Environmental Engineering Reference
In-Depth Information
6.5 How long is a 1m rod according to an observer moving at speed 0.95 c in a
direction parallel to the rod?
6.6 What is the distance to the surface of the Earth as determined in the rest
frame of a cosmic ray proton which is at an altitude of 12 km and which is
travelling directly towards the Earth's surface at a speed of 0.97c?
6.7 The distance to the farthest star in our galaxy is of the order of 10 5 light
years. Explain why it is possible, in principle, for a human being to travel to
this star within the course of a lifetime and estimate the required velocity.
6.8 As measured by an observer on Earth, a spacecraft runway has a length of
3.60 km.
(a) What is the length of the runway as measured by the pilot of a spacecraft
flying directly over the runway at a speed 4 . 00
10 7
ms 1
×
relative to the
Earth?
(b) An observer on Earth measures the time interval from when the spacecraft
is directly over one end of the runway until it is directly over the other
end. What result does she get?
(c) According to the pilot of the spacecraft, how long does the spacecraft
take to travel the length of the runway?
6.9 A pole 10 m long lies on the ground next to a barn 8 m long. An athlete picks
up the pole, carries it far away, and then runs with it toward the barn at speed
0 . 8 c . The athlete's friend remains at rest, standing by the open door of the
barn.
(a) How long does the friend measure the pole to be as it approaches the
barn?
(b) Immediately after the pole is entirely inside the barn, the friend shuts the
barn door. How long after the door is shut does it take for the front of
the pole to strike the back end of the barn, as measured by the friend?
(c) In the reference frame of the athlete what is the length of the pole and
the barn?
(d) How do you reconcile the closing of the barn door with the experience
of the athlete?
6.10 Sodium light of wavelength 589 nm is emitted by a source that is moving
toward the Earth with speed v . The wavelength measured by an observer on
Earth is 550 nm. Find v/c .
6.11 In a frame S , event B occurs 1.3 µ s after event A. Also in S the events are
separated by a distance of 1.5 km along the x -axis, i.e. x B
1500 m.
At what fraction of the speed of light must an observer be moving along the
x -axis in order to conclude that the two events occur at the same time?
6.12 Two events occur at the same place in a certain inertial frame and are separated
by a time interval of 4 s. What is the spatial separation between these two
events in an inertial frame in which the events are separated by a time interval
of 5 s?
6.13 Two events occur at the same time in inertial frame S and are separated by a
distance of 1 km along the x -axis. What is the time difference between these
x A =
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