Calculating Mass of Pith Balls in Space with Gravitational and Electrical Forces

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In summary, in order for two pith balls with identical masses and charges (q = 4e) to move at constant velocity in space, the net force on each ball must be zero. This means that the gravitational force (Fg) and the electrical force (Fe) must add up to zero. Using the known values of k = 9.0 x 10^9 Nm²/C², G = 6.67 x 10^-11 N /m²kg², and q = 4(1.60 x 10^-19 C), the mass of the balls can be solved for by setting the net force equal to zero.
  • #1
bjgawp
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Question:
Two pith balls are free to float in space. If only gravitational and electrical forces are acting, and the balls have identical masses and charges (q = 4e), find the mass of the balls if they are moving at constant velocity.

I'm pretty sure that there is something I'm missing because when I try to solve for the mass, there are just too many variables to work with. Here's my work:

http://img291.imageshack.us/img291/2433/unsolvablemg8.png

Known values:
k = 9.0 x 10^9 Nm²/C²
G = 6.67 x 10^-11 N /m²kg²
q = 4(1.60 x 10^-19 C)

Otherwise, there are 3 variables missing if we solve for m ...
 
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  • #2
You set the distance equal... that's not very meaningful! Instead, what must be true about the forces if the balls move at constant velocity?
 
  • #3
Ohh! Constant velocity indicate that Fnet = 0. But I don't understand how that applies here. Surely, Fg and Fe cannot equal to 0 o_O
 
  • #4
They don't have to equal zero, but they have to add to zero. The net force on each ball must be zero.
 
  • #5
I can't believe I didn't realize this. Nonetheless, thank you very much :)
 

What is Coulomb's Law?

Coulomb's Law is a fundamental law of physics that describes the electrostatic force between two charged particles. It states that the force of attraction or repulsion between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

What is the equation for Coulomb's Law?

The equation for Coulomb's Law is F = k(q1q2)/r^2, where F is the force between two charged particles, q1 and q2 are the magnitudes of their charges, r is the distance between them, and k is a constant known as the Coulomb's Law constant.

What is the unit of measurement for charge in Coulomb's Law?

The unit of charge in Coulomb's Law is Coulomb (C). It is a derived unit in the International System of Units (SI) and is defined as the charge transferred by a current of one ampere in one second.

What is the significance of Coulomb's Law?

Coulomb's Law is significant in understanding the behavior of electrically charged particles and the forces that act between them. It is also essential in the study of electromagnetism and is used in many practical applications, such as designing electrical circuits and analyzing the behavior of electrically charged molecules.

How does distance between two charged particles affect the force between them?

The force between two charged particles is inversely proportional to the square of the distance between them. This means that as the distance increases, the force decreases. As the distance decreases, the force increases. This relationship is known as an inverse-square law.

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