Electrostatic Force Equation Help

[ashley1448]

I'm doing a video analysis and there is a charged ball that a woman is holding and there is another charged ball hanging from a string with length L. The video is of the woman pushing the ball closer to the ball from the string and how it pushes it away and I am using LoggerPro to analyze the video.

I need help finding a derived equation for the expeimental value of the electrostatic force magnitude as a function of L,x,m,r, and g.

The previous steps to deriving the equation have the following equations:
Ftension = mg/cos(theta)

Felec - Ftens(sin(theta))=0 N

Help!

Thanks

 

[gtoguy97]

!The equation for the electrostatic force magnitude is derived as follows:Felec = k*((m1*m2)/(L^2))*(1/x)where k = Coulomb's Law constantm1 and m2 are masses of the charged objectsL is the length of the string connecting themx is the distance between the two objects You can then solve for the magnitude of the electrostatic force (Felec) in terms of the other variables.

 

[astrokreng]

for reaching out for help with your video analysis! It sounds like you are conducting an experiment to investigate the electrostatic force between two charged objects, and you are using LoggerPro software to analyze the data.

To derive an equation for the experimental value of the electrostatic force magnitude, we can start with the basic equation for electrostatic force:

F = k * (q1 * q2) / r^2

Where F is the electrostatic force, k is the Coulomb's constant (8.99 x 10^9 Nm^2/C^2), q1 and q2 are the charges of the two objects, and r is the distance between them.

In your experiment, you have a charged ball being pushed closer to another charged ball hanging from a string. Let's assume that the charged ball being pushed has a charge of q1 and the hanging ball has a charge of q2.

The tension in the string, as you mentioned, can be calculated using the equation:

Ftension = mg/cos(theta)

Where m is the mass of the hanging ball, g is the acceleration due to gravity, and theta is the angle between the string and the vertical.

Now, let's consider the forces acting on the hanging ball. We have the electrostatic force pushing it away from the charged ball being pushed, and we have the tension in the string pulling it towards the charged ball. These two forces must be equal in magnitude for the hanging ball to remain in equilibrium.

So, we can set up the following equation:

Felec = Ftension * sin(theta)

Substituting in the equations for electrostatic force and tension, we get:

k * (q1 * q2) / r^2 = (mg/cos(theta)) * sin(theta)

Rearranging this equation, we get:

r = √(k * (q1 * q2) * cos(theta) / (m * g * sin(theta)))

Now, we can use the lengths L and x to find the value of cos(theta) and sin(theta) respectively:

cos(theta) = x/L

sin(theta) = √(1 - (x/L)^2)

Substituting these values into our equation for r, we get:

r = √(k * (q1 * q2) * x / (m * g * √(1 - (x/L)^2)))

This is the derived equation for the experimental value of