L. Marcus Posted February 17, 2009 Report Share Posted February 17, 2009 Re: Longest Running Thread EVER Touch, limb position, chill, and heat, their receptors, and the nerve paths to the sensory cortex in the parietal lobe of the brain. Quote Link to comment Share on other sites More sharing options...
Bazza Posted February 17, 2009 Report Share Posted February 17, 2009 Re: Longest Running Thread EVER o. k. Quote Link to comment Share on other sites More sharing options...
Mantis Posted February 17, 2009 Report Share Posted February 17, 2009 Re: Longest Running Thread EVER I don't think you'd actually need sine or cosine to find it. I think Pythagoras would be sufficient. Consider: The diameter of the pipe is 10 feet. Half its diameter (the radius) is 5 feet. Half the circumference of the pipe (the bottom, where the chain is) is 5*pi. The length of the chain not touching the pipe is 40-5pi. This is the total length of chain from the hook to where it touches one side of the pipe and from the other side of the pipe back up to the hook (assuming the chain is tangent to the side of the pipe at its widest point). The distance from the hook to either side of the pipe is therefore half of 40-5pi, or 20-2.5pi. This gives you the hypotenuse (20-2.5pi) and one side (5) of a right triangle. The distance from the center of the pipe to the hook is the other side, which you can find using Pythagoras. Subtract the radius of the pipe (5) from this result, and you have the distance from the hook to the top of the pipe. Right? Wrong (IMHO). The question is unsolvable, because you have the diameter of the pipe, which is irrelevant. What you need is the length. Here's an image of a pipe held by a chain sling to demonstrate the problem: Although, there are other ways to sling a pipe, so perhaps it is solvable, except you don't know which method is used: My answer would have been "Insufficient information provided." Quote Link to comment Share on other sites More sharing options...
L. Marcus Posted February 17, 2009 Report Share Posted February 17, 2009 Re: Longest Running Thread EVER I'd assume the data provided had relevance, otherwise the examiner should be chargrilled. Quote Link to comment Share on other sites More sharing options...
Cancer Posted February 17, 2009 Report Share Posted February 17, 2009 Re: Longest Running Thread EVER I didn't post the figure that came with the question since I don't have a scanner at hand, but I'll describe it. Look at the pipe end-on, so you're looking at a circle. The chain is a single loop, running under the pipe, starting and ending at a hook above the pipe. So draw symmetric tangents to the circle which cross somewhere above the pipe, and that's where the hook is. Pipe outer diameter is specified as 10 feet. Total length of chain is specified as 40 feet. Start by drawing a circle with center O. Draw a vertical diameter to that circle, which passes through the bottom (point and top (point T) of the circle, and extends upward to point H (the hook). Draw a tangent to the circle that passes through point H. Label the tangent point X. The radius of the circle = side OX = r. The length of the arc from B to X, plus the length HX, sum to half the length of the chain, 20 feet. Let us call b (in radians) the angle BOX. The length of arc BX is simply r * b. Draw right triangle HOX. Angle H is equal to (b - pi/2). The ratio HX/OX is equal to tan(H) = tan(b - pi/2), so HX = OX * tan(b - pi/2), and OX = r, so HX = r tan(b - pi/2). From what we said above, r tan(b - pi/2) + r * b = 20 feet, and r = 5 feet, so we arrive at the transcendental equation tan(b - pi/2) + b = 4. Solve for angle b. Finally, the quantity that was asked for is HT = HO - r. HO = HX / cos(b - pi/2). Quote Link to comment Share on other sites More sharing options...
L. Marcus Posted February 17, 2009 Report Share Posted February 17, 2009 Re: Longest Running Thread EVER . . . I was nearly there! Quote Link to comment Share on other sites More sharing options...
Cancer Posted February 17, 2009 Report Share Posted February 17, 2009 Re: Longest Running Thread EVER Sorry. I did use the spoiler tag, but I guess I didn't say what was under it. Quote Link to comment Share on other sites More sharing options...
L. Marcus Posted February 17, 2009 Report Share Posted February 17, 2009 Re: Longest Running Thread EVER No, that's cool, I figured what it was. I was just tired of radians, and wanted the facit. Quote Link to comment Share on other sites More sharing options...
Cancer Posted February 17, 2009 Report Share Posted February 17, 2009 Re: Longest Running Thread EVER With luck, I'll be able to scale down a couple of kitten pics tonight and post them tomorrow. Black, long-hair, folded-ear kittens. Quote Link to comment Share on other sites More sharing options...
L. Marcus Posted February 17, 2009 Report Share Posted February 17, 2009 Re: Longest Running Thread EVER Are they Teh Kyootzorz? Quote Link to comment Share on other sites More sharing options...
Cancer Posted February 17, 2009 Report Share Posted February 17, 2009 Re: Longest Running Thread EVER Only you can decide that. The big problem is that black cats don't photograph easily. I've got an image or two that seems to look OK, though. Quote Link to comment Share on other sites More sharing options...
L. Marcus Posted February 17, 2009 Report Share Posted February 17, 2009 Re: Longest Running Thread EVER Are they that stealthy? Quote Link to comment Share on other sites More sharing options...
lemming Posted February 17, 2009 Report Share Posted February 17, 2009 Re: Longest Running Thread EVER Are they that stealthy? They absorb all light and heat in their vicinity. You just need to fuss with lighting more with them which makes them harder snapshot subjects. Quote Link to comment Share on other sites More sharing options...
L. Marcus Posted February 17, 2009 Report Share Posted February 17, 2009 Re: Longest Running Thread EVER Very stealthy. Quote Link to comment Share on other sites More sharing options...
SteveZilla Posted February 17, 2009 Report Share Posted February 17, 2009 Re: Longest Running Thread EVER As it was posted on the board upstairs' date=' "A decimal approximation will be sufficient, but explain all reasoning." Given that you have to solve a transcendental equation, I'd guess so.[/quote'] I haven't had the time to devote myself to cracking this just yet, but I want to post a musing about it. Draw a radius where the outermost point is also the point where the suspending chain separates from the pipe, and measure the angle from that to the vertical. I call this the "Angle of Contact". The Angle of Contact can vary between zero degrees (when the chain is the same length as the pipe's circumference, and 90 degrees (an infinitely long chain). Thus, IMO it seems that the distance from the top of the pipe to the hook relative to the *extra* length of chain (i.e., the part greater than the pipe's circumference) is a tangent-like function. But I could be way, way off. Once, I derived a formula for a problem with a very similar looking diagram. Imagine an astronaut approaching an unexplored planet. He can measure the angular size of the planet, and his radar tells him how far he is from the ground directly in line with his ship. He needs to calculate the planet's diameter from these two pieces of information. EDIT: I haven't peeked under Cancer's spoiler tag yet. Quote Link to comment Share on other sites More sharing options...
Bazza Posted February 18, 2009 Report Share Posted February 18, 2009 Re: Longest Running Thread EVER I have. like a kilt, better off not looking. Quote Link to comment Share on other sites More sharing options...
L. Marcus Posted February 18, 2009 Report Share Posted February 18, 2009 Re: Longest Running Thread EVER Curiosity kills. Quote Link to comment Share on other sites More sharing options...
Bazza Posted February 18, 2009 Report Share Posted February 18, 2009 Re: Longest Running Thread EVER the dogcow Quote Link to comment Share on other sites More sharing options...
L. Marcus Posted February 18, 2009 Report Share Posted February 18, 2009 Re: Longest Running Thread EVER Mrowf. Quote Link to comment Share on other sites More sharing options...
Bazza Posted February 18, 2009 Report Share Posted February 18, 2009 Re: Longest Running Thread EVER Mrowf. offically it is Moof. if you don't believe me look it up. Quote Link to comment Share on other sites More sharing options...
L. Marcus Posted February 18, 2009 Report Share Posted February 18, 2009 Re: Longest Running Thread EVER Depends on the breed of the dog part. That "mrowf" sound would be if the sire was a Great Dane. Quote Link to comment Share on other sites More sharing options...
Bazza Posted February 18, 2009 Report Share Posted February 18, 2009 Re: Longest Running Thread EVER Depends on the breed of the dog part. That "mrowf" sound would be if the sire was a Great Dane. na-ah, there is only one "breed" of dogcow. Quote Link to comment Share on other sites More sharing options...
L. Marcus Posted February 18, 2009 Report Share Posted February 18, 2009 Re: Longest Running Thread EVER Diff'rent cow breeds, diff'rent dog breeds . . . An SLB crossed with a Golden Retriever will certainly be dissimilar to a Chihuahua crossed with a Cape Buffalo. Quote Link to comment Share on other sites More sharing options...
Bazza Posted February 18, 2009 Report Share Posted February 18, 2009 Re: Longest Running Thread EVER Diff'rent cow breeds' date=' diff'rent dog breeds . . . An SLB crossed with a Golden Retriever will certainly be dissimilar to a Chihuahua crossed with a Cape Buffalo.[/quote'] I'm gonna have to educate you, you know! Quote Link to comment Share on other sites More sharing options...
L. Marcus Posted February 18, 2009 Report Share Posted February 18, 2009 Re: Longest Running Thread EVER Can't make me! Quote Link to comment Share on other sites More sharing options...
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