Homework Help: Minimum speed required for charge collision

1. Oct 15, 2012

digiholic

1. The problem statement, all variables and given/known data
A charge of 3.0 μC is distributed uniformly throughout the volume of plastic
sphere with a radius of 10.0 cm. An identical plastic sphere with charge 3.0 μC
is shot directly at the center of the first sphere, from very far away. The mass
of each sphere is 5.0 X 10^-5 kg. If the first sphere is held fixed, how fast must
the second sphere be launched so that the two spheres touch one another? How
will this change if the first sphere is free to recoil?

2. Relevant equations
F = (q1*q2)/(r^2*4*pi*ε)
E = Q/(4*pi*ε*r^2)

3. The attempt at a solution
I honestly don't know where to start on this one. I get the feeling it has something to do with the field causing an acceleration, which would mean I need to use kinematics, but the force would be increasing as the charged spheres got closer, and I don't know how to handle changing acceleration.

2. Oct 15, 2012

voko

Think about the kinetic and potential energies.

3. Oct 15, 2012

digiholic

So, assuming you need just enough energy to get the two to stop after colliding, the final Kinetic Energy should be zero, so Uinitial + 1/2*m*v^2 = Ufinal?

What's the equation for potential energy in this case?

4. Oct 15, 2012

voko

What is electric potential?

5. Oct 15, 2012

digiholic

U = k*Q*q/r,

but I don't know the radius between the two spheres at the start.

EDIT: I just realized that since they start so far apart they aren't affecting each other, I don't need the potential at the start, only at the end. So it'd just be 1/2*m*v^2 = Ufinal, right? Using the combined radius of the two as the distance r for U? For the unrestricted movement one, would I just calculate each one's potential at the end, so 1/2*m*v^2 = Umoving + Ustationary?

Last edited: Oct 15, 2012
6. Oct 15, 2012

voko

"Far apart" simply means that the potential is zero. What is the total energy initially and what is the total energy at the moment of collision?