Gravitational Force Vector exerted by 2 charged objects

Nal101

1. The problem statement, all variables and given/known data
Two thin hollow plastic spheres, about the size of a ping-pong ball with masses (m1=m2 = 2e-3 kg) have been rubbed with wool. Sphere 1 has a charge q1 = -4e-9 C and is at location < 40e-2, -20e-2, 0 > m. Sphere 2 has a charge q2 = -6e-9 C and is at location < -50e-2, 40e-2, 0> m

I've already calculated
Relative Position Vector: <-90e-2, 60e-2, 0>
Distance between q1 and q2: 1.0816653 m
Unit Vector: <-.8320502943, .5547001962, 0>
Magnitude of gravitational force exerted on q2 by q1: 2.29059829e-16
The Electrostatic Force between the two objects: 1.84615e-7

Questions:
1) What is the gravitational force (vector) exerted on q2 by q1?
2) What is the electric force (vector) exerted on q2 by q1?


2. Relevant equations
Fnet = G * [(m1 * m2)/r^2]
Felec = k * [(q1 * q2)/r^2]

3. The attempt at a solution
For question 1, I took each separate component of the unit vector and divided it by the magnitude.
i.e.
<(-.8320502943 / 2.29059829e-16), (.5547001962 / 2.29059829e-16), 0>
For question 2, I didn't know where to start, assuming I needed the answer to question 1.

Saladsamurai

Hey there NAl101

Why do you think that questions 1 and 2 are related?

You have already written the formula Felec = k * [(q1 * q2)/r^2]
which gives the electrostatic force bewteen two point charges (and I think it is safe to say that we can treat these as point charges).

Perhaps it is the sign of the charges that is troubling you? If so, I would simply treat the formula with their absolute values and then determine the direction by inspection.

That is: F_elec = k*[(|q1||q2|)/r^2]

Direction = "you tell me"

Nal101

Thanks.

Actually I do not know, it seems rather absurd at this point in time. I believe though at the time, since I couldn't figure out either one of them, they were seemingly related. I know this to be a false assumption though, seeing as they pertain to different aspects of the system.

The real problem I seem to be having is calculating the answers into a vector form. At first I thought it was simple, and for question 1, divide the unit vector by 2.29059829e-16 (magnitude of grav force) and on the same path, for question 2, divide the unit vector by 1.84615e-7 the electrostatic force between the two objects. This has apparently been disregarded as the correct answer, leaving me with no idea on how to calculate the answers.

Would I be correct in assuming the use of the two formulas towards my answer, having r = the values for x and y in the relative position vectors?

Saladsamurai

Hmm. I am not sure what the convention is here. We always used the "radial unit vector" to denote the direction. So the answer simply had a magnitude of |F_elec|=k*[(|q1||q2|)/r^2] and a direction of r_hat

If you want to write the answer in Cartesian Coordiantes, then you must take the Magnitude of the Vector:

|F_elec|=k*[(|q1||q2|)/r^2]

and then multiply it by the unit vector in the direction of r, which is what I think you are trying to say.

i.e. r_unit = (r_xi+r_yj)/|r|

Nal101

So.. for problem 2..

1.84615e-7 <-.8320502943, .5547001962, 0>

and problem 1, change the scalar to 2.29059829e-16 ?

Awsome! it worked. Many thanks saladsamurai.