WS#4: Energy & General Relativity
True for False. If false, explain why.
1. The first postulate of the theory of special relativity is that the laws of nature are the same in all uniformly moving reference frames. TRUE
2. The second postulate of the theory of relativity is that the speed of light in empty space depends on the motion of the source or of the observer. FALSE. The speed of light is always a constant in a vacuum, no matter what.
3. Just as it is possible to travel in a spaceship and come back to earth at a time far in the future, it is also possible to travel in a spaceship and come back to earth at some time in the past. FALSE. It is never possible to travel to the past.
4. The sun’s mass is decreasing. TRUE (mass is turning into energy given off by the sun)
5. Mass and energy are equivalent. TRUE (E=MC2)
6. According to the general theory of relativity, it is possible to reverse time and grow younger when you are hear a black hole. FALSE. It is never possible to travel to the past.
7. How much energy is contained in a 0.004 kg penny?
E = mc2 = (0.004kg)*(3.0x108m/s)2 = 3.6x1014J
8. In a typical nuclear reactor, Uranium-236 decays into Krypton-92 and Barium-141. In this reaction about 0.1% of the original Uranium turns into energy.
- How much energy is produced when one mole of Uranium-236 decays? (the mass of one mole of Uranium-236 is 236 g or 0.236 kg)
E = mc2 = (0.236kg)*(3.0x108m/s)2 = 2.12x1016J
- If one person uses 1.8x107 J of energy in one day, how many people could this reaction support for one day?
2.12x1016J / 1.8x107J = 1.18x109people
Note: to be correct, only 0.1% of the Uranium turns into energy so instead of 0.236 kg turning into energy it should only be 0.000236 kg. If I were to rewrite the worksheet, I would give you just the mass turning into energy. So answers should really be 2.12x1013 J and only 1.18x106 people could be supported.
9. A fusion reaction occurs in the sun’s interior, the sun gives off energy by emitting electromagnetic radiation. Its total power output if 3.92x1026 W.
- How much mass is the sun loosing each second?
E = mc2 à 3.92x1026J/sec = m(3.0x108m/s)2 à m = 4.36x109kg / sec
- How much mass is the sun loosing each year?
(4.36x109kg / sec) * (3.15x107 sec/1 year) = 1.37x1017 kg/ year
The sun has a mass of 1.99x1030 kg. What ratio of the sun’s mass is turned into energy each year? (Mlost/Msun)
1.37x1017 / 1.99x1030 = 6.89x10-14
10. In a spaceship accelerating at g, far from earth gravity, you do your maximum number of push-ups. How does this number compare to the number you can normally do here on earth? It is exactly the same because gravity is the same as an accelerated field.
11. Exactly what is equivalent in the principle of equivalence?
A gravitational field and an accelerated field are the same.
12. An astronaut awakes in her closed capsule, which actually sits on the moon. Can she tell whether her weight is the result of gravitation or of accelerated motion? Explain.
There is nothing she can do to determine if she is in an accelerated field or a gravitation field. That is the equivalence principle.
13. Should a person who is worried about growing old live at the top or the bottom of a tall apartment building?
The bottom of a building is in a slightly stronger gravitational field, so time is slower for people at the bottom.
14. What is the difference between special relativity and general relativity? Special relativity deals with inertial reference frames (ones moving in a straight line and at a constant velocity or not moving at all) while general relativity deals with gravitational fields and accelerating reference frames (non inertial frames)
15. What happens to light as it approaches a strong gravitational field? Light bends (gravitational lensing)