Manipulating Data to Form a Linear Graph: A Challenge

[cybernerd]

Homework Statement

I'm given a chart of Force vs Seperation with the following values:

SEPARATION (m)
0.1
0.2
0.3
0.4
0.5
0.6

FORCE (N)

0.79
0.48
0.20
0.05
0.022

Where FORCE is the y-axis, and 0.1 corresponds with 0.79.

I am not given any other values. All I know is that these are measures of distance and forces between two identical, equally charged spheres.

Now I am tol to manipulate the data until I get a set of values that will form a straight line when graphed.

Homework Equations

E = kq1q2/r^2

The Attempt at a Solution

I know that Coulomb's law works out to k x q1 x q2 x 1/r^2
So if I were to multiply by r instead of 1/r^2 I should get a linear graph...

Problem is, I don't have any values for either charge.

I'm totally stumped. Can someone point me in the right direction?

 

[cybernerd]

CORRECTION: The charges are not equally charged. Apparently A has a charge of 3.08 x 10^-7. I am not given the charge of B.

 

[nlightner]

Manipulating data to form a linear graph can be a challenging task, especially when dealing with limited information. In this scenario, we are given a chart of force vs separation values for two equally charged spheres. Our goal is to manipulate the data in such a way that it will form a straight line when graphed.

One way to approach this problem is to use Coulomb's law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In equation form, this can be written as F = kq1q2/r^2, where F is the force, k is the proportionality constant, q1 and q2 are the charges, and r is the distance.

Since we are given the values for force and separation, we can rearrange the equation to solve for the product of the charges (q1q2). This can be done by multiplying both sides of the equation by r^2, giving us F x r^2 = kq1q2. Now, we can plot F x r^2 on the y-axis and see if it forms a linear graph with separation on the x-axis. If it does, then we have successfully manipulated the data to form a straight line.

However, as stated in the problem, we do not have any values for the charges. In this case, we can use a technique called curve fitting. This involves using a mathematical tool, such as a graphing calculator or a spreadsheet program, to find the best fit line for the given data points. This will give us an equation that relates the values of force and separation, without needing to know the specific values of the charges.

Another approach could be to gather more data points by varying the distance between the two spheres and recording the corresponding forces. This will give us a wider range of data to work with and may make it easier to manipulate the data to form a linear graph.

In summary, manipulating data to form a linear graph can be challenging, but with the use of equations and mathematical tools, it is possible to find a solution. It is important to carefully consider the given information and use appropriate techniques to manipulate the data effectively.