# Relativity and Equivalence of Mass and Energy

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1. Mar 16, 2017

### Alena Selone

1. The problem statement, all variables and given/known data
An electron is accelerated to a speed that is 99 percent the speed of light, and is moving through a 2-km-long tunnel. The rest mass of the electron is 9.11*10^-31 kg. What is the mass of the electron at this speed?
c= speed of light
2. Relevant equations
t= (tsubscript(o))/ root(1-(v^2/c^2)
L= Lsubscript(o)* root(1-0)= Lsubscript(o)
p= (mv)/ root(1-0) = mv
KE= ((mc^2)/ root(1-(v^2/c^2))-mc^2
3. The attempt at a solution
I tried plugging the rest mass into the last equation on the top which gives me 9.11*10^-31/ root(1-((.99c)^2/c^2
which calculates out to
9.11*10^-31/ root(1-.9801)
9.11*10^-31/root(0.0199)
9.11*10^-31/0.14106736
=6.458*10^-30

I'm unsure if this is correct. It's listed as one of the answers but I don't know if I used the correct equation, so the fact that it's listed as an answer could be a trick. I also don't know how the 2km long tunnel plays into the equation. Please help!

2. Mar 16, 2017

### Staff: Mentor

Looks fine to me. The length of the tunnel is irrelevant. (Note that "relativistic mass" is a rather antiquated concept nowadays.)

3. Mar 16, 2017

### Alena Selone

So in a different equation using some of the same values, say,
An electron is accelerated to a speed that is 99 percent the speed of light, and is moving through a 2-km-long tunnel.
Could I calculate the length of the tunnel in the frame of reference of the electron or is that too irrelevant?

4. Mar 16, 2017

### Staff: Mentor

Sure you can. For that problem, the "rest" length of the tunnel is very relevant.

5. Mar 16, 2017

### Alena Selone

So how would I do that?

6. Mar 16, 2017

### Staff: Mentor

Look up the formula for "length contraction" (one of the key relativistic effects).