1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Relative Error?

  1. Sep 14, 2008 #1
    Relative Error!?

    If the relative error for the radius of a circle is 5%, what is the relative error for the circumference?

    I know that relative error is the ratio of the absolute error in a measurement to the size of the measurement, but I honestly have no idea how to complete the problem. These are one of the pre-lab problems, where we're supposed to try and figure it out before we're taught it, but I'm stumped on this one.

    PLEASE HELP!!
     
  2. jcsd
  3. Sep 14, 2008 #2

    LowlyPion

    User Avatar
    Homework Helper

    Re: Relative Error!?

    What is the formula for the circumference of a circle?

    If r is off by 5%, what effect will that have on the relative error of the formula for circumference?
     
  4. Sep 14, 2008 #3

    dlgoff

    User Avatar
    Science Advisor
    Gold Member

    Re: Relative Error!?

    Use the equation for finding the circumference from the radius. Since the radius is the measured variable, only error from it will apply.
     
  5. Sep 14, 2008 #4
    Re: Relative Error!?

    Well, I came up with two different answers using the circumference formula: 10% and 31.4%. I'm relatively uncertain if I've done this correctly, but I believe 31.4% to possibly be the correct answer. The problem that I'm stuck on seems to be the simplest!
     
  6. Sep 14, 2008 #5

    fluidistic

    User Avatar
    Gold Member

    Re: Relative Error!?

    The circumference of a circle is [tex]2\pi r[/tex]. As dlgoff said, we assume there is only an error in [tex]r[/tex], so what's the error of [tex]2\pi r[/tex]?
    EDIT: I think you got it right, the error would be [tex]2\pi \cdot 5[/tex]% which seems what you did.
     
  7. Sep 14, 2008 #6
    Re: Relative Error!?

    Wait...since circumference is proportional to radius, would that make the relative error of the circumference 5%, as well?
     
  8. Sep 14, 2008 #7

    LowlyPion

    User Avatar
    Homework Helper

    Re: Relative Error!?

    Try it this way. Think about what the relative error means.

    Doesn't it mean that the measured value can be as great as 5%?

    That (r+.05r)/r yields an error of 5%

    Now substitute that into the equation for the circumference.

    C = 2πr

    Now on the one hand the absolute error will be 2π greater, but then so would the nominal absolute result.

    In calculating your RELATIVE error you compare then the Error Result with the magnitude of the correct result.

    In that case it becomes (2π*(r+.05))/2π*r After simplifying though what are we left with? (r+.05)/r? And was that our original error in r?

    So what does that say about multiplying Relative errors by a constant?
     
  9. Sep 14, 2008 #8

    LowlyPion

    User Avatar
    Homework Helper

    Re: Relative Error!?

    There you go you beat me to it.

    Good thinking.
     
  10. Sep 14, 2008 #9
    Re: Relative Error!?

    Great! Thanks a lot for everyone's help! Great, GREATLY appreciated :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Relative Error?
  1. Thermo. Relative Error (Replies: 0)

Loading...