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MarWarHamp wrote:
Ed, I was going to offer titles to airplanes. 47 vs 67. But I knowWarren,
the one thing you are over looking. The tension on the first side. Sorry
friend but it is not pulling down. What it is doing is holding tension to
the pulley. Because the weight is pulling down on the other side. The force
trying to run to the weight. That force is the tension. The pulley is only
a transfer point of direction of that tension. Because of that side X and
side Y equal. The pulley supporting L the weight = the force on the pulley FOr do this. Draw this X = attach point. Above the X draw a O =
pulley. To the left make a W = weight. Now draw a line from X over O and
down to W.
Remember that W is trying hard to pull O and X at the same time. And
with equal force. Or put this way O and X together.
If your still confused. Here a bill of sale. Just how much do you
trust your words?:-)
I'd love to have an extra plane, but I really can't afford the upkeep on the one I have now. Also, you've been a good friend to us all and I want to keep you flying that plane.
Here's another way to view it. Copy this diagram into your word processor and make be Courier type so it comes out the way I'm drawing it.
diagram A diagram
B
|
|
_S1_
S4
/ O \
|
| |
|
| |
|
| |
|
| |
|
| |
|
| |
|
_S2__S3_
__S5_
| 200lb. |
|____|
|________|
100lb.
Where
S1 is the spring scale at the pulley end of the assembly.
O is the pulley with the cable free to go around.
S2 is the spring scale at the fixed end of the pulley (attached to
a weight).
S3 is the spring scale at the adjustable end of the pulley (also attached
to a weight).
S4 is the spring scale at one end of a straight cable
S5 is the spring scale at the other end of a straight cable.
Diagram B
It's obvious that if you have a 100 lb. weight suspended from the cable
on the right, S5 will show 100 lb. force. Also obviously, the spring scale
S4 will also show 100 lb. force (because it's pulling exactly the same
as S5.
Diagram A
Not so obviously,
If S3 is pulling (and showing) 100 lb. of force, S2 will pull and show
the same force, 100 lb.
Since this cable is redirected around a pulley, both ends of the cable
can be attached to the same weight giving TWO pulls on the weight of 100
lb.
If the ASSEMBLY is being pulled down the page by the weight, with two ends of the cable, each pulling (through the spring scale) 100 lb., the assembly of the two strands (from the top of the diagram to the bottom) can support 2 x 100 lb. It can support 200 lb.
There's a 200 lb. force pulling down on the assembly and the force on the attachment point on the top, at S1, is 200 lb. (it's got to hold the weight up).
This is the mechanical advantage principal used in a block and tackle. A block and tackle with multiple pulleys can lift a lot of weight without your pulling too hard on the loose end of the rope. The rule is: you divide the total force of the block and tackle ASSEMBLY (how much it's lifting) by the number of strands going between the two arrays of pulleys to get the force you need to pull on the loose end of the rope.
Example: if I have an array with three pulleys ganged together at the top and three at the bottom, I end up with six strands of rope between the two sets of pulleys. If I pull on the loose end of the rope with 100 lb. of force, I can lift a 600 lb. weight -- but I've got to pull 6 feet of rope to lift the weight 1 foot.
What they're trying to say, is, if you have a control assembly with two cables, each pulling 175 lb., the force pulling on the the rivets at the tail attachment point is 350 lb. and that seemed like a lot of continuous pull.
My physics textbooks are in boxes buried in my store room and I can't spare the time to dig them out and scan and post the pages, but it really is so. If you can find a physical science textbook or a first year physics book, you will find in the section on mechanical advantage this exact discussion. It's not easy to conceptualize and believe right down deep. It may be necessary to get some string, weights, pulleys and spring scales and play with it to convince yourself.
But I guarantee that if you have a pulley with two strands shown like diagram A, above, each strand will show a pull of X and the force pulling the two ends of the assembly toward each other is TWO times X.
Ed Burkhead
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