rope tension problem. A cord is put under P pounds of tension at the horizontal. A mass with weight W is attached to the center. The rope sags, creating an angle theta. What is the tension on the rope now?
Re: rope tension problem Mate, consider it this way (this way is called vector analysis). It took several face to face lessons to learn this as an engineering student (25 years ago), and now I'll try and explain it by typing a few sentences.Think of it as a load suspended by two ropes. Each rope is taking two tension components, a vertical and a horizontal. The two vertical force components (one for each rope) add to the weight of the load and prevent it from accelerating due to gravity. The two horizontal tensions are of equal magnitude, but in opposite directions; thus summing to zero. (Otherwise the unbalanced force would accelerate the load away.)To quantify the tensions use your scale drawing. Draw the angles correctly. Solve each right angle triangle separately, the sides of the triangle will be proportional to the force components; with the hypotenuse proportional to the rope tensions. To figure out the proportions use the things you know 1) Load W 2) Now the length shown by the sag will be proportional to half load W and 3) The two horizontal tensions are of equal magnitude.The above will work on any load suspended by two ropes. Given you are talking hammocks and thus (I suspect) having the load about half way between two anchors that are about the same height your two triangles are very similar. This makes the math much simpler (avoids simultaneous equations). It was a struggle raking that unused info from my tired old brain, but I hope that helps.AnywaysBottom line is:- the flatter your suspension lines the higher their tensions. This is a trigonometric ratio (not proportional). As the two suspension ropes approach a straight line the tension in them approaches infinity (so they stretch longer and sag out of line, and thus relive themselves - until....) A hang that flat is not comfortable so this won't be a problem for hammockers - unless you use a structural ridge line, In which case make sure your ridge line only slightly deflects your suspension lines. I weigh 100kg and use 600kg UHDPE suspension lines. This gives a SF of about 3 - not 6. (I've not measured the angles & done the calc.)