Unit 5 - Physics 225 Relativity and Math Applications...

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Physics 225 Relativity and Math Applications Spring 2010 Unit 5 E = mc 2 N.C.R. Makins University of Illinois at Urbana-Champaign © 2010
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Physics 225 5.2 5.2
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Physics 225 5.3 5.3 Unit 5: E = mc 2 Relativistic kinematics and dynamics We have learned a great deal about relativity: how space and time transform between frames of different relative speed, and how this leads to the strange phenomena of time dilation and length contraction. All of this came from Einstein’s postulate that all observers see light traveling at the same speed c , no matter what the observer’s motion is relative to the light source. But we have yet to encounter Einstein’s most famous equation: E = mc 2 In fact, this is probably the most famous equation in all of physics. It involves energy, and indeed, it’s time to turn our attention from space and time to the dynamical concepts of energy and momentum . As we will discover, we have to make some changes to Newtonian mechanics. What are the basic principles of Newtonian mechanics? Let’s remind ourselves: Newton’s First Law : the law of inertia A particle will remain at rest or continue at a constant velocity unless acted upon by an external unbalanced force. This tendency of an object to remain as it is (constant velocity) is known as inertia , and the law of inertia actually traces back to Galileo. This law can be more precisely stated as follows: it is possible to select a set of reference frames , called inertial frames , observed from which a particle moves without any change in velocity if no net force acts on it. An inertial frame is literally “one in which Newton’s first law holds”, and as we know, inertial frames are related to each other by constant relative speed. The second fundamental pillar of mechanics is Newton’s Second Law Observed from an inertial reference frame, the net force on a particle is proportional to the time rate of change of its linear momentum: ! F = d ! p dt where ! p = m ! v These relations allow us to get quantitative and calculate an object’s equation of motion. We will take a historical perspective today, discovering relativistic mechanics along with Einstein. There will be some changes … but realize that what Einstein was trying to do was to preserve the fundamental principles of Newtonian mechanics in the face of Maxwell’s theory of electromagnetism and its description of light .
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Physics 225 5.4 5.4 Exercise 5.1: Something’s wrong For a first glimpse of how mechanics has to be modified when light or speeds close to c are involved, let’s have a look at an actual experiment. This particular experiment was run in 1962 and filmed to make a documentary called The Ultimate Speed . The goal of the experiment was to use a linear accelerator (“linac” for short) to accelerate electrons to the highest possible speeds. As this is not Physics 212: Electromagnetism, we will skip the details of how the linac worked. All you need to know is that each time the experimental was run, the linac delivered a
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Unit 5 - Physics 225 Relativity and Math Applications...

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