Hurling protons at one another to find where they stop

[HellaciousD]

Two protons that are very far apart are hurled straight at each other, each with an initial kinetic energy of 0.19 MeV, where 1 mega electron volt is equal to (1*10^6)*(1.6*10^-19) joules. What is the separation of the protons from each other when they momentarily come to a stop?
separation = 1 m

Maybe I'm just missing the necessary formula. Is there a way to incorporate Electric Potential Energy formula and the energy principle here?

 

[willem2]

Two protons that are very far apart are hurled straight at each other, each with an initial kinetic energy of 0.19 MeV, where 1 mega electron volt is equal to (1*10^6)*(1.6*10^-19) joules. What is the separation of the protons from each other when they momentarily come to a stop?
separation = 1 m

Maybe I'm just missing the necessary formula. Is there a way to incorporate Electric Potential Energy formula and the energy principle here?

Certainly. The protons will stop when all their kinetic energy is converted to electric potential energy.
Both of the protons have kinetic energy at the start. The potential energy [tex] \frac {k q_1 q_2} {r} [/tex] is shared by both protons.

 

[tomcue]

Yes, there is a way to incorporate the Electric Potential Energy formula and the energy principle in this scenario. The Electric Potential Energy formula for two point charges is given by:

PE = (k*q1*q2)/r

Where k is the Coulomb's constant (8.99*10^9 Nm^2/C^2), q1 and q2 are the charges of the protons, and r is the separation between them.

In this case, the initial kinetic energy of each proton is 0.19 MeV, which is equal to 0.19*(1*10^6)*(1.6*10^-19) joules. This energy will be converted into potential energy as the protons come closer to each other.

Using the energy principle, we can equate the initial kinetic energy to the final potential energy at the moment when the protons come to a stop. Therefore, we have:

0.19*(1*10^6)*(1.6*10^-19) = (k*q1*q2)/r

Rearranging this equation, we get:

r = (k*q1*q2)/(0.19*(1*10^6)*(1.6*10^-19))

Substituting the values of k, q1, and q2, we get:

r = (8.99*10^9 * 1.6*10^-19 * 1.6*10^-19)/(0.19*(1*10^6)*(1.6*10^-19))

Simplifying this, we get:

r = 1 meter

Therefore, the separation between the protons when they momentarily come to a stop is 1 meter. This calculation takes into account the electric potential energy and the energy principle to determine the separation between the protons.