Electric potential energy of two charged spheres

[semc]

Two insulating spheres have radii 0.3cm and 0.5cm, masses 0.1kg and 0.7kg and uniformly distributed charges of -2 $$\mu$$C and 3 $$\mu$$C. they are released when the distance from their center are 1m apart. How fast will each be moving when they collide.

Firstly, what is the radius of the sphere use for? Secondly, I calculated the electric potential energy of the system but what is this energy equivalent to? Lastly, how can we solve this question if the spheres were conducting spheres?

 

[kelly_kelly]

Okay, well, first let me say that I'm not sure how to answer your question, but I would like to think through it a bit myself. The electrical potential energy at the beginning should be equal to the sum of the kinetic energies of the spheres at the end. I think conservation of momentum still holds, so using the energy and momentum equations I think one should be able to calculate both velocities. I'm not sure how the radius of the spheres comes into play either. It would affect the potential energy of each spherical charge distribution, but that doesn't seem like it should be relevant to me since the spheres aren't changing, so we can set our zero of potential energy at the total potential energy inherent within the spheres. If the spheres were conducting, it seems to me that the charge on each sphere should redistribute itself such that field is zero and the spheres don't move. Is this possible?

Sorry for the long, useless response, but I would like an answer to your question as well!

Kelly

 

[semc]

That's what I had in mind at first, so do you think the energy lost by the system is equivalent to the kinetic energy gain by the sphere? So can we treat one sphere as stationary and just calculate the relative velocity of the moving sphere? I think if the spheres are conducting they would polarize each other as they move together?

 

[ideasrule]

Firstly, what is the radius of the sphere use for? Secondly, I calculated the electric potential energy of the system but what is this energy equivalent to? Lastly, how can we solve this question if the spheres were conducting spheres?

The radii are used for calculating the potential energy of the system after the collision. The electric potential energy isn't equal to anything, but the difference in electric potential energy is equal to the total kinetic energy of the system, since total energy is conserved.

If the spheres were conducting, the separation of charges would make the problem much harder to solve. I don't think the solution is trivial.

 

[ideasrule]

That's what I had in mind at first, so do you think the energy lost by the system is equivalent to the kinetic energy gain by the sphere? So can we treat one sphere as stationary and just calculate the relative velocity of the moving sphere?

The potential energy lost by the system is equal to the kinetic energy gained by TWO spheres. You can't treat one sphere as stationary because in any inertial reference frame, it isn't.

I think if the spheres are conducting they would polarize each other as they move together?

Yes. That would make the problem extremely difficult to solve.

 

[semc]

So if we use $$\Delta$$U = $$\frac{1}{2}$$m₁v₁² +$$\frac{1}{2}$$m₂v₂² and conservation of momentum m₁v₁= -m₂v₂ simultaneously is able to solve it? I am not able to get the answer?

 

[ideasrule]

Yes, that's how you do it. You should be able to get an answer. How did you try to solve the equations?

 

[semc]

k_e $$\frac{Qq}{r^2}$$= $$\frac{1}{2}$$ m₁v₁² + $$\frac{1}{2m2}$$ (m₁v₁)²
The distance r is 1m?

I gotten v₁ to be 0.793m/s but its not the answer. So how do we use the radius of the sphere?