Science Puzzle
Can You Pull a Rope Perfectly Straight?
Two strong people stand a few metres apart and pull on the ends of a rope. A 1 kg bag of sugar hangs from the middle of the rope, so it sags into a shallow V. The harder they pull, the straighter the rope gets.
If they were strong enough, and the rope never snapped, could they pull it perfectly straight?
The Answer
No. A rope holding up any weight at all can never be pulled perfectly straight.
Each half of the rope pulls along its own length. Only the part of that pull that points upwards helps hold the bag up; the rest just pulls against the other person. When the rope sags steeply, a good share of each pull points upwards. As the rope gets flatter, that share shrinks, so the people must pull harder and harder to keep supporting the same 1 kg.
The numbers climb fast. With each side of the rope dipping at 10 degrees, each person must pull with about three times the bag's weight. At 1 degree, it's nearly 30 times. At a tenth of a degree, nearly 300 times. A perfectly straight rope would point no part of its pull upwards at all, so it would need an infinitely strong pull. Even with no bag, the rope's own weight means it always sags a little.
Engineers design for this. Power lines are hung with a deliberate sag, because a line pulled nearly straight would have to carry enormous tension and could snap, especially in winter, when cold makes the metal shrink and pull tighter. The main cables of suspension bridges sag in great curves for the same reason.
The principle: Resolving forces. Only the part of a force acting in a given direction counts in that direction; as a supporting rope approaches horizontal, the tension needed to hold a load grows without limit.