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Gravitational Force Vector exerted by 2 charged objects 
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#1
Sep1609, 09:18 PM

P: 16

1. The problem statement, all variables and given/known data
Two thin hollow plastic spheres, about the size of a pingpong ball with masses (m1=m2 = 2e3 kg) have been rubbed with wool. Sphere 1 has a charge q1 = 4e9 C and is at location < 40e2, 20e2, 0 > m. Sphere 2 has a charge q2 = 6e9 C and is at location < 50e2, 40e2, 0> m I've already calculated Relative Position Vector: <90e2, 60e2, 0> Distance between q1 and q2: 1.0816653 m Unit Vector: <.8320502943, .5547001962, 0> Magnitude of gravitational force exerted on q2 by q1: 2.29059829e16 The Electrostatic Force between the two objects: 1.84615e7 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 / 2.29059829e16), (.5547001962 / 2.29059829e16), 0> For question 2, I didn't know where to start, assuming I needed the answer to question 1. 


#2
Sep1709, 06:47 AM

P: 3,016

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*[(q1q2)/r^2] Direction = "you tell me" 


#3
Sep1709, 08:15 AM

P: 16

Thanks.
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 2.29059829e16 (magnitude of grav force) and on the same path, for question 2, divide the unit vector by 1.84615e7 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? 


#4
Sep1709, 08:33 AM

P: 3,016

Gravitational Force Vector exerted by 2 charged objects
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*[(q1q2)/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*[(q1q2)/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_{x}i+r_{y}j)/r 


#5
Sep1709, 08:48 AM

P: 16

So.. for problem 2..
1.84615e7 <.8320502943, .5547001962, 0> and problem 1, change the scalar to 2.29059829e16 ? Awsome! it worked. Many thanks saladsamurai. 


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