einsteins special relativity questions

[wilfred]

hey exams are getting so close and we have still not finished relativity
so got a couple of questions i have no idea on hope someone can help

1.An electron receives .80 MeV of energy in a linear accelerator
a) what is the relativistic mass of the electron?
b) what is its velocity
c) what would be the velocity according to newton's equation

2. When an electron and a positron collide the produce energy. According to einstien how much energy is released by the collision? (rest mass of electrons and positrons is 9.1 x 10^-31)


any help would be awesome

[kamil9876]

Not sure if you guys use this in year12, but:



I will call m the rest mass and the relativity mass. You should be familiar with:



Now the electron initially has rest mass mc^2. but it is given an extra 0.8MeV and so the total energy is:



and so:



and this can be transposed to:



interestingly the expression is famously known as the particles "Relativistic Kinetic Energy" and so it makes sense that the 0.8MeV go into the kinetic energy if we assume the electron is initially at rest.

Anyway, using the equation we can easily work out (m is rest mass of electron) and then use the equation to find the relativistic mass.

b.) the velocity can be easily worked out now that we know the gamma factor.

c.) Newton would say that the 0.8MeV was invested into kinetic energy(We agreed on this) hwoever the kinetic energy had the formula:

Knowing the mass of an electron you can work out v.

[wilfred]

this all looks good but i think im still missing something big do you recon for the first one at least you could just do step by step because i get the right answer. like in the first one how can we times the lorenz factor by m if we dont know the velocity?
sorry to be a pain

[kamil9876]

ok well these are the actual steps for part a (In the first post I presented this with a bit of explanation as to why so i guess you may have been confused between steps and explanation):

Once you get the equation:




You sub in m=mass of electron(at rest). And then transpose to find . Notice that we don't actually need to know what the velocity is at this point as the equation is enough to find .

Now that you know you sub it into:



where m=mass of electron at rest.

b.)
Sub in and you have an equation with only v as the unknown, which is what you want to find.

[dcc]

But does the car fit in the garage, or not? (And more importantly, does it get wet?)

[kamil9876]

It fits in the garage if the proper length of the car divided by the gamma factor is less than the garage length(and that the width and height of the car is less than those of the garage). Of course one could argue that from the car's perspective the garage is shorter than the car  But hopefully relativity of simultanaeity will fix that paradox like always. (also one wouldn't want a moving car in a garage, but hey, let's make this question fun)

Now as for the more important part, I wouldn't know as we havn't covered Meteorology yet :/

[dcc]

But does the car get wet?

(Go anyone doing advanced physics at UoM!)

[kamil9876]

check out relativity challenge thread on teh physics board, is the question any similair to boulder falling?