New Force After Objects Are Touched Together?

[aeromat]

I didn't use latex because for some reason, a term with the 10 to the power of -# isn't working properly:

$$1.0*10^-1$$

Homework Statement

Two identical objects have charges +6.0 microcoulombs and -2.0 microcoulombs, respectively. When placed a distance "d" apart, their force of attraction is 2.0N. If the objects are touched together, then moved to a distance of separation of 2d, what will be the new force between them?

Homework Equations

Coulomb's Law

The Attempt at a Solution

I solved for "d"
d =
sqrt{(9*10^9)(6.0*10^-6)(2.0*10^-6)
-------------------------------
(2.0)}

The d I got was 0.232m, so I doubled that to get 0.464m, since it says they would be at a distance 2d. Since they separated from each other, then that means they are both the same charge.

FQ =
(9.0*10^9)(6.0*10^-6)(2.0*10^-6)
-------------------
(0.464)

= 0.2327N
approx. 0.23N
However, the answer at the back is "0.17N". What did I do wrong?

 

[Filip Larsen]

You forgot to include the change in charge for each object as they touch.

 

[aeromat]

I apologize, but I don't understand what you mean.

 

[Filip Larsen]

The problem text says " ... the objects are touched together". Think about what that means for the distribution of charge on the two objects.

 

[rwisz]

I would like to point out that the question itself is not completely clear. When it says "objects are touched together", it is not specified whether they are touching in a way that their charges are combined or if they are just physically touching each other. This could affect the calculation.

However, assuming that the objects are touching in a way that their charges are combined, the new force between them would be 0.17N. This can be calculated by using Coulomb's Law again, but with the new charge of +4.0 microcoulombs for the combined object. The equation would be:

F = (9.0*10^9)(4.0*10^-6)(4.0*10^-6) / (2*0.464)^2 = 0.17N

This is because when the objects are touched together, their charges combine and become +4.0 microcoulombs. This results in a smaller force of attraction between the objects, since the charges are now closer together.

In conclusion, the new force between the objects after they are touched together and separated to a distance of 2d would be 0.17N. However, I would recommend clarifying the question for a more accurate answer.