We started our journey by predicting what would happen to balloons if we rubbed them with animal fur. My group predicted that this would somehow cause a difference in the charges present in the balloon. And ,as a result it would be electromagnetic. Glass is a material that lets its electrons move very easily. So, when the balloon is left against the glass, it would stick.
We were a little bit nervous as Prof. Mason demonstrated what would happen, but it turned out we were right.
Then, instead of rubbing the the balloon with fur, it was rubbed with silk, and the question was to think about what would happen now. But the effect is similar to what happened earlier. Basically, there is still a difference in charges present in the balloon but this time it's the opposite way. Before, the side that was rubbed gained a positive charge and the glass gained a negative charge. This time the balloon's side gained negative charge, and the glass reacted by having its surface change to positive charge. The result is the same and the balloon stays on the glass without falling.
Then, we tried to define mass and charge. My group defined mass as the amount of stuff that attracts other stuff via gravity and charge as the amount of stuff that attracts other stuff via electricity. Their equations look very similar, and they are both forces at a distance.
Then we did an experiment with electrostatic forces. We cut two strips of Scotch tape that were 10 cm long and taped them to the table. At the same time we peeled them off and brought them close together with their non-sticky sides facing each other.
We observed that they seemed to repelled each other more and more as we brought them close together. Then we labeled these strips 'bottom' and got a couple more that we labeled 'top.' We taped the bottom ones to the table and then taped the top ones to these. Then, one of us grabbed one of the couples that were taped together and the other one grabbed the other couple that were taped together and simultaneously peeled them off from the table. Then we peeled them off from each other. When we brought the two top strips together, we saw they repelled each other. The same happened with the two bottom strips. Nevertheless, when we brought a top strip and a bottom strip together, they attracted each other as they got closer. In the picture below, we summarized our results.
This experiment is consistent with the hypothesis that there are two types of charge.
Next we decided to quantify this new force law with a pendulum. But first we wanted to calculate the angle the it would move as a functions of known quantities. So, we used the length of the pendulum and the horizontal distance that it moves. This yields the formula shown below.
Then we drew a free-body diagram wrote down the sum of forces in the horizontal and vertical directions to find an equation for the new force which is the one that keeps the body at an angle. This formula uses measurable and known quantities.
Next we drew what we think is the relationship between this new force and the distance at which interactions happened. We used the graph of the gravitational force vs r as a model, but it works pretty well for the interactions between this new force and r. If we were to write this in equation in the form of F=A*r^B, B would have a value of -2. And, we would solve for the the value of A in the equation.
Next we used video analysis with Logger Pro to get our data which looked like the picture in the below.
Next we calculated the new force using the formula we derived above and the data we collected from the video analysis. The data we used is mass, acceleration of gravity, the horizontal displacement and the length of the pendulum. Then we plotted the values of this force vs horizontal displacement and matched a couple of best fit equations. First we tried to fit the data with an equation that looked like F=Ar^-1, then we tried to fit the data with an equation that looked like F=Ar^-2, and we tried to fit the data with an equation that looked like F=Ar^B.
The equation that had r squared inverse had a pretty good RMSE value. The value for B was 1.998 giving a percent difference of 99.9 %. Hence, it seems like having B=-2 is a simple way that works for measuring our values. If the charges would've been the same, then they would've been 0.102 nC. If the charge on the hanging ball is half the charge of the other ball, then the charge of the hanging ball would've been 0.144 nC and the other would've been 0.722 nC. Nevertheless, it is not possible to tell which is the sign of the charges with the data we have. We can only tell that both are positive or negative, but we can't tell which because we have nothing to test it or compare it to. Also, some of the measurements may be a little off and that is because it when we were marking the points, the marks weren't perfect. This could explain why not all the points fit the curve perfectly or why the points may not be in full agreement with Coulomb's Law.
Next we starting 'reading' the equation and getting used to interpreting it with some exercises. These were focused on the placement and direction of the unit vector r hat if the forces were repulsive or attractive. If we are talking about the distance between the atoms starting on q2 and ending on q1, we write r hat 12 meaning on 1 from 2.
In the Coulomb equation, the magnitudes of the charges are proportional to the force. And, the magnitude of the force decreases as the distance increases. The reason is that their relationship is inverse and squared. Coulomb's Law is consistent with Newton's Third Law because it shows that there are two forces with the same magnitude but opposite direction.
Next, we solved a problem involving Coulomb's Law.
We found the force between two point charges, 2.0 *10^-9 C and -3.0*10^-9 C, at a distance of 2 cm. We got that to be -1.35*10^-9 N i^.
Then, calculated the components of a vector in 2D. Since r12 hat is a unit vector, its components are simply the cosine and sine of the angle theta.
This formula is going to help us solve the electromagnetic force problems in 2D like the next one.
In here, we have the same conditions as the previous problem. The previous problem is written to the left and the new problem is solved to the right. The difference is in that q2 is now at (5,6) where the numbers mean distances in centimeters from the origin. Hence, we had to find the sum of the horizontal and vertical forces and then we wrote our answer in vector form.
Finally, we called it a day by observing some wonderful machines transform mechanical work into electricity.
Demonstrations of the Van de Graff Generator directing electrons to objects and making them move
Demonstration of the Storm Ball
Summary
Today we saw a lot cool things. We started by observing and studying what happens when we rub a balloon and let it get stuck against a glass by itself. And, we found out that the force keeping it there is the electromagnetic force which is a new kind that we haven't studied yet. Then, we defined charge and mass as the quantities that generate attraction through electricity and gravity, respectively. And, we did an experiment to test our hypothesis that there are only two charges and to see how they interact with each other and other materials. Then, we prepared ourselves to do another experiment by finding how to calculate an angle through distances we can measure. This would allow us to calculate the force that moves a point charge on a swing. Also, it allowed us to find relationships between the electromagnetic force and distance between the charges by applying this formula to a range of data points. And, we played a little with it by calculating the charges on a couple of possible scenarios: one where the charges are the same and the other where one of the charges is half the other. Next we studied Coulomb's Law itself a little bit by looking closer at what it stated about distances, charges, forces and their directions (if they had any). Later, we solved a couple of problems with Coulomb's Law: one with charges on 1D and another one on 2D. Finally, we observed a Van de Graff Generator direct charges on materials and saw them move and expand as they gained charges. We also observed the Storm Ball direct electrons towards the glass and pass charges across the students.
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