Phy107Spr06Lect19

# Phy107Spr06Lect19 - Exam Mass-energy equivalence T h is re...

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1 Phy107 Lecture 19 1 Hour Exam 2 : Wednesday, March 8 • In-class, covering waves, electromagnetism, and relativity • Twenty multiple-choice questions • Will cover: March Chap 6-7,9-12 Griffith Chap 12,15,16 All lecture material • You should bring – 1 page notes, written double sided – #2 Pencil and a Calculator – Review Monday March 6 – Review questions online under “Review Quizzes” link Exam Phy107 Lecture 19 2 Mass-energy equivalence • This results in Einstein’s famous relation • This says that the total energy of a particle is related to its mass. • Even when the particle is not moving it has energy. • We could also say that mass is another form of energy – Just as we talk of chemical energy, gravitational energy, etc, we can talk of mass energy E = " m o c 2 , or E = mc 2 Phy107 Lecture 19 3 Example • In a frame where the particle is at rest, its total energy is E = m o c 2 • Just as we can convert electrical energy to mechanical energy, it is possible to tap mass energy • A 1 kg mass has (1kg)(3x10 8 m/s) 2 =9x10 16 J of energy – We could power 30 million 100 W light bulbs for one year! (~30 million sec in 1 yr) Phy107 Lecture 19 4 Nuclear Power • Doesn’t convert whole protons or neutrons to energy • Extracts some of the binding energy of the nucleus 90 Rb and 143 Cs + 3n have less rest mass than 235 U +1n: E = mc 2 Phy107 Lecture 19 5 Energy and momentum • Relativistic energy is • Since γ depends on velocity, the energy is measured to be different by different observers • Momentum also different for different observers Can think of these as analogous to space and time, which individually are measured to be different by different observers • But there is something that is the same for all observers: • Compare this to our space-time invariant E = m o c 2 E 2 " c 2 p 2 = m o c 2 ( ) 2 = Square of rest energy x 2 " c 2 t 2 Phy107 Lecture 19 6 A relativistic perspective • The concepts of space, time, momentum, energy that were useful to us at low speeds for Newtonian dynamics are a little confusing near light speed • Relativity needs new conceptual quantities, such as space-time and energy-momentum • Trying to make sense of relativity using space and time separately leads to effects such as time dilation and length contraction • In the mathematical treatment of relativity, space-time and energy-momentum objects are always considered together

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2 Phy107 Lecture 19 7 General Relativity and Gravity • Special Relativity deals with inertial reference frames , frames moving with a constant relative velocity. • It has some rather unusual predictions
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Phy107Spr06Lect19 - Exam Mass-energy equivalence T h is re...

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