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Setting Up Pulleys
Name: Ryan
Status: educator
Grade: 9-12
Location: MN
Country: N/A
Date: 4/1/2005
Question:
I am getting ready to do a unit on simple machines and
remember a lab I did as a student. We had to lift 150 lbs using 4
pulleys, one of which can change direction. The 150 lbs has to be lifted
using as little weight as possible. I do not remember what the best way
to set this up is. I have come up with some ways myself but would like to
know the very best set-up to share at the end. Do you have any
suggestions?
Replies:
Simply put, your best answer will be the one that has the rope doubling back
on itself as many times as possible. One pulley on the ceiling does nothing
but change the direction. A pulley on the load, with a fixed point on the
ceiling gives you a 2:1 mechanical advantage. (Rope goes down, Rope goes up)
If you are using the first one on the ceiling to change direction, you will
still have only a 2: 1 advantage. take the rope you're pulling though, put
it through a second pulley on the load, and you get a 4:1 advantage. Rope
goes down, Rope goes up, rope goes down (again), Rope goes up (again). Your
4th pulley reverses direction, allowing you to pull the rope more
efficiently.
Ryan Belscamper
Ryan-
At first all I could think of was this:
.___2_____1_2_4____.
| | | | | |
| /O\ | | | |
| | |1 | | | |
| | | | | | |
| m1 | | | | |
| | | | | |
| | | | | |
| \O/ | | |
| 2 | | | |
| \O/ | |
| 4 | | |
| \O/ |
| 8 | |
|__________M8______|
which I would describe, working from load (M8) to worker (m1),
as "3 cascaded 2:1's and a direction-changer".
The mechanical advantage is 2^3 = 8:1, which felt a little disappointing
for 4 pulleys.
Finally I realized that the direction changer could come first:
.__________16______.
| | |
| /O\ |
| 8 | | 8 |
| /O\ | |
| 4 | | | |
| /O\ | | |
| 2 | | | | |
| /O\ | | | |
| 1 / | | | | |
| m1 | | | | |
| | | | | |
| | | | | |
| | | | | |
|_______|_|_|_M8___|
1 2 4
and that it helps a lot to do so,
because all those floor-anchors can be detached from the floor and
re-attached to the load.
Then the ideal advantage approaches 15:1:
._______16_______.
| | |
| /O\ |
| 8 | | 8 |
| /O\ | |
| 4 | \| |
| /O\ | 12 |
| 2 | \ | |
| /O\ \| |
| 1 / \ | 14 |
| m1 \ | |
| \| |
| | 15 |
| | |
|_________M15____|
A pulley can do 2:1. 4 pulley's can do 2^4 = 16:1.
Take away 1 for having a direction reverser (the one at the top).
After all, your question specified downwards pull, which cannot be
directly used to help lift the load.
That is the "1 unit" of force which is lost.
So I suspect this is about the best you can do with the ropes all roughly
vertical.
In a cascading sequence of pulleys, often the counter-balancing ropes of
each pulley are anchored to ceiling or floor.
You can detach each of these and re-attach to the axle of a later pulley
(or to the load),
as long as you are displacing the attachment towards the "lower-gear" end
of the pulley sequence.
Displacing an attachment to a "higher-gear" place creates "fool's tackle",
a mechanical short-circuit,
or at least it makes the mechanical advantage smaller instead of larger.
(By "low-gear" I mean high-force / low-displacement, and the opposite
for "high-gear".)
This 15:1 cascade can only lift the load about 1/8 of the distance from
floor to ceiling.
Then the pulley nearest the worker reaches the floor.
Conventional tackle only gets 4:1 using 4 pulleys because they want to
retain 100% range of travel.
It can get shorter to "zero" length, or longer indefinitely, as long as
the worker pulls or feeds more rope.
Jim Swenson
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Update: June 2012
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