Manipulating inverse square graph into straight line graph

  1. 1. The problem statement, all variables and given/known data

    In the course of performing several trials I determined that if you have 2 charged metal spheres (with the same amount of charge on them) and they are both positively charged, then the force of repulsion between them is changed by 1/4 each time you double the distance between them.

    This experiment no doubt sounds very familiar as it has been done many times before.

    I collected my data (16N@1.0cm, 4N@2.0cm, 1N@4.0cm, and 0.25N@8.0cm) and graphed it and of course I end up with a classic looking descending, concave looking graph which is the inverse square graph, I think.


    2. Relevant equations

    Now I have been puzzling over this for quite a while and even asked my boss and some co-workers to help and even together we can not figure it out - the question is:

    "manipulate the data so that the graph is a straight line graph"


    3. The attempt at a solution

    I have tried doubling the charge, halving the distance, square rooting the distance, etc.

    It always seems to end up with the same shape.

    I think I might be missing the fundamental lesson here. Hopefully someone here can offer some insight.
     
  2. jcsd
  3. mgb_phys

    mgb_phys 8,952
    Science Advisor
    Homework Helper

    You have a relationship that is force = some_factor/distance^2
    And a straight line is y=mx + c

    So you need to put it into this form.
    y (ie. force) = m x (ie. 1/r^2 )
     
  4. Thank you very much - I knew it was something fundamental.

    I have been out of school for several years and am taking a course to upgrade and the formula for the graph of a line is something I have completely forgotten!

    So I need to manipulate my F=kq/r^2 into a form that matches y=mx + c?

    I will make an attempt to do so.
     
  5. mgb_phys

    mgb_phys 8,952
    Science Advisor
    Homework Helper

    Yes just plot force against 1/r^2
     
  6. Ok, I am still struggling with this.

    If i used y=mx or in this case F=m(1/r^2) I am going to get the same answers am I not?

    I can't see the difference between F=m/r^2 and F=m(1/r^2) where m is equal to kq.
     
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