On Wed, 10 Sep 2008 20:15:50 -0700, "P D Fritz"
wrote:


"Larry Jaques" wrote in message
.. .
| On Wed, 10 Sep 2008 18:04:02 -0400, with neither quill nor qualm,
| "Mark Dunning" quickly quoth:
|
|
| wrote in message
| ...
| When applying force perpendicular to a tight wire, the force
| multiplies by a large factor.
|
| I don't grok that, Ivan. A pull on the middle of the rope would be
| equal on all 3 ends, wouldn't it?
|
| No, this is not a simple straight line mechanics problem of pulleys
| acting as levers, it's a vector addition problem. When you pull the
| rope out of line at the center, the component of tension perpendicular
| at each end of the main rope has to be very high to match the small
| component needed to offset the sideways pull, and this approaches
| infinity the tighter the main rope gets.
|
| What's the math/law/formula, Mark?
|

The Resultant Force(Fr) produced along a straight line perpendicular to the
pull force(Fa) would equal to the Force Applied(Fa) X Cotangeant of the
Angle(A) between the straight line and the pulled rope angle. [Fr = Fa(Cot
A)]
The resulting tension(Ft) on the rope would be equal to Fa/Sin A. [Ft
=Fa/SinA]

It is Applied Trigonometry in Mechanics.

That's how I pulled the shrubbery stumps out of the flower bed this
spring, a choker around the stump with a cable across the lawn to a
come-along anchore to a good size maple tree. A couple timber blocks
under the cable near the stump to re-direct the pull upward then apply
tension and jump on the mid point of the cable. took about an hour to
get the two stumps (one Yew, one Spruce) out. Next door neighbour was
impressed!
Gerry :-)}
London, Canada