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Understanding Special Relativity: Events, Time Dilation, and Momentum

This chapter delves into the principles of special relativity, focusing on the concepts of reference frames, time dilation, and relativistic momentum. We explore how the laws of physics remain consistent across inertial frames and the speed of light as an invariant. The journey includes calculations of time experienced by observers in motion, length contraction of moving objects, and the relationship between energy and mass as described by Einstein's equation E=mc². Real-world examples, such as space travel to Mars, illustrate these principles in action.

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Understanding Special Relativity: Events, Time Dilation, and Momentum

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Presentation Transcript

  1. AP Physics Chp 28

  2. Event – physical occurance • Reference Frame – x,y,z axes and time • Inertial reference frame a=0 and Fnet =0

  3. Postulates of Special Relativity • 1) Laws of Physics are constant in every inertial reference frame • 2) Speed of light in a vacuum is c regardless of how fast the source and/or observer are moving relative to each other

  4. Absolute velocity? • Luminiferous Ether

  5. Time Dilation • ∆to is the observers time that is at “rest” • ∆t is the time for observers that are in motion compared to the “event” • v is the relative velocity between the two observers • c is 3.00 x 108 m/s

  6. Length contraction • Lo is the proper length – distance at rest with object • Only in direction of motion • Proper doesn’t mean “correct” or “absolute”

  7. If you fly to Mars at 0.8 c and it takes 182 seconds to get there for those on the spaceship, how long does it seem for us left on earth? And if the ship is 1500 m long what length would it appear while moving?

  8. Relativistic Momentum • p= mv for low velocity situations

  9. Energy • Eo=mc2 this is the rest energy

  10. E = KE + Eo • KE = E - Eo

  11. A change in energy causes a change in mass. • Often it is too small to notice.

  12. Total Energy and Momentum • E2 = p2c2 + m2c4 • Why is c the maximum? KE vs work

  13. Relative and Relativistic Velocities • Tossing a ball from a moving vehicle • Vab = Vac + Vbc Ex. 22 m/s + 5 m/s = 27m/s

  14. Velocity addition formula

  15. If the large haldron collider can get a proton up to 0.9999c what is the classical momentum and what is the relativistic momentum for the proton? • Classical • p = mv = 1.67x10-27Kg (0.9999) 3x108m/s • p = 5.01 x 10-19 Kgm/s

  16. Relativistic • p= 3.5x10-17 Kgm/s so momentum is greater

  17. What are the rest energy, total energy, and kinetic energy for the accelerated proton? • E0 = mc2 = (1.67x10-27Kg)(3x108m/s)2 • E0 = 1.44x10-10 J

  18. KE = E-E • KE = 1.06x10-8 J - 1.44x10-10 J = 1.05 x 10-8 J

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