Two protons moving toward each other

[rkjul]

Homework Statement

Two protons that are very far apart are hurled straight at each other, each with an initial kinetic energy of 0.16 MeV, where 1 mega electron volt is equal to 10^6*(1.6*10^-19) joules. What is the separation of the protons from each other when they momentarily come to a stop?

Homework Equations

E=mc^2+K+U
U,electric=(1/4 pi epsilon)*(q1q2/r)

The Attempt at a Solution

I've been trying to figure this one out for about a half hour. I tried finding the potential energy U by rearranging terms in the equation for E. I then took that number and set it equal to (1/4 pi epsilon)*(q1q2/r)) and tried to find r (the distance) that way, but my answer was wrong. Any ideas?

 

[Mentz114]

I can't work out what you did but if you set the initial kinetic energy equal to the final potential energy, it's trivial, surely ?

 

[rkjul]

I can't work out what you did but if you set the initial kinetic energy equal to the final potential energy, it's trivial, surely ?

Thanks...that's what I did. I took that number and then used that in the equation for electric potential energy to obtain the distance.

Sometimes I have a habit of making silly mistakes/overthinking things.

 

[dynamicsolo]

The Attempt at a Solution

I've been trying to figure this one out for about a half hour. I tried finding the potential energy U by rearranging terms in the equation for E. I then took that number and set it equal to (1/4 pi epsilon)*(q1q2/r)) and tried to find r (the distance) that way, but my answer was wrong. Any ideas?

Your description is a bit nebulous. Could you please show your numerical calculations? What result have you been getting?

 

[astros10]

I am attempting to solve this problem. It seems simple enough but I seem to be getting the wrong answer.

Here is what I have done:
Uf=Ki

9e9*(1.6e-19)2
--------------------- = (.16)(1e6)(1.6e-19)
r

2.304e-28 = 2.56e-14*r
r=9.0e-15

Can someone help me figure out where I went wrong?

 

[hage567]

Remember your initial energy is 2*(0.16 MeV), since both protons are moving.

 

[astros10]

That was the problem. Thank you very much.

 

[Psyc]

I have this same homework question (but my Ki is .21MeV). Can someone explain it to me in detail? I'm trying to make sure I understand why it's done this way.