Using electric force to find the force of gravity

AI Thread Summary
The discussion revolves around calculating the gravitational force acting on a charged plastic sphere held stationary by an electric field. Initially, the approach involved determining the sphere's mass using gravitational and electric force equations, leading to a calculated gravitational force of 5.2 x 10^-2 N. However, it was clarified that since the sphere is floating, the upward electric force must equal the downward gravitational force, simplifying the problem. The correct gravitational force was recalculated as 5.8 x 10^-14 N, aligning with the balance of forces. The conversation highlights the importance of recognizing the relationship between electric and gravitational forces in such scenarios.
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Homework Statement



A plastic sphere with a positive charge of 4.8 x 10^-19 C is held stationary in a gravitational field of strength 9.8 m/s^2 by an electric field of strength 1.2 x 10^5 N/C. What is the force of gravity on the sphere?

Homework Equations



F_e=qE=kQq/r^2
F_g=mg=GMm/r^2
g=GM/r^2

The Attempt at a Solution



I think the only way to find the force of gravity is to find the mass of the sphere first. Since r^2=kQ/E, g=GM/(kQ/E)=EGM/kQ. So M=gkQ/EG

M=(9.8 m/s^2)(9.0 x 10^9 N x m^2/C^2)(4.8 x 10^-19 C)/(1.2 x 10^5 N/C)(6.67 x 10^-11 N x m^2/kg^2)=5.3 x 10^-3 m

If this mass is the mass of the sphere and not some other random object, then the number can be substituted into F_g=mg

F_g=(5.3 x 10^-3 m)(9.8 m/s^2)=5.2 x 10^-2 N

If M isn't the mass of the sphere, then I'm completely wrong, but that's the only solution I've been able to come up with. Can anyone tell me if I'm right?
 
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if i understand the question correctly... the sphere is floating so like one force acts upwards and one acts downwards. If it is floating, what does that say about the magnitudes of the electric and gravitational forces?

I'm not sure if what you did is right, but if I understand the problem correctly, you just need to do one calculation...
 
I guess I was needlessly complicating the problem. The strength of the gravitational field must have been a red herring.

If the sphere is indeed floating, then the upward electric force must balance the downward gravitational force, so that their magnitudes are equal. F_g=F_e=QE
So F_g=(4.8 x 10^-19 C)(1.2 x 10^5 N/C)=5.8 x 10^-14 N

That probably is the right answer. Thanks for your help.
 
yea that's what I was thinking, glad to help
 
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