# Finding speed from acceleration through a potential difference

1. Oct 2, 2006

### metalmagik

I need help finding the speed of a proton in terms of c (speed of light) when all I have is an acceleration through a potential difference of 77 MV.

I started by saying this was 77,000,000 Volts, and then using PE = qV to solve for energy. I used E = mc^2 to find mass and used this and rest mass of a proton to find gamma by using m = mo(gamma). I found gamma to be less than one. How is this possible? What did I do wrong? Any help is greatly appreciated.

2. Oct 2, 2006

### Hootenanny

Staff Emeritus
One should use the expression for relativistic kinetic energy;

$$E_{k}=m_{0}c^2(\gamma - 1)$$

3. Oct 2, 2006

### metalmagik

but I need to find V, velocity.

4. Oct 2, 2006

### metalmagik

Oh wait, I see what you're saying, I will try this and post again if I have not done it correctly again. Thank you

5. Oct 2, 2006

### metalmagik

thanks very much, I got the question right. I have one more question if you are still around.

6. Oct 2, 2006

### Hootenanny

Staff Emeritus
No problem, I'm still here.

7. Oct 2, 2006

### metalmagik

Great, I was going to post a new topic but I didn't want to flood the board too much.

What is the Schwarzschild radius for a typical galaxy (with mass on the order of 10^41 kg)?

I do not understand the "with mass on the order of 10^41 kg"

I tried plugging (1e41) with the Schwarzchild radius formula but I got the wrong answer when I entered it into the test. I have one more response left so I need to get it right, thanks so much for the help so far, I'd be grateful if you could work with me on this one.

8. Oct 2, 2006

### Hootenanny

Staff Emeritus
On the order of means exactly what you did. Off the order usually means powers of ten. If this is a webassign homework you probably know already, but you need to be very careful with the way you enter your answers (significant figures, units metres of kilometres etc). I've just done a quick calc myself and arrived at a radius of about 1.48x1014m.

9. Oct 2, 2006

### metalmagik

Ah! that must be why! I got the same exact answer, but they want it in km. I did not realize the Schwarzchild radius formula is worked to give answers in meters. So, since my webassign quiz wants it in km, it should be, 1.48x10^11 km, correct?

10. Oct 2, 2006

### Hootenanny

Staff Emeritus
If your unsure check your units, assuming you entered everything into the equation in SI units;

$$R = \frac{2GM}{c^{2}} =\frac{(m^{3}kg^{-1}s^{-2})(kg)}{(ms^{-1})^2} = m$$

Assuming webassign wants it to 3sf then yes, your answer should be correct.

11. Oct 2, 2006

### metalmagik

got it right! 100% score wahoo

thanks a lot Hootenanny, thanks verryyy much for your time.

12. Oct 2, 2006

### Hootenanny

Staff Emeritus
Well done mate.
My pleasure