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Physics 228 Spring 2008
Relativistic time dilation and length contraction (Ch. 37)
Due at 11:59pm on Monday, March 3, 2008
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Postulates of Special Relativity
Learning Goal:
To understand the postulates of special relativity and their relationship to Galilean relativity.
Einstein's theory of special relativity is based on two postulates:
1.
The principle of relativity: The laws of physics are the same in any inertial coordinate system.
For
example, by watching the action of the balls on a pool table that is on a ship, you cannot tell whether the ship
is at the dock or moving through the water at a constant speed. (You can think of an inertial coordinate system
as a nonaccelerating coordinate system. There are actually other subtle conditions, but for now they are not of
concern.)
2.
The speed of light in vacuum is constant.
This says that observers in any inertial coordinate system will
measure the same value for the speed of light, independent of the origin of that light.
The simplicity of these assumptions belies their brilliancethey directly contradict our intuitive ideas of relativity, yet
by accepting them we can easily build a theory of relative motion that is in accord with all observation.
We now discuss these ideas more fully, showing where they depart from the previously held ideas about relativity.
Part A
Consider a pool game being played on a pool table on the deck of an aircraft carrier near the bow (front). Assume
that the carrier is moving north at 25.0
. As a result of the initial break, a ball flies over the edge of the table
and over the edge of the deck with a horizontal component of velocity directed toward the bow of the ship of 5.00
. What is
, the horizontal component of the speed with which this ball strikes the water in front of the ship
(i.e., what is the speed of the ball relative to the water)?
Express your answer numerically in meters per second. Use ordinary (Galilean) physics.
Hint A.1
Galilean relativity for velocity addition
Hint not displayed
ANSWER:
=
30
Part B
You have used the ideas of Galilean relativitythat time and distance are absolute and independent quantities and
that velocities therefore add. In particular, the formula for relative velocity addition is
, where
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View Full Documentis the velocity of the ball relative to the water,
is the velocity of the ball relative to the carrier, and
is the
velocity of the carrier relative to the water. These ideas are embodied in Isaac Newton's
Principia
.
Newton started this seminal work by stating which of the following?
ANSWER:
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 Spring '08
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 Special Relativity, Frame, Assignment Print View, Albert

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