Special Relativity homework problems

[Gogsey]

Hi,

These are not homework problem, but problems from my textbook. I am studying for a final exam in 2nd year Modern Physics that is on Monday and need some help with question. This set will be about special and genreal relativity, and I'll post another on quantum physics.

1). How fast must a plane 50m long travel to be found by observers on the ground to be 0.10nm shorter than 50 m?

2).At eraths location, the intensityof sunlight is 1.5kW/m^2. If no energy escaped earth, by how much would Earth's mass increase in 1 day?

3). Radiant energy fromthe sun, approximately 150000000000m away, arrives at Earth with an intensity of 1.5kW/m^2. At what rate is mass beig converted on the sun to produce this radiant energy?

4). A spring has a force constant of 18N/m. If it is compressed 50cm from its equilibrium lenght, how much mass has it gained?

5). A famous experiment detected 527 muons per hour the top om Mt. Washington, New Hamptshire, eleavation 1910m. At sea levelthe same equipment detected 395 muons per hour. A discriminator selected for muons whose speed was between 0.995c and 0.0054c. Given that the mean lifetime of a muon in it res frame is 2.2 microseconds and that muons decay with the regular fotrula, prove this results are sensible.

6). A 10kg object is moving to the right at 0.6c. It explodes into 2 peices , one of mas m1 moving to the left at 0.6c and one of mass m2, moving to the right at 0.8c.
a). Find the masses of m1 and m2
b). Find the change in kinetic energy in this explosion.

7). The boron-14 nucleus (mass: 14.02266u) "beta decays" spontaneously becoming an electron(mass: 0.00055u) and a carbon-14 nucleus(mass: 13.99995u). What will be the speeds and kinetic energies of the carbon-14 nuclleus and the electron? A neutrino is also produced but in this case, its energy and momentum is negligible. Also, because te carbon_14 nucleus is is much more massive then the electron, it recoils "slowely" ( gamma =1).

8). According to an observer at the Earths eqautor, by how much would his clock and one on a satellitein geosynchronous orbit differ in one day?

Thank you

 

[malawi_glenn]

Attempt to solution MUST be provodided. Read AND follow forum rules!

 

[Gogsey]

Ok,

1). I know you use the binomial expansion, or taylors expansion, but after this I'm not sure how to solve for velocity. I thought about equating the series with gamma.

2). and 3). I don't really knowhoe to calculate gain or loss in mass. So I'm not sure where to start.

4). I used the 0.5kx^2 formual to get the potential of the spring, again not sure how to claculate gain in mass. Only thing I could think of is to set potentil energy to kinetic energy, solve foe v and then calculate gamma and then multiply by the rest mass to gentthe new mass. Thing is the kinetic energy is dependent on velocity, and the oblect is stationary.

5). I tried to claculate the time in the moving frame using time dilation, after calculating gamma, then using the formula for muons, trouble is I don't know what No is. The only thing is possibly for the one at sea level No could be the ones that survived to the 1910m elevation. But then what is NO for the upper elevation?

6) and 7) I tried conservation of energy, but with no luck. I know that mass is lost, but I don'y know how to do this.

8). I have no idea. The question doesn't give you much, except the time ellaped.

 

[malawi_glenn]

1) why don't use lorentz transformation and length contraction formula?

2) What is relationship between mass and energy?

3) same as 2

4) same as 3

5) you can chose No as whatever you want, the exponentail law does not depend on it, you just want the life time.

6) why don't you show what you did so someone might help you and said what you did wrong?

7) same as 6

8) Why? the tangential velocity is proportional to radius.. give it a try.

 

[Gogsey]

1). I'll try that thanks, its just the length different is so small.

2), 3), and 4), E = gamma mc^2( for total energy that is).

5). Does it sound correct what I'm doing otherwise?

8). Ok, but what the radius. Is it just the radius of the earth? Do yu mean mvr is equal to something? What?

 

[malawi_glenn]

2,3,4) And if the Earth absorbs photons, you have E = mc^2, einsteins famous formula. try it.

5) don't know, didn't read so much.
use N = No*Exp(-t/lifetime)

8) use the fact that fixed points on a spinning, solid, circle has same period and angular frequency. Just say R > R_earth.