Two charges, find collision point

[DaNiEl!]

any help in showing the way to solve this problem would be apreciated:

the problem is: given to charges q1=2 micro colomb, q1=4 micro colomb, 10 inches apart, find the collision point.an obvious approach would be calculating the position equation but in this problem the aceleration is not constant. as charges get close their interactions become stronger in a non linear fashion.

i'm wondering if there is a 'shortcut' for the solution and this is why I'm posting here, so that i don't waste time needlessly. maybe it has to do with energy since the problem is near the other energy problems but i don't see how.
please help me!

ps: another way is a numerical aproximation but i don't think that's what the professor wants.

 

[G01]

Your correct. This is an energy problem.

HINT: Start the problem like any conservation of energy problem. Start by letting the total initial energy be equal to the total final energy. Set the collision point as x. Finally remember that they each gain an equal amount of kinetic energy. You should then be able to solve for x in the energy equation.

Can you set up the conservation of energy equation now, or are you still a little confused?

 

[kdv]

Your correct. This is an energy problem.

HINT: Start the problem like any conservation of energy problem. Start by letting the total initial energy be equal to the total final energy. Set the collision point as x. Finally remember that they each gain an equal amount of kinetic energy. You should then be able to solve for x in the energy equation.

Can you set up the conservation of energy equation now, or are you still a little confused?

Can you say how to see that they must gain the same amount of kinetic energy? at first sight it does not seem to be the case. The work done on each is the integral of the force dotted with the displacement. At all times they feel forces of equal magnitudes (and opposite directions) so saying that they must gain the same amount of kinetic energy would seem to imply that they would have to travel the same distance.

 

[G01]

Can you say how to see that they must gain the same amount of kinetic energy? at first sight it does not seem to be the case. The work done on each is the integral of the force dotted with the displacement. At all times they feel forces of equal magnitudes (and opposite directions) so saying that they must gain the same amount of kinetic energy would seem to imply that they would have to travel the same distance.

Yes, I'm sorry, I was incorrect before. They would not gain the same amount of kinetic energy. Hmm this problem is ore complicated than I thought... I'll have to think about this.

 

[CaptainZappo]

any help in showing the way to solve this problem would be apreciated:

the problem is: given to charges q1=2 micro colomb, q1=4 micro colomb, 10 inches apart, find the collision point.


an obvious approach would be calculating the position equation but in this problem the aceleration is not constant. as charges get close their interactions become stronger in a non linear fashion.

i'm wondering if there is a 'shortcut' for the solution and this is why I'm posting here, so that i don't waste time needlessly. maybe it has to do with energy since the problem is near the other energy problems but i don't see how.
please help me!

ps: another way is a numerical aproximation but i don't think that's what the professor wants.

Do you know the mass of each charge?