# Relativistic kinetic energy versus classic kinetic energy [closed]

I have a homework problem where I am getting the wrong answer and I just want advice on the route I took.

So I am told that electrons in a television set are accelerated through a potential difference of 50 000 volts. I am to find speed of the electrons using relativistic kinetic energy and classical Kinetic energy. The answer I found relativistically is correct. Since $E_K=W$ and $W=qV$, I know work, so I know $E_K$, then I solved for speed, 0.412c. All good.

So here's the question. I want to use $E_K = (1/2)mv^2$ to solve it again, and I am supposed to get 0.422c. I use the same $E_K$ as the first time, based on my $qV$. (I suspect this is the problem, but please tell me why or why not is it the correct value to be used here. If it is the incorrect value, I don't know then what I should have for $E_K$). When I solve for $v$ now, I get 0.44c.

I have ruled out sig fig problems. Thanks for your help.

Oh, and then I'm supposed discuss if this difference (0.412 vs. 0.422) makes a difference in designing television sets. I suppose it must, but I don't know how tvs work. Some guidance here would help too. Thanks.

• I get $0.442\, c$. Without more information, my hunch is that the answer you're "supposed" to get is wrong; such things happen. – Javier Jan 21 '15 at 22:25

You are definitely right with $0.44c$ I have checked the calculation and also found the exact question here http://www.phas.ubc.ca/~mcmillan/rqpdfs/1_relativity.pdf with a worked solution, all on page 11.
I honestly can't remember much about how CRT televisions work but I seem to remember that they use electromagnets to direct electrons to different parts of a phosphorus screen to produce images. So this would mean that the electrons feel a force based on the magnetic part of the Lorentz force law $$\vec{F}=q\left( \vec{E}+\vec{v}\times \vec{B} \right)\underset{\vec{E}=0}\rightarrow q\vec{v}\times \vec{B}$$