# Speed of electron accelerated by a potential difference

1. Sep 2, 2014

### Brianrofl

1. The problem statement, all variables and given/known data

The full problem can be seen here - however, I only need help with one part: http://puu.sh/biN9W/ee2a7bf393.png [Broken]

I'm not sure how to find the velocity of a particle when accelerated to the point that it exceeds or approaches the speed of light when the classical equations are used. I'd really appreciate if someone could help me with it.

2. Relevant equations

K = (γ-1)mc^2
P = γmv
Mass of electron: .511MeV/c^2 or 9.11*10^-31kg

3. The attempt at a solution

I've got 5+ pages of scratch work scribble but I've tried many things. I've tried just using classical equations, which nets a velocity greater than the speed of light, so that can't work. I've tried finding the value of gamma from K = (γ-1)mc^2 and using that value of γ to find a velocity, but that didn't give me the correct answer either.

An explanation or tips would really be appreciated. Also, another problem that I've been having a lot of trouble with can be seen here http://puu.sh/biNDy/4bdaa9d2b3.png [Broken]. This one really racks my brain. For this one, I've had two thoughts:

1. The velocity needed to travel the distance in a certain time
and
2. The velocity needed to dilate time to a specific number

and it's this that kills me. I feel like, as #1 changes, #2 also changes. I've tried making two equations - one setting v equal to the distance of the planet divided by time, and another one setting time equal to the time dilation equation (ΔT/sqrt(1-u^2/c^2))

Any tips for this one would also be appreciated!

Last edited by a moderator: May 6, 2017
2. Sep 2, 2014

### nrqed

For the first one, did you try simply setting the relativistic KE equal to Q times the difference of potential?

For the second, you have to pick a frame. For example, working in the frame of the spaceship, the time interval is 11 years and the distance travelled will be the round trip distance as measured on Earth divided by the gamma factor. You set that up and solve for the speed. (Edit: by that I mean: you set speed = distance / time, using the values in the astronaut`s frame)

Last edited by a moderator: May 6, 2017
3. Sep 2, 2014

### Brianrofl

Ok, I'll let you know how it goes.

Edit: as for the first idea, Q * V turns out to be equal to 48MeV

However, I found out something I was doing wrong with the equation. When I substituted e = .511MeV/c^2 into the mass m in (γ-1)mc^2, I didn't include the /c^2. This was making my gamma value ridiculously small.

After fixing that I got a gamma value of 28.397 (note: I'm doing a practice problem where V = 14MV), and then I used the equation

P = γmv where I put in (28.397)(.511MeV/c^2)(.9994c) and I get 14.50MeV/c - which is the right answer so looks like I've solved this one.

I'll try out the astronaut problem again in a few minutes.

Last edited: Sep 2, 2014