Finding q: Balancing Gravitational & Electrostaic Potential Energy

AI Thread Summary
Two identical steel spheres, each with a mass of 1.0 kg, are analyzed for the balance between gravitational and electrostatic potential energy as their separation changes. The discussion involves using the formulas for gravitational potential energy and electrostatic potential energy, setting them equal to each other to solve for the charge q. It is noted that the variable r, representing distance, cancels out in the equations, simplifying the problem. Questions arise about the interpretation of changes in potential energy and the meaning of "opposite charge." Ultimately, the goal is to find the value of q that balances these energies effectively.
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Imagine that two identical steel spheres, each having a mass of 1.0 kg, are placed a certain distance apart. They are given an equal charge q such that when the separation between the objects changes, the change in the gravitational potentail energy between the objects is exactly balanced by an opposite charge in the electrostaic potential energy between the objects.
What is q?

I used both formulas; V(r) = +k q1q2/r, and V(r)= -G m1m2/r
I then set the two equal to each other and solved for q.
Should this method yield the correct answer?
thanks
 
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Anyone know what my "r" will be in this case?
 
The best you can get with one equation and two unknowns is a proportionality between the two. Yes that's the way you'd go about solving that problem but q is going to be related to r in some way. Edit I can't believe I didn't see this but r isn't relevant since both forces are inversely proportional to distance. (Not that it makes a difference but I thought your question asked for forces originally).
 
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maybe I should of done the simple algebra first...duh..the r's cancel out
thanks
:redface: i ended up w sq.root of G/k
 
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I don't understand your question. You say that "when the separation between the objects changes" (which I interpret as: when the distance between them changes, i.e. becomes larger or smaller) "the change in the gravitational potentail energy between the objects is exactly balanced by an opposite charge in the electrostaic potential energy between the objects." What opposite charge? Where is it comming from? It is clear that changing r will change the potential energy of the system. Are you asking for the value of q that will make the potential energy of the system is 0?
 
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