Day 7 - Electrostatic Forces

Video experiment analysis

For the video presented in class, our task was to analyze the video such that we could determine the charges of each ball in the video. We found the charge for each ball by means of Coulumb's law using the values for the distance and masses that we knew.

Using Loggerpro we were able to manually plot the movement of the ball for each specified frame. The initial starting point of the second ball was used as our frame of reference for the origin. After playing the video, we were able to approximate the values for x_1 and x_2, the distance between the ball on the rod and the origin, and the traveled distance of the hanging ball from the origin, respectively.

Above is our free body diagram done in class which we used to determine the forces affecting the hanging sphere, and thus the electric force. The resulting electric force was a nostalgic F_e=mgtan(theta).

We rewrote this equation as: F_e=mg((x_2)/(L^2-x_2^2))

We then calculated this formula in logger pro below:

Electric Force vs Separation Graph:

- Based on the graph we found the relationship to be inversely proportional.



Conclusion Questions:

1. It was evident that there is an inversely proportional relationship between the electric force and the squared distance of the two charges. The graph shows that the force of the charge decreases as distance increases, which confirms what we would intuitively think.

2. A) The percent difference of the experimental and theoretical exponent was 13.2 percent.

% difference = 1- Experimental/Theoretical = 1-1.763/2.0 = 13.2%

B) When we assumed that the charges were the same we were able to calculate the charge by manipulating Coulumb's Law, which resulted in a charge of 3.91*10^-6.
F= kq^2/r^2
q=((Fr^2)/k)^0.5 = .00000391

C) When we assumed that the charge of the hanging sphere was half that of the other sphere, we multiplied q_2 by 0.5 since the first was equal to half of the second, and then substituted q_1's new form into the equation. This resulted in values of q_1 and q_2 being 2.76*10^-8 and 5.53*10^-8, respectively.
q_1=0.5q_2
F=K(0.5q_2)^2/r^2
q_2=(2Fr^2/k) = .000000053
q_1= .0000000276

3. The charges can not be determined, since if they were both negative or both positive they would still both repel each other, and since coulumb's law has the two charges multiplied, the end result will always be positive.

4. The largest source of error/uncertainty in this lab was the fact that we had to manually trace the distances shown in the video in logger pro. Other groups likely had slightly different values compared to ours. Deviating measurement values would ultimately give different graph values for each group. A comparison of all other groups would give insight to what the proper data set should look like.