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Air resistance in pendulum experiment

  1. Feb 23, 2008 #1
    hey guys, i've been experimenting with a pendulum and while doing the error discussion for my experiments i got stuck with the air resistance involved...
    I've used the formula to find the force applied by the air resistance to the pendulum and ended up with F=2,76*10^-5 *v^2 . (v= velocity of the pendulum).

    Basically i just want to estimate how much of an error percentage of my results air resistance has caused, but i don't have much of an idea how to calculate this percentage.
    thanks for your help!
  2. jcsd
  3. Feb 24, 2008 #2
    I suppose you mean drag force.

    F = K S v^2

    K: Constant
    S: widest cross-section
    v: velocity

    The velocity is changing time by time. Yo may not use one velocity to calculate it. In fact the velocity of body has,

    V = Vm Sin(wt)

    where V: sudden, Vm: max, w=2(pi)f and t: time

    But if we use a average worth, i would put my money to :) ,

    V = Vm/sqrt(2)

    this is better than others.

    F = K S ( Vm/sqrt(2) )

    this is a suggestion. Maybe there is a better solution.
  4. Apr 27, 2009 #3
    How do you calculate the cross section?
    Last edited: Apr 28, 2009
  5. Apr 28, 2009 #4
    What is the K?
  6. Apr 28, 2009 #5
    Sorry, assumed you know. Known air resistance formula,

    F= - 1/2 p v^2 A C

    p: density of the fluid
    v: speed of the object relative to the fluid
    A: reference area
    C: drag coefficient

    You can look at below link

    Mostly you don't calculate the effective cross sectional area. It is "reference area" in last equation. For a spherical body, widest cross section area is a circle which has the same radius of sphere. And forget K :) use the latest formula.

    Warning, I have no idea about finding(calculating) the effect of air resistance for pendulum. I am not sure about certainty of above(first) suggestion. Just an approach. I wanted to help you to find a good average drag force. So I find a good average velocity to use in formula.

    If you use a long string, even max. velocity will be more little. So drag force(air resistance) effect will be much less. But calculation is not so easy.
  7. Apr 28, 2009 #6
    So, basically calculating it is not even worth it if it is so small. So that probably wouldn't have an effect on our experiment. Thanks for the help.
  8. Apr 28, 2009 #7
    Don't forget, use little angles(less then 10 degree). This is for both simple pendilum condition and required for less velocity(air resistance).
  9. Apr 28, 2009 #8
    But how come, even when we used 45 degrees, the period, according to the photogate was still T=2π √(L/g)=1.22?

    L was 37cm=.37m

    My data was like this:

    Theta in degrees, T
    05, 1.194
    10, 1.196
    15, 1.201
    20, 1.203
    25, 1.209
    30, 1.215
    35, 1.223
    40, 1.238
    45, 1.241

    I am guessing that the ball was steel.....So is wind resistance even a factor there? Is it just my error?
  10. Apr 28, 2009 #9
    Look at here http://en.wikipedia.org/wiki/Pendulum you will see another period equation for larger amplitudes.

    Maybe because of bigger air friction :) larger degrees are not much big as expected. But look closer, T is already growing. Learn the exact acceleration of gravity and compare with yours then see which one is closer to formula.
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