The ends of the rope are at the same height h, and at a horizontal separation d.
2007-07-13 01:48:22 · 4 answers · asked by John S2005 3 in Science & Mathematics ➔ Mathematics
A horizontally suspended slack rope describes a parabola.
y=X^2
2007-07-13 01:55:44 · answer #1 · answered by Anonymous · 0⤊ 2⤋
It is a Catenary. What makes it interesting is that it is the shape that describes the "least energy" position for a suspended rope. Just like everything else in nature, if there were a way the rope could find a lower-energy configuration, it would.
I also blame this idea for why I don't go to the gym, slack on homework, etc. ;)
2007-07-13 09:21:12 · answer #2 · answered by Anonymous · 0⤊ 0⤋
The curve is named a catenary and its equation is
y = A cos hyp (x/B)
You can introduce your conditions:
At x=h y = h and at x= d y=h
(wrong)I would like to add that initial conditions are
At x = d/2 y=h and the other equation to define A and B depends on the weight per unit length of the rope
2007-07-13 09:05:29 · answer #3 · answered by santmann2002 7 · 0⤊ 0⤋
y = ax^2 + bx + c........a>0
height h = y value
horizontal separation d => min. Y value = h-d
h = ax^2 + bx + c
2007-07-13 09:02:30 · answer #4 · answered by harry m 6 · 0⤊ 0⤋