a) Two particles have energies E1 and E2, and momenta p1 and p2. Write down an expression for the invariant mass of this two-particle system. Leave your answer in terms of E1 and E2, and p1 and p2.
b) A typical photon (γ) in the Cosmic Microwave Background (CMB) has an energy of kBTCMB, where...
Ah, I think I got it. We can use reverse Lorentz transsform
$$ t = \gamma (t' + \frac {vx'} {c^2}) $$
where the prime is the Earth so t' = 0 and x' = 2.9*10^12
Two spaceships are heading towards each other on a collision course. The following facts are all as measured by an observer on Earth: spaceship 1 has speed 0.74c, spaceship 2 has speed 0.62c, spaceship 1 is 60 m in length. Event 1 is a measurement of the position of spaceship 1 and Event 2 is a...
I did that, except that I used
$$ E_{\mu} = \gamma m_{\mu} c^2 $$for the energy of the muon.
With the way you mentioned, I was getting 3 unknowns (the moment of the photon and the muon and the gamma/speed of the muon).
Getting stuck at this:
$$ E_{\mu} = m_{\pi} - \gamma m_{\mu} v_{\mu} $$
But...
I think I figured it out. I was doing in the rest frame and the exercise asked in the frame of the original pion.
I still got the answers in the opposite sequence they asked... I first c) then b).
This is rest of the same exercise.
b) Determine the energy (in MeV) of the µ+ as determined in the rest frame of the original π+. You should assume that the µ+ has a mass of 106 MeV/c2 , the π+ has a mass of 140 MeV/c2 and the νµ has zero mass.
c) What is the speed of the µ+ as determined in...
Yes, I used this trick (you mentioned it before on another thread).
I am just annoyed I keep getting the exact same result.
$$ v \gamma \tau = d $$
then
$$ v \gamma = \frac d \tau $$
square both sides
$$ \frac {v^2} {1-v^2} = \frac {d^2} {\tau^2} $$And so on to give me v = 0.993c
I...
Can you explain a little more? This should be really simple as far as I can see and I can't spot my mistake.
From what I can see I am using the same equations...
$$ d = vT, T = \gamma \tau $$
therefore
$$ d = v \gamma \tau $$