How Do You Calculate Proton Speed and Momentum in Special Relativity?

[delongk]

Special Relativity I NEED HELP ASAP!

Find the speed and momentum of a proton (m=1.67*10^-27) that has been accelerated through a potential difference of 2000MV. Give your answers to three sig figs. Ans: .948c and 1.49*10^-18kg m/s

I keep trying different ways to get this, but keep getting different answers. How do you go about this problem? I need an answer ASAP because I leave in 15 minutes to take an exam.

 

[Hootenanny]

It's a bit late to be revising for an examination now, your best just trying to relax about it. However, this question is fairly straight forward. Do you know the expression for relativistic kinetic energy? Use this to find the velocity of the particle, then use the relativistic expression for momentum to find the moment of the proton.

 

[Andrew Mason]

Find the speed and momentum of a proton (m=1.67*10^-27) that has been accelerated through a potential difference of 2000MV. Give your answers to three sig figs. Ans: .948c and 1.49*10^-18kg m/s

I keep trying different ways to get this, but keep getting different answers. How do you go about this problem? I need an answer ASAP because I leave in 15 minutes to take an exam.

Use: $$KE = E - m_0c^2 = (\gamma -1)m_0c^2$$

AM

 

[delongk]

Is 2000MV equal to the KE then?? How do you find KE to use that to find v? ANd I have studied for a week... I just couldn't get this one problem when I was reviewing this morning.

 

[Andrew Mason]

Is 2000MV equal to the KE then?? How do you find KE to use that to find v? ANd I have studied for a week... I just couldn't get this one problem when I was reviewing this morning.

Yes, the 2000mV is the KE. Use that to determine the $\gamma$. That will allow you to determine v using:

$$\gamma = \frac{1}{\sqrt{1-v^2/c^2}}$$

AM

 

[Hootenanny]

Is 2000MV equal to the KE then?? How do you find KE to use that to find v? ANd I have studied for a week... I just couldn't get this one problem when I was reviewing this morning.

You must first convert the 2000MV into Joules, i.e. find the work done on the proton. Recall the voltage is defined as the work done per unit charge; thus, the energy supplied to the proton would be the product of the potential difference in volts and the charge of the proton in coulombs. Do you follow?

 

[delongk]

That's where I went wrong... I kept putting 2000MV into the KE and got the wrong answers... but I have to convert it to J. Thanks!

 

[Hootenanny]

That's where I went wrong... I kept putting 2000MV into the KE and got the wrong answers... but I have to convert it to J. Thanks!

Yeah, that's right, an easy slip to make (I've done it myself a few times). Good luck with your exam.