1. Relativistic Mass and Energy
Physics 12

2. Jokes of the day:

3. Clip of a day:

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
The blue glow is from high speed electrons (beta particles)

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 :
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10. Where is the Energy?
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!

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. Light in Spacetime
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

18. Gravitational Lensing
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

19. Clip: SpaceTIme

20. Try it :
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