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How many pieces of paper will fit under the string?

  1. Oct 12, 2011 #1
    1. The problem statement, all variables and given/known data

    The earth is a sphere with a radius of 24, 843 miles. You wrap a piece of string around
    the earth so that it fits snuggly. THEN, you cut it, add 10 feet to the string, and adjust
    it so that it has equal height all around the world. Question: How many pieces of
    paper will fit under the string (thickness = 0.01 inches).

    2. Relevant equations

    C=2pi(R)

    3. The attempt at a solution

    C1=2pi(24,843)
    C2=2pi(24,843.00189)

    C2-C1=0.1189997 miles

    0.1189997 miles/ 2p i= R= 0.001893939miles

    0.001893939mile x 5280/1mi = 9.999998174 feet

    9.999998174 feet x 12in/1 ft =119.9999781 in

    119.9999781 in/0.01 in = 11999.99781 sheets of paper

    My answer seems unrealistic. I thought to solve this problem I would subtract the two circumferences and then divide the answer by 2pi to find the length of the gap and then i would use conversion factors to figure out the amount of papers that would stack up.
     
  2. jcsd
  3. Oct 12, 2011 #2

    SammyS

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    It's several time too big.
     
  4. Oct 12, 2011 #3
    Did I do it wrong?
     
  5. Oct 12, 2011 #4

    SammyS

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    C = 2π(R)

    And C + 10 = 2π(R+h), where h is the height of the string above the surface of the sphere. Expand the right side out. Then substitute C for the 2πR on the right side & solve for h.
     
  6. Oct 12, 2011 #5
    2∏(24848) +10 = 2∏(24848) + 2∏h

    10=2∏h

    10/2∏=h

    h=1.5915

    h/0.01 = 159.154 sheets of paper

    Is this correct?
     
  7. Oct 12, 2011 #6

    NascentOxygen

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    Did you convert inches to feet? I make it fewer than 2000 sheets.
     
  8. Oct 12, 2011 #7

    SammyS

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    This gives C + 10 = 2π(R) + 2π(h)
          = C + 2π(h)​
    Solve for h.

    This gives h in feet. multiply by 12 to get inches.

    I agree with NascentOxygen's calculation.
     
  9. Oct 13, 2011 #8
    I think I got it this time. Thanks for the help.

    2πr +10 = 2πr+ 2πh
    2π(24848)+10 = 2π(24848)+ 2πh

    10π=2h

    10/2π=h

    h=1.5915 ft
    h=1.5915ft x (12 in)/(1 ft)
    h/0.01 = 1909.8 sheets of paper
     
  10. Oct 13, 2011 #9

    SammyS

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    Looks good.

    Notice that you really didn't need to plug in 24848 ft for r.
     
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