Electric Potential Energy of protons

[syjxpatty]

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 1x10^6 multiply (1.6x10^-19) joules. What is the separation of the protons from each other when they momentarily come to a stop?

Homework Equations

Ue = (1/4\pi\epsilon)((q_{1}q_{2})/r)
E_{f} = E_{i} + W

The Attempt at a Solution

I am very confused on how to get this problem started, especially since they give the kinetic energy. I tried to manipulate the kinetic energy formula ((1/2)mv^2) but I am still really confused on how to approach this problem.

 

[kdv]

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 1x10^6 multiply (1.6x10^-19) joules. What is the separation of the protons from each other when they momentarily come to a stop?

Homework Equations

Ue = (1/4\pi\epsilon)((q_{1}q_{2})/r)
E_{f} = E_{i} + W

The Attempt at a Solution

I am very confused on how to get this problem started, especially since they give the kinetic energy. I tried to manipulate the kinetic energy formula ((1/2)mv^2) but I am still really confused on how to approach this problem.

Conservation of energy

Total Kinetic energy at the beginning + potential energy at the beginning = total kinetic energy at the final position plus potential energy at the final position

The initial position is when they each have the kinetic energy you gave but they are very far from each other. The final position is when they are at the point of closest approach

 

[syjxpatty]

Ohh alright so do I still do,

e = kq^2/r where r is distance between protons
k is 9*10^9
0.16 * 1*10^6*1.6*10^-19 = 9*10^9 * (1.6*10^-19)^2 / r
then I got r as (9x10^-15)

the thing is that I got it wrong when i did it this way.

 

[kdv]

Ohh alright so do I still do,

e = kq^2/r where r is distance between protons
k is 9*10^9
0.16 * 1*10^6*1.6*10^-19 = 9*10^9 * (1.6*10^-19)^2 / r
then I got r as (9x10^-15)

the thing is that I got it wrong when i did it this way.

Each has an energy of 0.16 MeV so your initial total kinetic energy is twice what you wrote

 

[syjxpatty]

ok! I got the separation as 4.5x10^-15 m ! Thank you!

 

[kdv]

ok! I got the separation as 4.5x10^-15 m ! Thank you!

You are very welcome!