Balancing Electric and Gravitational Forces Between Two Objects

[DubbzWubbz]

Homework Statement

Two small objects of equal mass 3.0g are placed a certain distance apart. How many electrons must be transferred from one to the other so that the electric force between them is equal to the gravitational force between them?

Homework Equations

Coulomb's Law: F = K (|q1||q2|)/r^2
Gravitational Force: F= GMm/r^2

The Attempt at a Solution

Well I assumed I was looking for a proportion between gravitational force and electric force which would allow me to decide the electrons necessary...so I attempted to set the two equations equal to each other, however, I really don't know what to do with this information or if it is even right. Could I get some advice on how to start appropriately.

 

[SteamKing]

Homework Statement

Two small objects of equal mass 3.0g are placed a certain distance apart. How many electrons must be transferred from one to the other so that the electric force between them is equal to the gravitational force between them?

Homework Equations

Coulomb's Law: F = K (|q1||q2|)/r^2
Gravitational Force: F= GMm/r^2

The Attempt at a Solution

Well I assumed I was looking for a proportion between gravitational force and electric force which would allow me to decide the electrons necessary...so I attempted to set the two equations equal to each other, however, I really don't know what to do with this information or if it is even right. Could I get some advice on how to start appropriately.

You shouldn't let doubt and lack of self-confidence overwhelm you so early in doing your work.

Since you know the forces due to gravitational attraction and electrostatic charge are supposed to balance, how would you write that relationship in terms of the two laws governing these phenomena?

 

[DubbzWubbz]

(GMm)/k = |q1||q2| ?

 

[haruspex]

(GMm)/k = |q1||q2| ?

Yes. Assuming the objects are initially neutral, what is the relationship between q1 and q2?

 

[ehild]

(GMm)/k = |q1||q2| ?

Read the problem How many electrons must be transferred from one to the other...

 

[DubbzWubbz]

Yes. Assuming the objects are initially neutral, what is the relationship between q1 and q2?

The product of the two charges are proportional to the force?

 

[haruspex]

The product of the two charges are proportional to the force?

No, that's a relationship between the charges and the force, that you already found. I'm asking about a relationship just between the two charges. Read the question statement, and assume the two bodies are initially neutral.

 

[DubbzWubbz]

No, that's a relationship between the charges and the force, that you already found. I'm asking about a relationship just between the two charges. Read the question statement, and assume the two bodies are initially neutral.

If both q1 and q2 are neutral, there would be no attraction? I assume I am transferring electrons to create a charge.

(GMm)/kq2 = |q1| q1 is proportionate to GMm/k multiplied by 1/q2. Would q2 be the charge of an electron?

 

[haruspex]

If both q1 and q2 are neutral, there would be no attraction? I assume I am transferring electrons to create a charge.

Initially neutral, before the transfer of electrons. What is net charge of the pair of objects after the transfer?

 

[SteamKing]

If both q1 and q2 are neutral, there would be no attraction? I assume I am transferring electrons to create a charge.

(GMm)/kq2 = |q1| q1 is proportionate to GMm/k multiplied by 1/q2. Would q2 be the charge of an electron?

There are certain units associated with q1 and q2. You must use these units for the Coulomb's Law equation to work properly.

 

[DubbzWubbz]

Initially neutral, before the transfer of electrons. What is net charge of the pair of objects after the transfer?

The net charge wouldn't change because charge is conserved?

 

[haruspex]

The net charge wouldn't change because charge is conserved?

Right, so what relationship does that give you between q1 and q2?

 

[DubbzWubbz]

Right, so what relationship does that give you between q1 and q2?

q1 = q2?

 

[haruspex]

q1 = q2?

Not quite. If the two charges are q1 and q2, what is the total charge?

 

[DubbzWubbz]

Not quite. If the two charges are q1 and q2, what is the total charge?

Wouldn't the total combined charge be 0? this way they are balanced?

 

[haruspex]

Wouldn't the total combined charge be 0? this way they are balanced?

Right, so express that as an equation in q1 and q2.

 

[DubbzWubbz]

Right, so express that as an equation in q1 and q2.

Do I incorporate this into the previous equation I had?

 

[haruspex]

Do I incorporate this into the previous equation I had?

In post #13 you wrote q1=q2. That is not quite right. I'm just trying to get you to the right version of that. You wrote, correctly, in post #15, that the net charge will be zero. Express that as an equation using q1 and q2. I'm not asking for anything obscure here, it's very straightforward.

 

[DubbzWubbz]

In post #13 you wrote q1=q2. That is not quite right. I'm just trying to get you to the right version of that. You wrote, correctly, in post #15, that the net charge will be zero. Express that as an equation using q1 and q2. I'm not asking for anything obscure here, it's very straightforward.

Are you asking for simply q1q2 = 0

 

[haruspex]

Are you asking for simply q1q2 = 0

That's so close I suspect a typo. Is that what you meant to write?

 

[DubbzWubbz]

That's so close I suspect a typo. Is that what you meant to write?

q1/q2 = 0 Is this what you're looking for

 

[haruspex]

q1/q2 = 0 Is this what you're looking for

No.
Consider any two objects. One has charge q1, the other has charge q2. What is the net charge? (Note: net charge is the same as total charge.)

 

[DubbzWubbz]

No.
Consider any two objects. One has charge q1, the other has charge q2. What is the net charge? (Note: net charge is the same as total charge.)

q1 + q2 = 0

 

[haruspex]

q1 + q2 = 0

Yes.