Monster E&M Question (Coulomb's Law, Electric Potential, Kinematics)

[kosovo dave]

Homework Statement

A proton (charge +1e and mass 1.67e-27kg) and an alpha particle (charge +2e and mass 6.64e-27kg) are placed 3 fm (1 fm=10e-15m) apart.
a)what is the force on each particle
B)what is the potential energy of the system?
c)what is the acceleration of each particle at the beginning?
d)after a long time the two particles are far apart. what is the speed of each particle at this point?

Homework Equations

$F = ( q_1 q_2) / 4 π ε_0 r^2 = (k q_1 q_2) / r^2$
$U = q v = ( q_1 q_2) / 4 π ε_0 r$
$K E = 1 / 2 m v^2$
$F = E q = m a$

The Attempt at a Solution

a) Using Coulomb's Law, I found the force to be 51.2 N.
b) substituting my values into the second equation above, I got that the potential energy of the system is 1.5e-13 J.
c)Using the fourth equation above I found the accelerations. For the proton I got 3e28 m/s^2. For the alpha particle I got 8e27 m/s^2.
d) This part got a little tough. Realizing that the acceleration decreases as the particles move apart, I tried to integrate their acceleration from their initial separation out to infinity, but this quickly proved to be tedious/confusing. Looking at it again, I realized that as the particles move towards infinity all of the potential energy will be converted into kinetic energy. So I solved equation 3, substituting my answer from b) in for the kinetic energy and the mass of each particle. I found the velocity of the proton to be 1.34e7 m/s and the velocity for the alpha particle to be 6.72e6 m/s.

Did I do this correctly? This question is from an old test my prof gave us to study (I don't have the solution) and I have no intuition for how quickly these types of particles should be moving.

 

[Princu]

Yes.The procedure you did is correct.

 

[kosovo dave]

Thanks! If I wanted to continue on my initial path of integrating (no pun intended) the acceleration to get the final velocity, could somebody show how that would work?

 

[postfan]

What the supposed pun supposed to be?

 

[kosovo dave]

path of integrating = path integral. not a good one, but gimme a break -- I've been studying all day.