1. Limited time only! Sign up for a free 30min personal 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!

Potential energy of rubber bands

  1. Apr 11, 2017 #1
    <Mentor's note: moved from a general forum and therefore no template>

    upload_2017-4-12_4-28-28.png
    This is the equation of potential energy in rubber bands, however, I don't know how to calculate the inertia of the arm of catapults or get the k constant. And what does n mean? Basically, i don't understand the whole equation.
    The energy balance, where N is the number of rubber bands, k is the spring constant of a single rubber band, x0 is the unstretched length of a rubber band, m the mass of the ball, and I is the moment of inertia of the arm.
    Can someone please show me an example of how to calculate this?
    I used a marshmallow which is 0.007 kg, I stretched the catapults to 0.1 m, it has an angle of 35 degrees
    range=0.793
    initial velocity=2.88 m/s
    time=0.337 s
    max height=0.139 m
    horizontal velocity=2.36 m/s
    vertical velocity=1.65 m/s
    Thats all i know and i hope it helps! please help me figure this out!
     
  2. jcsd
  3. Apr 11, 2017 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    That equation is rather unusual. It implies the force needed to stretch the rubber rises as the square root of the extension, whereas the usual law says it rises linearly. Is it possible that x here refers not to the actual extension but to some other displacement within a mechanism supporting the rubber band? Is there a diagram?
     
  4. Apr 11, 2017 #3
    Yes here you go
    upload_2017-4-12_6-3-53.png

    And here is a link with further information
    http://www.sciencebuddies.org/content/pdfs/projectideaskits/phys_p089/phys_p089_20131021.pdf
     
  5. Apr 11, 2017 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Ok, I see that the text states that the rubber bands provided do have a nonlinear force/extension relationship.
    It gives a formula in note 3 under Experimental Procedure.
    However, I see that it defines I as the moment inertia about the mass centre of the arm. That is not what you want. The arm rotates about one end, not its mass centre. The text says to use I = 1.1 x 10-3kg*m². If that really is the MoI about the mass centre then you need to add ML2/4 where L is the length of the arm and M its mass. But it is possible they mean the MoI about one end is 1.1 x 10-3kg*m².
    You can check this by measuring L and M and using:
    MoI about mass centre = ML2/12
    MoI about one end = ML2/12+ML2/4=ML2/3.
    See which of those is closer to 1.1 x 10-3kg*m².
    See note 5 under Experimental Procedure.
    As you wrote, N is the number of bands in parallel. I think it is up to you how many you attach.
     
  6. Apr 11, 2017 #5
    Ohh i see thank you so much for your reply, however it only applies for non-linear? but my graph is linear... is there any other way to get the potential energy for linear relationship?
     
  7. Apr 11, 2017 #6

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    What graph? What values are you plotting on the axes?
     
  8. Apr 11, 2017 #7
    upload_2017-4-12_7-23-32.png
     
  9. Apr 11, 2017 #8

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

  10. Apr 12, 2017 #9
    Oh sorry Im a newbie in physics and math, could you explain what x2-x0 mean? :frown::frown::frown::frown::frown::oldfrown:
     
  11. Apr 12, 2017 #10

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    They appear in the equation you posted originally. They are defined in the link you provided. I have the feeling you have not read that page fully.
     
  12. Apr 12, 2017 #11
    no, I did but I didn't cover much of physics so i couldn't understand thats why i asked in this website so i can learn more
     
  13. Apr 12, 2017 #12

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    This much is not a question of physics. What does it say x0, x1 and x2 represent?
     
  14. Apr 12, 2017 #13
    I don't really know but at first, I thought it might mean initial velocity, is it?
     
  15. Apr 12, 2017 #14

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    No, they're lengths of the elastic. As it says, x0 is the unstretched length. I thought it defined x1 and x2, but maybe I imagined it. x1 is the stretched length just before firing. At the end of firing (release of projectile) it may not have returned to its unstretched length, instead being length x2.
     
  16. Apr 12, 2017 #15
    ohhh alright thank you sir! i will read more about the topic and if i have more questions ill ask :woot:
     
  17. Apr 13, 2017 #16
    In general, rubber is nonlinear and nonconservative. This means that
    (1) force will not be proportional to the elongation;
    (2) work put in will not be fully recovered when the stretched piece of rubber is released.
    This makes energy calculations with rubber bands rather iffy.
     
  18. Apr 13, 2017 #17

    kuruman

    User Avatar
    Homework Helper
    Gold Member

    To which I will add that rubber bands also display hysteresis; the work that is recovered depends on what has already been done to the band in terms of stretching and relaxing.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Potential energy of rubber bands
  1. Rubber band (Replies: 7)

Loading...