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Experiment to Investigate Air Resistance

  1. Oct 28, 2015 #1
    1. The problem statement, all variables and given/known data
    I collected data for an experiment involving air resistance. We made paper disks and timed how long they took to fall over a fixed distance. We changed the radius of the disk. We found that as you increase the radius they take longer to fall. I am trying to explain my results but with some difficulty.

    2. Relevant equations


    3. The attempt at a solution
    We have been taught about forces expeienced by falling object e.g. weight and drag. I was thinking that if you double the radius of the circle then the area will increase by a factor of 4 which means the weight force will increase by a factor of 4. Since we found that it took longer for a bigger radius, the air resistance must not be proportional to the area. We have not been given any equations for air resistance but I did some research and found this one (https://en.wikipedia.org/wiki/Drag_equation). You can see that the drag force is in fact proportional to the surface area. However, if you double the radius the area should increase by a factor of 4 which means the weight will increase by a factor of 4 but according to this equation so should the drag force which means a paper circle of a bigger radius should take the same time to fall. What am I missing here? I know I am missing somehting because if this were true then for a given material e.g. a parachute it wouldn't matter how big you make the surface area and we all know that it does.
     
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  3. Oct 28, 2015 #2

    mfb

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    Usually paper circles doesn't fall in a smooth and repeatable way. How did you perform your experiment?
     
  4. Oct 28, 2015 #3

    PeroK

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    What about the coefficient of drag? Which is part of the drag equation.
     
  5. Oct 28, 2015 #4
    Hi. We actucally used a pair of scissor and made a single cut to the centre of the circle and gently twisted it into a cone. We then dropped the cone with the tip pointing downwards so that it fell nicely. Surely I have something wrong with the physics though because if you had some material to make a parachute then a parachute with a bigger surface area would be more effective? However, since the parachute is roughly circular then doubling the surface area should double the weight?
     
  6. Oct 28, 2015 #5

    PeroK

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    It doesn't double the weight of the parachutist, though!
     
  7. Oct 28, 2015 #6
    Thanks. So would a paper circle with a bigger surface area have a different coefficient?
     
  8. Oct 28, 2015 #7
    Why not? If it has roughly the same thickness then wouldn't a parachute with twice the surface area effectively mean you have twice as much parachute (so twice as much weight)?
     
  9. Oct 28, 2015 #8

    PeroK

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    What do you think? Does size matter?
     
  10. Oct 28, 2015 #9

    PeroK

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    The parachutist is the person hanging on the parachute. Their weight doesn't change.

    7467702-parachutist--Stock-Vector-parachute-skydiving.jpg
     
  11. Oct 28, 2015 #10
    No, I meant that if you designed two separate parachutes - the second one with twice the surface area.
     
  12. Oct 28, 2015 #11

    PeroK

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    I'd quite happily throw a toy soldier out of an aeroplane with a pocket hankerchief as a makeshift parachute, but I wouldn't bet on it holding my weight as I fell to Earth! Would you?
     
  13. Oct 28, 2015 #12

    JBA

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    You should realize that generally the weight of a parachute itself is only a portion of the weight it is carrying; and, as a result, the small percentage of added material weight has much less effect than the increased area drag. For example, if the parachutist weighs 200 lbs and the parachute weighs 15 lbs., then, a 10% increase in the parachute weight is 1.5 lbs or 16.5 lbs total. As a result. the total % increase in the parachutist + parachute = 216.5 / 215 = 1. 007% as apposed to a 10% increase in drag.

    Actually, the total packed weight of a parachute including an aerobatic harness with a 240 lb rated load is 15 lbs.
     
  14. Oct 28, 2015 #13
    No indeed not. I understand that though because with much smaller parachute you would have a lot less air interacting with it as it fell so it would not work with someone who has a much larger weight force. I am more interested with object itself falling and not with a parachute with someone on the end. If a paper circle has four times the surface area then why does it fall slower because it should also have increased its weight by four times?
     
  15. Oct 28, 2015 #14

    PeroK

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    Well, then we're back to coefficient of drag. Can you think of any reason why the coefficient might depend on size, not just shape?
     
  16. Oct 28, 2015 #15
    No not really. The way I see it is that an object with four times the surface area will experience four times more resistive forces as it interacts with the air molecules. Could you kindly explain?
     
  17. Oct 28, 2015 #16

    PeroK

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    Where do the air molecules go? Perhaps think about something flat falling.
     
  18. Oct 28, 2015 #17
    They would get deflected downwards as they collide with the surface?
     
  19. Oct 28, 2015 #18

    PeroK

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    And perhaps sideways as well?
     
  20. Oct 28, 2015 #19
    Yeh I guess some of them would get deflected sideways.
     
  21. Oct 28, 2015 #20

    PeroK

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    How far sideways?
     
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