One of my homework questions says 'An electron is to be accelerated from a velocity of 4.00×10^6m/s to a velocity of 9.00×10^6m/s . Through what potential difference must the electron pass to accomplish this?' I have no idea what to do with this. If I knew the mass of the electron, I'd set up conservation of energy, but even if I did, q*(v1-v2) terms would just cancel out since the charge isn't changing. I'm confused. Help please?

Question

One of my homework questions says 'An electron is to be accelerated from a velocity of 4.00×10^6m/s to a velocity of 9.00×10^6m/s . Through what potential difference must the electron pass to accomplish this?'  I have no idea what to do with this.  If I knew the mass of the electron, I'd set up conservation of energy, but even if I did, q*(v1-v2) terms would just cancel out since the charge isn't changing.  I'm confused.  Help please?

anonymous · Answer

Somebody was viewing this, but apparently college-level physics scared them off.  I pressed the show answer button on this question(online homework website) and apparently the answer was -185 volts.  I have NO idea where that came from.  Help?

anonymous · Answer

I don't see how the problem can be solved without knowing the mass of the electron, so I'm just going to look it up: m =  9.1094e-28 g.

So, dE = 1/2 m (vf^2 - vi^2) = e dV, where e = charge on the electron, solve for dV, I do indeed get 185. V.  Whether it's +185 V or -185 V just depends on how you measure it.

anonymous · Answer

A small wrinkle here is that the final velocity is 3% of the speed of light, which means the error in not using relativistic kinematics is probably larger than the precision of the data.  Are you supposed to know how to use the right relatavisitic formulae?

anonymous · Answer

No, I don't think so.  I've never even heard the word relatavistic mentioned in any of my physics classes thus far.

anonymous · Answer

I'm sure you've heard the word "relativity," as in Einstein's famous theory.  "Relatavistic" is just the adjectival form: things that come from the theory of relativity are called "relatavistic."

anonymous · Answer

And it's probably actually spelled "relativistic," oops.

anonymous · Answer

My physics classes thus far haven't really gone over relativity.  I'm totally dumb for not looking up the electron mass since it was written in kg right on my equation sheet(although rounded differently than you rounded it). If we'd ever used that mass constant in class, maybe I would have thought to use it for this problem.