Relativistic Mass and Energy

1. Relativistic Mass and Energy Physics 12

2. Jokes of the day:

3. Clip of a day: • http://www.youtube.com/watch?v=lR4tJr7sMPM&list=PLDA75FE6344666889

4. Universal Speed Limit • When considering gamma, we know that we must be dealing with real numbers so the value under the root must be positive • Therefore speed (v) cannot be greater than or equal to the speed of light (c) or the denominator becomes imaginary or zero • This speed limit only applies to objects with mass (therefore the massless photon can travel at the speed of light)

5. Cerenkov’s Glow • While it is impossible for anything to travel faster than light in a vacuum, it is possible for an object to travel faster than light in a medium • This is what leads to Cerenkov’s Radiation which is seen in the cooling pools of a nuclear power plant • The particles in the water are travelling faster than the speed of light in the water and the glow is thus produced

6. Mass and Energy • While the gamma term leads to the mathematical understanding that the speed of light is the limit for massive objects, it does not explain why! • The reason is found in Newton’s Second Law and Einstein’s Special Theory of Relativity • Einstein found that in addition to time dilation and length contraction, mass is also affected by relativistic effects

7. Relativistic Mass • As a result, the mass increases as an object’s speed increases • m= relativistic mass • m0 = rest mass

8. Example:

9. Try it : • Page 825 • 2, 3,4 • Page 830 • 7-9

10. As an object approaches the speed of light, more energy must be added for each change in speed Since we know that this energy must go somewhere, Einstein introduced the following equation: This means that mass and energy are the same thing and can be used interchangeably! Where is the Energy?

11. Relativistic and Classical Kinetic Energy • We know that at relativistic speeds, kinetic energy is equal to: • Ek = mc2 – m0c2 • But at classical speeds, kinetic energy is equal to: • Ek = ½mv2 • Let’s prove this does not violate Einstein’s first postulate!

12. Relativistic and Classical Kinetic Energy • This means that both the classical equation we have been using and Einstein’s relativistic equation give the same results at classical speeds • Therefore, Einstein’s first postulate is upheld

13. Total Energy: • The total energy (relativistic mass times the square of the speed of light) of an object is the sum of the rest energy (rest mass times the square of the speed of light) and its kinetic energy.

14. Example: b)

15. The other one: General Relativity • In the Special Theory of Relativity, only non-accelerated (inertial) frames of references can be treated • In the General Theory of Relativity, acceleration is allowed which allows it to be applied to non-inertial frames of reference

16. Spacetime • General relativity often describes spacetime as a flexible sheet • If the sheet has no masses placed on it, it would be a plane • However, when masses are placed on the surfact, spacetime is warped which changes the behaviour of objects travelling in spacetime

17. One of the effects of the warping of spacetime is that light will be bent by gravity Classically this does not make sense as light is massless and should not be affected by gravity Light in Spacetime

18. Due to general relativity, the effect of gravitational lensing can be explained If light from a star travels close to another star, it will be bent due to the curvature of spacetime and appear in the “wrong” part of the sky Gravitational Lensing

19. Clip: SpaceTIme • http://www.youtube.com/watch?v=Cyuc-ncs11k

20. Try it : • Page 833 • 10, 11, 13-16