Question

A) 1 Formulate two postulates of the Einstein’s special theory of relativity.

2 According to the special theory of relativity, if you are in a train that moves at nearly the speed of light what would you see if you look into a mirror? Explain your answer.

b 1 What is the rest energy of a 130 g apple?

The rest energy, E₀ =

2 The Sun loses about 4 million tonnes of mass each second due to nuclear fusion. How much energy per second (power) does it generate? 1 tonn = 1000 kg.

The Sun's power, P =

A spacecraft is observed to be 50 meters long when at rest on Earth. It passes you and appears to be 10 meters long. With what velocity does the spacecraft travel? First find the gamma factor.

The gamma factor, γ =

The speed of the spacecraft, v =

Answer 1

A. The first postulate of special relativity is the idea that the laws of physics are the same and can be stated in their simplest form in all inertial frames of reference.
The second postulate of special relativity is the idea that the speed of light c is a constant, independent of the relative motion of the source.

2. This is precisely the sort of thought experiment Albert Einstein started out with. It turns out that yes, you will be able to see your image in the mirror when you move close to the speed of light.
You will also not notice anything strange about that image, or anything strange about things that are moving with you in your local reference frame.

This might seem strange in the sense that the rays of light will appear to take a much longer time to reach the mirror, and a much shorter time to be reflected back to the moving observer, when looking at
that observer and his mirror from an inertial reference frame "at rest". This "strangeness" is easily resolved though, if you give up the idea that time is some sort of omnipresent thing which both observers
always agree on. This, as special relativity has shown (and general relativity elaborated on), is simply not true for the universe we live in; if you start moving, we will start disagreeing on how time works
(but still both be correct).

b. Eo = mc^2
m = 130 g
Eo = 0.13*3*3*10^16 = 1.17*10^16 J
  
2. m = 4*10^6 tonnes = 4*10^6 *10^3 kg
Eo = mc^2 = 4*10^9*(3*10^8)^2 = 36*10^25 J
Power = 36*10^25 W

lo = 50 m
l = 10 m
then
l/lo = 1/gamma
gamma = lo/l = 5

and
gamma = 1/sqrt(1 - v^2/c^2)
v = 0.97979c = 2.939387*10^8 m/s