At relativistic speeds near that of light, the half-life of an unstable particle moving at high speed is longer than when it is at rest. an object is longer when moving than when it is stationary. light emitted by a moving source moves at the same speed with the same frequency. lengths and times only appear different, they are really just the same. effects precede causes in some inertial frames.
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- An object moves by an observer at 0.400 c. The total energy of the object will be what factor times that of the rest energy?Electromagnetic radiation from a star is observed with an earth-based telescope. The star is moving away from the earth with a speed of 0.580c. If the radiation has a frequency of 8.64 x 1014 Hz in the rest frame of the star, what is the frequency measured by an observer on earth?A particle detector can be used to measure the speed of an unstable particle if the lifetime is known. Particle 'X' has mean lifetime 7 in its rest frame. Suppose 'X' particles are created in an experiment inside the detector by a nuclear reaction. If the 'X' particles leave tracks with mean length L before they decay into other particles, what is the mean speed of the 'X' particles? Express the answer in terms of the speed of light. T = 282.0 ps; L= 10.5 cm;
- If a m = 81.1 kg person were traveling at v = 0.980c, where c is the speed of light, what would be the ratio of the person's relativistic kinetic energy to the person's classical kinetic energy? kinetic energy ratio: What is the ratio of the person's relativistic momentum to the person's classical momentum? momentum ratio:An Other Frame moves with a speed of 0.80 relative to the Home Frame. An object at rest in the Other Frame has a length of 30 ns as measured in the Home Frame. What is the object's length in the Other Frame?When one compares the relativistic kinetic energy to the classically calculated kinetic energy for a moving object, at which of the speeds listed below does the classical calculation give a greater value than the relativistic calculation? 0.2 c 0.707 c 0.5 c None of the values provided will give such a result.
- 1. Consider inertial reference frame S to be the lab frame. A proton is moving in the positive x (+x) direction at a kinetic energy of 1250 MeV, as measured in frame S. Inertial reference frame S' moves at a speed of 0.55c in the positive-x (+x) direction relative to frame S. a) Find the speed of the proton in terms of the speed of light, c, as measured in frame S. b) Find the magnitude and direction of the speed of the proton as measured in frame S'.To understand length contraction and time dilation. An inertial frame of reference is one in which Newton's laws hold. Any frame of reference that moves at a constant speed relative to an inertial frame of reference is also an inertial frame. The proper length l0 of an object is defined to be the length of the object as measured in the object's rest frame. If the length of the object is measured in any other inertial frame, moving with speed u relative to the object's rest frame (in a direction parallel to l0), the resulting length lll is given by the length contraction equation l= l0 *sqrt(1-u^2/ c^2) where c is the speed of light. Similarly, if two events occur at the same spatial point in a particular reference frame, and an observer at rest in this frame measures the time interval between these two events, the time interval so measured is defined to be the proper time Δt0. When the time interval is measured in any other inertial frame, again moving with speed uuu relative to the…An interstellar space probe is launched from Earth. After a brief period of acceleration, it moves with a constant velocity, 74.0% of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 19.4 years as measured in a rest frame. Note that radio waves travel at the speed of light and fill the space between the probe and Earth at the time the battery fails. (a) How long do the batteries on the space probe last as measured by mission control on Earth? (Ignore the delay between the time the battery fails and the time mission control stops receiving the signal.) yr (b) How far is the probe from Earth when its batteries fail as measured by mission control? (Ignore the delay between the time the battery fails and the time mission control stops receiving the signal.) ly (c) How far is the probe from Earth as measured by its built-in trip odometer when its batteries fail? ly (d) For what total time…
- A particle with mass m has speed 0.555c relative to inertial frame S. The particle collides with an identical particle at rest relative to frame S. Relative to S and in terms of c, what is the speed of a frame S' in which the total momentum of these particles is zero? This frame is called the center of momentum frame. Number 0.278 Units m/s 'СJohn, in his spaceship, observes as Sally, in her spaceship, passes him at a speed of v=0.8c. John who was born and raised on his spaceship, is 20 years old. According to Sally, how old is he? How many birthday parties should he have had and how many presents should Sally have sent him?1. You are an observer in a 100-m long spacecraft traveling from the earth to the moon at 0.8c. (a)What is the proper length of the spacecraft? (b) For a proper time interval of 1 sec., the relativistic time interval for the spacecraft measured from the earth reference frame would be: (c)Time dilation does not apply to all time-dependent physical and biological processes. T/F? (c) What is the relativistic length, DL measured from the reference frame of earth? (d) An APOLLO crew left a flat mirror reflector on the surface of the moon (for all you deniers out there, in the 50th anniversary year of APOLLO 11!). If the average surface-to-surface distance from the earth to the moon is 3.83 x 10^8 m, then how long does it take moonlight to reach earth?