If a galaxy 12.0x109ly... Problem 90AP: Suppose a spaceship heading straight toward the at 0.750c can shoot a canister at 0.500c relative to... Problem 91AP: Repeat the preceding problem with the ship heading directly away from the Earth. Problem 92AP: If a spaceship is approaching the Earth at 0.100c and a message capsule is sent toward it at 0.100c... Problem 93AP: (a) Suppose the speed of light were only 3000 m/s. A jet fighter moving toward a target on the... Problem 94AP: If a galaxy moving away from the Earth has a speed of 1000 km/s and emits 656 nm light... Problem 95AP: A space probe speeding towards the nearest star moves at 0.250c and sends radio information at a... Problem 96AP: Near the center of our galaxy, hydrogen gas is moving directly away from us in its orbit about a... Problem 97AP: (a) Calculate the speed of a particle of dust that has the same momentum as a proton moving at... Problem 98AP: (a) Calculate for a proton that has a momentum of (b) What is its speed? Such protons form a rare... Problem 99AP: Show that the relativistic form of Newton’s second law is (a) F=mdudt1( 1 u 2 / c 2 )3/2 (b) Find... Problem 100AP: A positron is an antimatter version of the electron, having exactly the same mass. When a positron... Problem 101AP: What is the kinetic energy in MeV of a meson that lives s as measured in the laboratory, and when at... Problem 102AP: Find the kinetic energy in MeV of a neutron with a measured life span of 2065 s, given its rest... Problem 103AP: (a) Show that that at large velocities This means that at large velocities(b) Is when as for the... Problem 104AP: One cosmic ray neuron has a velocity of 0.250c relative to the Earth. (a) What is the neutron's... Problem 105AP: What is for a proton having amass energy of 938.3 MeV accelerated through an effective potential of... Problem 106AP: (a) What is the effective accelerating potential for electrons at the Stanford Linear Accelerator,... Problem 107AP: (a) Using data from Potential Energy of a System... Problem 108AP: (a) Calculate the energy released by the destruction of 1.00 kg of mass. (b) How many kilograms... Problem 109AP: A Van de Graaff accelerator utilizes a 50.0 MV potential difference to accelerate charged particles... Problem 110AP: Suppose you use an average of 500 k W·h of electric energy per month in your home. (a) How long... Problem 111AP: (a) A nuclear power plant converts energy from nuclear fission into electricity with an efficiency... Problem 112AP: Nuclear-powered rockets were researched for some years before safety concerns paramount. (a) What... Problem 113AP: The sun energy at a rate of 3.85×10 26 W by the fusion of hydrogen. About 0.7% of each kilogram of... Problem 114AP: Show that for a particle is invariant under Lorentz transformations. Problem 77AP: (a) Find the value of for the following situation. An astronaut measures the length of his spaceship...
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You are an engineer assigned to build a spaceship. The length and diameter of your spaceship as measured by an astronaut on board are 80.0 m and 25.0 m, respectively. The spaceship moves at 70% the speed of light relative to you on Earth in a direction parallel to its length. What are its dimensions as measured by you on Earth?
Definition Definition Rate at which light travels, measured in a vacuum. The speed of light is a universal physical constant used in many areas of physics, most commonly denoted by the letter c . The value of the speed of light c = 299,792,458 m/s, but for most of the calculations, the value of the speed of light is approximated as c = 3 x 10 8 m/s.
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