mass, distance, and forces between particles

[combatwombat]

Two particles are held in equilibrium by the gravitational and electrostatic forces between them. Particle A has mass ma and charge qa, while particle B has mass mb and charge qb. The distance between the charges is d. Which of the following changes will cause the charges to accelerate towards one another?

A. ma is doubled and mb is doubled
B. ma is doubled and mb is halved
C. qa is doubled and qb is doubled
D. d is doubled

(From EK Physics, #151).

I put D, thinking that if separated, the two charges would accelerate towards each other until they reached that same equilibrium distance. However, the book gives the answer as A, saying that doubling both masses would increase the gravitational attractive forces (wouldn't this be counterbalanced by electrostatic forces?), while doubling the distance would not change the forces. Can anyone explain this a bit better?

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[Naijaba]

First you need to realize that the competing forces equation looks like this:

(G x ma x mb) / d^2 = (k x qa x qb) / d^2

with either qa or qb being negative.

Now, let me try to explain why all of the answers except A are incorrect:

B. If you double ma and halve mb, the force due to gravity is still the same because the doubling and halving cancel each other out.
C. If you double both qa and qb, the two charges will move away from one another because the repulsive force now dominates the equilibrium. The question asks for the situation when the two charges will move towards each other.
D. If you double the distance both the force due to gravity and the electrostatic force will decrease by 1/4, meaning that the net force on both objects will remain zero and they will remain stationary.

 

[G1SG2]

C. If you double both qa and qb, the two charges will move away from one another because the repulsive force now dominates the equilibrium. The question asks for the situation when the two charges will move towards each other.

What repulsive forces? I don't think the question specified the signs of the two charges (whether or not they were the same).

 

[combatwombat]

What repulsive forces? I don't think the question specified the signs of the two charges (whether or not they were the same).

In this case, I don't think it matters. If they repel one another, then that repulsive force is balanced out by the gravitational attractive force. If they are attracted to one another, same thing.

 

[G1SG2]

In this case, I don't think it matters. If they repel one another, then that repulsive force is balanced out by the gravitational attractive force. If they are attracted to one another, same thing.

The reason I'm asking is because the above poster's explanation for C being incorrect was:

C. If you double both qa and qb, the two charges will move away from one another because the repulsive force now dominates the equilibrium. The question asks for the situation when the two charges will move towards each other.

Wouldn't that only hold if the charges were repulsive? If they were attracted to one another, wouldn't doubling qa and qb make them even more attracted to each other, and thus make them move towards each other?

 

[Naijaba]

Since gravity is ONLY an attractive force, the electrostatic force MUST be repulsive in order for the two charges to be in equilibrium.

I did, however, make an error when I said that either qa or qb was negative. It must be the case that qa and qb have the same sign (because same signed charges repel).

 

[G1SG2]

Oh, okay yeah the negative part kinda threw me off; I thought they might have had opposite signs, but I get it now. Thanks!