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Energy question - How much will this rope swinger rise

  1. Feb 7, 2009 #1
    1. The problem statement, all variables and given/known data
    JayJay is running topspeed of 8 meters/seconds, he grabs a string handing vetical fr. a tall-tree. how high will he swings upwards,b.does the length of the string affect the total height?c. if it tkaes him 2s to reach that height, how long is the string.d.explain why the lengh of the string does or doesn't affect the heght.e. find the horizontal distance of the swing.


    2. Relevant equations

    PE=mgh KE=1/2(mv2) v=(2piA)/T
    KEmax=1/2(mv2)max=PEmax=1/2(kA2)
    T=s[o(sq.root of l/g)
    3. The attempt at a solution

    what i did was using PE and equals it to KE, because this will cancel out the m(unknown). so i have 3.2m as the height he will swing upward. I said yes to b. because if the length of the string is longer then, the total height will increase also. for c, i used the v eq. and have 2.55m for the lengthof the string. I don't know how to find the horizontal distant of the swing. thank you for the help.
     
  2. jcsd
  3. Feb 7, 2009 #2

    Doc Al

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    Re: plz help..

    OK.
    When you found the height (part a) did you need to use the length of the string?
    How did you solve for the length? I don't understand.


    Also: "plz help" is not a good title for a thread. (All threads in Homework Help are requests for help. :wink:) Try to be more descriptive.
     
  4. Feb 7, 2009 #3
    Re: plz help..

    eheheh sorry for the title, i'll be more descriptive next time. sorry.

    for part b. no, i didint use te length of the string to find part a. so i guess the answer is no then. when it said total height, i thought it meant the height he jumped and the vine length.

    for c. i used the v=(2piA)/T
    he 2 seconds and his velocity 8m/s was given. so
    8m/s= 2pi(A)/2s, so A=2.55m , A=length
    i hope i made it clear enough. thank you
     
  5. Feb 7, 2009 #4
    Re: plz help..

    you know i just thought of, for e. can i use v=d/t ? because v and t is given. so vt=d. 8*2=16m?
     
  6. Feb 7, 2009 #5

    Doc Al

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    Re: plz help..

    That's an equation for the speed for uniform circular motion--not relevant here.

    Hint: Think pendulum.
     
  7. Feb 7, 2009 #6
    Re: plz help..

    so does it make sense to us eht T=2pi(sq.root(l/g)? i appreciate your help and coping with my ignorance =x
     
  8. Feb 7, 2009 #7

    Doc Al

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    Re: plz help..

    Yes, that's what you need. Use it wisely.
     
  9. Feb 7, 2009 #8
    Re: plz help..

    when i used the pendulum eq.
    2s = 2pi(sq.root l/9.8 m/s2)
    i got l= .9929 m

    so now i got 3.2m as the height he swing upwards
    b. no, the lenght of the string doesn't affect the total height
    d. because i didnt need the height of the string to find the height jayjay swing upwards
    c. length of the vine is .9929m which is approx. 1meters
    e. to find the horizontal distance of the swing use v=d/t
    which is 8m/s=d/2s = horizontal distance is 16 m
    is that right/good?
     
  10. Feb 7, 2009 #9

    Doc Al

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    Re: plz help..

    Careful. 2s is the time it takes to go from the bottom position to the highest point, not the period of the pendulum motion. What is the full period?
     
  11. Feb 7, 2009 #10
    Re: plz help..

    can you give me a hint on how to find the full period of the pendulum motion?
     
  12. Feb 7, 2009 #11

    Doc Al

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    Re: plz help..

    For a full period, the pendulum must complete a full cycle. That means if you start counting when the pendulum is at the bottom and moving to the right (say) the cycle won't be complete until its gone all around and once again is at the bottom and moving to the right.

    In your problem, the "pendulum" only swings for a portion of the cycle. What fraction of the period does it swing when it goes from the bottom to the top?
     
  13. Feb 7, 2009 #12
    Re: plz help..

    1/4?
     
  14. Feb 7, 2009 #13

    Doc Al

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    Re: plz help..

    Right!
     
  15. Feb 7, 2009 #14
    Re: plz help..

    yay! i finally got that right...gosh..i thought i'll never get it...thank you thank you.

    ok....so lets try this again.

    so now i got 3.2m as the height he swing upwards
    b. no, the lenght of the string doesn't affect the total height
    d. because i didnt need the height of the string to find the height jayjay swing upwards
    c. length of the vine is (1/4)2s = 2pi(sq.root l/9.8 m/s2) which is .062059225m...is that an odd answer for length of a string?...i think i did something wrong??
    e. to find the horizontal distance of the swing use v=d/t
    which is 8m/s=d/2s = horizontal distance is 16 m

    is that right/good?
     
  16. Feb 7, 2009 #15

    Doc Al

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    Re: plz help..

    Yes, you made a mistake. The time given (2 s) is 1/4 of the period. So what's the full period?
    No. To find the horizontal distance you'll use the length of the string and the height of the swing and a bit of trig/geometry. (Note that 8 m/s is only the speed at the bottom of the swing; as the swing proceeds, the speed and direction changes.)
     
  17. Feb 7, 2009 #16
    Re: plz help..

    eheh i thought that too...it should of been 2s*4=2pi(sq.root l/9.8m/s2) which is 15.88m for the length of the string.

    so would i use a2 + b2 = c2?
    if so would it be (3.2)2 + b2 = (15.88)2?
    I really appreciate your help
     
  18. Feb 8, 2009 #17

    Doc Al

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    Re: plz help..

    Good.
    That's the right equation, but the height of the swing is not one of the sides of the triangle. Draw a picture of the initial and final positions of the string.

    Also: Recalculate the height a bit more accurately.
     
  19. Feb 8, 2009 #18
    Re: plz help..

    yea that makes sense, because the height of the swing is not involved in the triangle...
    the position of the string from initial and final had changed but the length of the string didnt change. so a2 + b2=c2 a and b is actually 15.88
    so (15.88)2 + (15.88)2 = distance of the horizontal swing squared
    which is 22.34m

    the more accurate height is 3.265m

    is this all correct??
     
  20. Feb 8, 2009 #19

    Doc Al

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    Re: plz help..

    While the height of the swing is not a side of the triangle, it is needed to calculate one of the sides.
    No. The triangle you want is a right triangle whose hypotenuse is the length of the string.

    Good. Use it to find the vertical side of the triangle above.
     
  21. Feb 8, 2009 #20
    Re: plz help..

    hypotenuse is the length of the string, which is 15.88.
    using a2 + b2 =c2
    i dont know how to use 3.265m ..the only thing i can think of is ....... cos 90 degrees=adj/hyp = 3.265m/15.88?
     
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