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Two pipes are tied together

  1. Apr 10, 2010 #1
    1. The problem statement, all variables and given/known data
    The problem is pretty long but it is easy except one part where I need to calculate the length of a rope where 2 pipes are tied together tightly. We can reduce this to 2 dimensions so I drew a rough sketch of it. I didn't quite succeed with the the perfect drawing but you get the idea.

    Here's the sketch __alright.PNG

    So the informations we are given that the diameter of the bigger pipe's is 90cm, the smaller one's is 30cm.


    2. Relevant equations
    i = r*a(rad)
    K = 2*r*pi

    The total cc of the big circle is:~282.7cm ,and the smaller one is: ~94.2 cm

    3. The attempt at a solution
    I tried with Pythagoras' theorem but I realized with this kind of calculation, I get an approximation and not real solution.


    I then figured that I have to calculate the circumference of both circles then substract the lenght of the arc. Then I still have to find the distance between the two circles connected by the bridges.

    Since we only have the information of the radiuses I was thinking that we have to find a ratio between the circles and then can get the arc. I tried simplify it by creating 2 equal sized circles then shrinking one of them, but I got confused and couldn't get my ratios.


    So forum, can you lead me to success?
     
  2. jcsd
  3. Apr 10, 2010 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi Icelove! :smile:

    The straight parts will be the common tangents of the two circles, so draw the two radii: you know their lengths, and the distance between the centres, and you know that the tangent is perpendicular to the radii …

    from that, you can find the length of the tangent, and the angle between the radii and the line through the centres. :wink:
     
  4. Apr 10, 2010 #3
    tiny-tim, you are opening my math eye. I love you, thanks AGAIN. :)
     
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