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164. Problem 21.1 (RHK) Quite apart from effects due to the Earth’s rotational and orbital motions, a laboratory frame is not strictly an inertial frame because a particle placed at rest there will not, in general remain at rest; it will fall under gravity. Often, however, events happen so quickly that we can ignore free fall and treat the frame as inertial. Consider, for example, a 1.0-MeV electron (for which v = 0.941 c) projected horizontally into a laboratory test chamber and moving through a distance of 20 cm. We have to find (a) the time it would take to travel 20 cm and (b) the distance the electron would fall during this interval. We have to comment on the suitability of the laboratory as an inertial frame in this case. |
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Solution: Click For PDF Version (a) The speed of 1.0-MeV electron is 0.941 c. The electron has been projected horizontally into a laboratory test chamber and it moves through a distance of 20 cm Time taken by the electron to travel 20 cm will be
(b) In this time the electron would have dropped vertically because of the surface gravity of the Earth by distance
(c) We can therefore safely conclude that effects of the Earth’s gravity will be
insignificant and as time intervals involved in relativistic motion of
elementary particles are of the order of
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non-inertial
effects due to Earth’s rotational and orbital motions will also be negligible
and thus the laboratory can be treated as an inertial fralme.