Balancing Electric and Gravitational Forces Between Two Objects

In summary, the two charges q1 and q2, which are initially neutral, must be balanced if the electric force between them is to be equal to the gravitational force between them.
  • #1
DubbzWubbz
11
0

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.
 
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  • #2
DubbzWubbz said:

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?
 
  • #3
(GMm)/k = |q1||q2| ?
 
  • #4
DubbzWubbz said:
(GMm)/k = |q1||q2| ?
Yes. Assuming the objects are initially neutral, what is the relationship between q1 and q2?
 
  • #5
DubbzWubbz said:
(GMm)/k = |q1||q2| ?
Read the problem How many electrons must be transferred from one to the other...
 
  • #6
haruspex said:
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?
 
  • #7
DubbzWubbz said:
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.
 
  • #8
haruspex said:
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?
 
  • #9
DubbzWubbz said:
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?
 
  • #10
DubbzWubbz said:
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.
 
  • #11
haruspex said:
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?
 
  • #12
DubbzWubbz said:
The net charge wouldn't change because charge is conserved?
Right, so what relationship does that give you between q1 and q2?
 
  • #13
haruspex said:
Right, so what relationship does that give you between q1 and q2?
q1 = q2?
 
  • #14
DubbzWubbz said:
q1 = q2?
Not quite. If the two charges are q1 and q2, what is the total charge?
 
  • #15
haruspex said:
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?
 
  • #16
DubbzWubbz said:
Wouldn't the total combined charge be 0? this way they are balanced?
Right, so express that as an equation in q1 and q2.
 
  • #17
haruspex said:
Right, so express that as an equation in q1 and q2.

Do I incorporate this into the previous equation I had?
 
  • #18
DubbzWubbz said:
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.
 
  • #19
haruspex said:
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
 
  • #20
DubbzWubbz said:
Are you asking for simply q1q2 = 0
That's so close I suspect a typo. Is that what you meant to write?
 
  • #21
haruspex said:
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
 
  • #22
DubbzWubbz said:
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.)
 
  • #23
haruspex said:
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
 
  • #24
DubbzWubbz said:
q1 + q2 = 0
Yes.
 

1. How do electric and gravitational forces interact between two objects?

The electric and gravitational forces between two objects are both attractive forces, but they act on different properties of matter. The electric force is caused by the attraction between positive and negative charges, while the gravitational force is caused by the attraction between masses. These forces can either work together or against each other, depending on the properties of the objects involved.

2. How do the magnitudes of electric and gravitational forces compare?

The magnitude of the electric force between two objects depends on the distance between them and the amount of charge each object possesses. The magnitude of the gravitational force, on the other hand, depends on the distance between the objects and the mass of each object. In general, the electric force is much stronger than the gravitational force, but at large distances, the gravitational force can become dominant.

3. Can the electric and gravitational forces ever cancel each other out?

Yes, it is possible for the electric and gravitational forces to cancel each other out. This occurs when the magnitude of the electric force is equal to the magnitude of the gravitational force, but they act in opposite directions. This is known as equilibrium and can be seen in systems such as charged particles orbiting around each other.

4. How does distance affect the balance between electric and gravitational forces?

The balance between electric and gravitational forces is heavily dependent on distance. As the distance between two objects decreases, the electric force becomes stronger while the gravitational force remains the same. This can cause the electric force to dominate and pull the objects closer together. On the other hand, as the distance increases, the gravitational force becomes stronger and can overpower the electric force, causing the objects to move further apart.

5. Is balancing electric and gravitational forces important in everyday life?

Yes, balancing electric and gravitational forces is important in everyday life. These forces play a crucial role in many natural phenomena, such as the movement of planets in our solar system and the behavior of atoms and molecules. They are also essential in the functioning of technology, such as electricity and magnetism, which are based on the interaction of electric and magnetic forces.

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