Finding the Initial Charge on a Sphere Based on Coulomb's Law

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Two identical metal spheres with different charges attract each other with a force of 75.6 mN, indicating opposite charges. When brought into contact, the charges redistribute until both spheres have the same final charge. After separation to a distance of 3.33 m, they repel each other with a force of 8.316 mN. The problem requires calculating the initial charge on the first sphere using Coulomb's Law, specifically the formula F = Ke * q1 * q2 / r^2. Understanding the charge redistribution and the relationship between initial and final charges is crucial for solving the problem.
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Homework Statement


Two identical small metal spheres with q1 > 0 & |q1| > |q2| attract each other with a force of magnitude 75.6 mN, as shown in the http://localhostr.com/files/ffac57/1.JPG" .

The spheres are then brought together until they are touching. At this point, the spheres are in electrical contact so that the charges can move from one sphere to the other until both spheres have the same final charge, q.
http://localhostr.com/files/62ffcf/2.JPG"

After the charges on the spheres have come to equilibrium, the spheres are moved so that they are again 3.33 m apart. Now the spheres repel each other with a force of magnitude 8.316 mN.
http://localhostr.com/files/6911b9/3.JPG"

The Coulomb constant is 8.98755*10^9 N*m^2/C^2

What is the initial charge q1 on the first sphere?
Answer in units of µC.


Homework Equations


F = Ke q1*q2/r2



The Attempt at a Solution



I was thinking that using this formula, I can get to q1. But apparently, it's not leading me anywhere.

Can anyone tell me if I'm using the right formula or not? If not, then which formula do I use? I didn't understand this material in class very well, so, if someone kindly explains how to do this problem, I'll really appreciate it.


Thanks
 
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Since they are attracting initially, q1 and q2 must have opposite charges.
When they are brought in contact, they will have the equal charges of the same sign, and the charge in each sphere will be ...?
 
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Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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