Slopes of a Force vs. Charge and Force vs. Distance Graph

[heatherann]

Homework Statement

We did a lab using two balls (one with a neutral charge and one with a negative charge). The independent variables were distance between the two balls and charge, while the dependent variable was force. We were to hang the neutral ball so that the negatively charged ball could affect the distance. We moved the negatively charged ball closer to the neutrally charged one, and usually a repulsion occurred. We found that the force vs. distance graph was directly proportional and the force vs. charge graph was inversely proportional. What do the slopes of each graph represent?

Homework Equations

Force/Distance = ?
Force/Charge = ?

The Attempt at a Solution

Force's units divided by distance's units = N/m.
Then for the charge graph, I'm not sure what the units of charge even are.

 

[rock.freak667]

Force's units divided by distance's units = N/m.
Then for the charge graph, I'm not sure what the units of charge even are.

For the one with Force vs charge. The units are N/C... Recall what the force exerted per coulomb of unit +ve charge placed at a point represents..

But what it seems that you were doing was testing Coulomb's law of

$$F=\frac{Q_1Q_2}{4\pi \epsilon_0 r^2}$$

 

[Moetasim]

I would first clarify the units of charge being used in the experiment. Depending on the system of units being used, charge could be measured in coulombs (C), electrons (e), or other units. Once the units are clarified, I would explain that the slopes of the graphs represent the relationship between the two variables being plotted. In this case, the slope of the force vs. distance graph represents the force constant, which is a measure of the strength of the interaction between the two charged objects. The steeper the slope, the greater the force constant and the stronger the interaction between the objects.

On the other hand, the slope of the force vs. charge graph represents the inverse of the distance between the two objects. This is because, as the distance between the objects decreases, the force between them increases. Therefore, the slope of the graph becomes steeper as the distance decreases, indicating a stronger force between the objects.

In summary, the slopes of the graphs in this experiment represent the strength of the interaction between the charged objects, with the force constant and inverse distance being the factors affecting the slopes in the force vs. distance and force vs. charge graphs, respectively.