How Can You Determine Coulomb's Constant from a Force vs. Distance Graph?

[ulash]

Homework Statement

Determining Coulomb's constant through a force vs. separation distance graph.

Homework Equations

F = kqQ/r^2

The Attempt at a Solution

So, I'm a little confused about what I should do! We were shown a video of two charges moving towards each other. We were given force/distance data, and I used this to plot a graph. However, I need to make a straight line in the graph...which can be done by working with the equation u = 1/r^2. I've tried using the force values and the distance values but to no avail. I used the distance values as r and then sub those into the x-axis, which is what I did ... so should I simply try to change the scale of the graph ... or something else

 

[Delphi51]

Welcome to PF, uflash.
So, you are trying to find the k, right?
The usual approach is to make a graph whose slope is the thing you want to find. You must make F = kqQ/r² look like y = mx so you would choose x to be qQ/r² and y to be F. Then the slope will be k. That is, graph F vs qQ/r² and find the slope.

 

[srivi]

if u =1/r²

then F = ( KqQ ) u , which closely resembles the straight line equation y = mx +b.

where F represents the "y" values, kqQ is the slope, and u represents the "x" values. In this case, the "b" value (y-intercept) equals zero.

so , try substituting u= 1/r² values into the x-axis to get the solpe .

 

[ulash]

Thank you so much! That really cleared it up for me.

 

[rwisz]

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Determining Coulomb's constant can be done through various methods, including using a force vs. separation distance graph as you have attempted. However, it is important to note that the equation F = kqQ/r^2 is for the force between two point charges, not for the force between two charges moving towards each other.

To accurately determine Coulomb's constant from the given data, you will need to use the correct equation and make sure that the force and distance values correspond to the same point in time. Additionally, it may be helpful to plot multiple data points and use a curve fitting method to find the best fit line, rather than trying to manually make a straight line on the graph.

It is also important to consider any potential sources of error in your data and to repeat the experiment multiple times to ensure accuracy. Overall, determining Coulomb's constant requires careful analysis and consideration of all relevant factors.