Searching \ for '[TECH] The theory of pulleys' in subject line. ()
Make payments with PayPal - it's fast, free and secure! Help us get a faster server
FAQ page: www.piclist.com/techref/index.htm?key=theory+pulleys
Search entire site for: 'The theory of pulleys'.

Exact match. Not showing close matches.
PICList Thread
'[TECH] The theory of pulleys'
2010\05\18@005738 by Russell McMahon

face picon face
What Vic said.

Note that you can arrange some confusing arrangements that appear to
alter the arrangement but don't.

So:

- Tension in rope is supported_load / ropes_supporting load when ropes
are perpendicular to gravitational field

- Tension in rope is constant everywhere for a static load.

- if you build  systems with ropes at angles to the gravitational
field then you need simple force- vector additions BUT the principle
is the same. (Sum of vertical forces applied to the load is zero. Some
of all horizontal forces applied to the load is zero).

- Dynamic / moving system, all bets are off.


            R

2010\05\18@011909 by Marechiare

picon face
>> Now I detach myself from the floor
...
> Can't picture this!

Perhaps this way:
http://bulfinch.englishatheist.org/baron/images/img_39[1].jpg

2010\05\18@093508 by Russell McMahon

face picon face
> To make this very simple terms.  Take the number of ropes attached to to
> the MOVEABLE pulleys divide that into the weight being lifted  and that
> is the force required to lift the object.

As long as all ropes are vertical :-)

            R

2010\05\18@100604 by Alan B Pearce

face picon face
>> To make this very simple terms.  Take the number of ropes attached to to
>> the MOVEABLE pulleys divide that into the weight being lifted  and that
>> is the force required to lift the object.
>
> As long as all ropes are vertical :-)

Well, only if it is lifting a free hanging mass.

But the principle is exactly the same for a block and tackle pulling
something up an incline, all the rope lengths going to the moving mass are
under equal tension.

2010\05\18@110200 by Alan B Pearce

face picon face
>> To make this very simple terms.  Take the number of ropes attached to to
>> the MOVEABLE pulleys divide that into the weight being lifted  and that
>> is the force required to lift the object.
>
> As long as all ropes are vertical :-)

Well, only if it is lifting a free hanging mass.

But the principle is exactly the same for a block and tackle pulling
something up an incline, all the rope lengths going to the moving mass are
under equal tension.

2010\05\18@111512 by Russell McMahon

face picon face
> >> To make this very simple terms.  Take the number of ropes attached to to
> >> the MOVEABLE pulleys divide that into the weight being lifted  and that
> >> is the force required to lift the object.
> >
> > As long as all ropes are vertical :-)
>
> Well, only if it is lifting a free hanging mass.
>
> But the principle is exactly the same for a block and tackle pulling
> something up an incline, all the rope lengths going to the moving mass are
> under equal tension.

E&OE :-) ...

My point (not being quoted above) about ripes being vertical is that
ropes can be at an angle to the resisting force field so that only a
component of the rope tension supports or pulls the load. Such cases
complicate the simple examples for beginners.

eg -  2 horse pull a cart up a ramp by a rope fastened to a pulling
collar on each horse and passing through a single pulley in the front
middle of the cart. The horses are 6 feet apart and the pulling collar
attachment s are 10 feet in front of the cart.

If the drawbar pull on the cart is say 200 lbf the rope tension will
NOT be 200/2 = 100 lbf.
The up slope component will be 100 lbf but rope tension will be
sqrt(100+9)/10 x 100 lbf = 104 lbf.
Hardly any difference.
But if the horses were 10 feet apart it becomes sqrt(125)/10*100 = 112 lbf.
When/if the ropes get out to 45 degrees either side rope tension is
141 (100 x sqrt(2) lbf.
All the increase comes from pulling at an angle so that only a
component applies.

This increase has nothing to do with pulleys per se but can be
introduced into examples to complicate them without people being very
aware that it has happened.

As long as the ropes ascend vertically from YesNopeGus's head all is well.

               R

2010\05\18@130951 by Mark Scoville

flavicon
face
> eg -  2 horse pull a cart up a ramp by a rope fastened to a pulling
> collar on each horse and passing through a single pulley in the front
> middle of the cart. The horses are 6 feet apart and the pulling collar
> attachment s are 10 feet in front of the cart.

Can't we just put the cart on the train leaving Boston at 2pm? :-)

-- Mark


2010\05\18@132833 by Michael Rigby-Jones

flavicon
face


> -----Original Message-----
> From: spam_OUTpiclist-bouncesTakeThisOuTspammit.edu [.....piclist-bouncesKILLspamspam@spam@mit.edu] On Behalf
> Of Russell McMahon
> Sent: 18 May 2010 14:35
> To: Microcontroller discussion list - Public.
> Subject: Re: [TECH] The theory of pulleys
>
> > To make this very simple terms.  Take the number of ropes attached to to
> > the MOVEABLE pulleys divide that into the weight being lifted  and that
> > is the force required to lift the object.
>
> As long as all ropes are vertical :-)

'parallel' might cover more situations!

Mike

=======================================================================
This e-mail is intended for the person it is addressed to only. The
information contained in it may be confidential and/or protected by
law. If you are not the intended recipient of this message, you must
not make any use of this information, or copy or show it to any
person. Please contact us immediately to tell us that you have
received this e-mail, and return the original to us. Any use,
forwarding, printing or copying of this message is strictly prohibited.
No part of this message can be considered a request for goods or
services.
=======================================================================

2010\05\18@234600 by Russell McMahon
face picon face
--001636e0a649d2356e0486ea4b6b
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable

> I want to pull the container down an incline that drops about 1 rod
> per 100 feet.

Rods do not compute.
Presumably you mean 40 millifurlong per 100 feet.
That's a ramp angle of about 160 milliradian, which is usefully steep.
Rollers and several helpers and it would  probably be "on a roll" all
by itself.

> I am going to assume the incline won't make much difference..... it
> may assist me a bit.
> I will put some logs under it to reduce the drag friction.

Is your life and "accident" insurance up to date?

> I have winch that claims it can lift 2000 lbs
> My plan is to use a system of pulleys to move the container.
>
> The Truck is green. =A0The container is blue.

System is built wrongly.
You need to be able to pull on the end of the actual supporting rope
with the truck.
Look at the many 'block and tackle" references using Gargoyle images
eg

http://www.photographers1.com/Sailing/BlockAndTackle.gif

http://www.tpub.com/content/construction/14043/css/14043_116.htm

http://www.britannica.com/EBchecked/topic-art/483111/4560/Block-and-tackle

www.google.co.nz/images?hl=3Den&source=3Dimghp&q=3Dblock+and+tackle&=
gbv=3D2&aq=3Df&aqi=3Dg4&aql=3D&oq=3D&gs_rfai=3D

> Will the winch have a mechanical advantage of 4 due to the pulleys ?

No. System has ma of 1 as pull on main rope does not affect rope
attached to container.

> Will the winch be powerful enough ?

With a 4:1 system, once achieved, coefficient of sliding friction will
almost certainly be < 1 so force on winch will be < 2000 lbf.

BUT static force to get going is unknown. Rollers will help muchly.
Any sliding surface that stops container front edge digging in will also he=
lp.

If required a system of small rollers (eg water pipe) and some timber
to make levers to lift container to inswrt rollers initially, would
allow say 2 or 3 people to "easily enough" do this without a truck.
Over any distance it gets annoying.

> I expect the container moves
> with less than an
> 8000 lb pull.

As above.

With rollers no b&t should be needed and will complicate things.

With an N:1 advantage the pulling vehicle etc moves N times as far as
the pulled object. SO here the truck moves 4 ramp lengths with a 4:1
B&T. May need several bites depending on available room.


R

--001636e0a649d2356e0486ea4b6b
Content-Type: image/jpeg; name="BlockAndTackle2.jpg"
Content-Disposition: attachment; filename="BlockAndTackle2.jpg"
Content-Transfer-Encoding: base64
X-Attachment-Id: f_g9dlj8rm0
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==
--001636e0a649d2356e0486ea4b6b
Content-Type: text/plain; charset="us-ascii"
MIME-Version: 1.0
Content-Transfer-Encoding: 7bit
Content-Disposition: inline

2010\05\19@003351 by Lee Jones

flavicon
face
> Okay   what I am actually planning to is:
> I have a shipping container that weighs  8000 pounds.

> I want to pull the container down an incline that drops about
> 1 rod per 100 feet.  I am going to assume the incline won't
> make much difference.....  it may assist me a bit.
> I will put some logs under it to reduce the drag friction.

If the surface is hard and you have enough logs, then you may
have a very interesting time as the container goes careening
down the incline.

{Quote hidden}

Yes.

> Will the winch be powerful enough ?

Maybe.  Ensure it is rated for a dead lift of 2000 lbs (which
may leave you with no margin for error (due to stiction) ).

> I expect the container moves with less than an 8000 lb pull.

Maybe, maybe not.  Depends on the surface, if a corner digs in,
if it snags on a tree root, etc.


I'd be _VERY_ carefull about the ratings of the various
components.  Where are you going to find a rope (i.e. blue
rope) with 8 tons breaking strengh?  Steel wire rope?  With
this much tension, if something breaks the resulting shrapnel
could maime or kill.  Quick list:

- the winch mounting (and truck structure under the winch
 mount on the truck).

- the 3 pulleys near the green truck, the red rope, and
 the red rope's anchor on the truck.  They will all have
 roughly 2000 lbs of force applied.

- the yoke by truck (2 pulleys & blue rope attachment),
 blue rope itself, the pulley by the tree, and whatever
 mechanism you devise to anchor the pulley to the tree;
 all will have roughly 8000 lbs force.

- if the ground is soft/soggy, the force may not break
 the tree, but it could pull it over -- a falling tree's
 top can reach out farther than you estimate

I did a similar project about 2 years ago but objects were
under 400 lbs each.  It was hard to find sufficiently robust
pulleys and slings to handle those loads (with some safety
margin) [well, within my limited budget for a one-off].  I
would be real concerned about scaling it all up by a factor
of 10 to 20.

If I were doing it, I'd mount the yoke (2 pulleys by truck)
to the tree, loose the "blue rope", and move the "red rope"
anchor from truck to the container.  Then the rope would
only need a breaking strengh of 2 tons (yes, factor of 2
safety margin).  And there would be fewer points/parts
that take a full 8000 lbs stress.

                                               Lee Jones

2010\05\19@081006 by Olin Lathrop

face picon face
Russell McMahon wrote:
> System is built wrongly.
> You need to be able to pull on the end of the actual supporting rope
> with the truck.

I took the diagram to mean that the truck was merely a anchor and that the
winch would do the work.  If he expects the truck to do the work, then
you're right, the pulleys are in the wrong place to provide mechanical
advantage.  However, what would be the point of having a winch if it's not
intended to do the actual pulling?


********************************************************************
Embed Inc, Littleton Massachusetts, http://www.embedinc.com/products
(978) 742-9014.  Gold level PIC consultants since 2000.

2010\05\19@081724 by Olin Lathrop

face picon face
Lee Jones wrote:
> - the yoke by truck (2 pulleys & blue rope attachment),
>   blue rope itself, the pulley by the tree, and whatever
>   mechanism you devise to anchor the pulley to the tree;
>   all will have roughly 8000 lbs force.

No.  The tree and the pulley attached to it will see double that force.  He
needs to check the tree's datasheet very carefully to make sure it is rated
for 16,000 pounds.  That's a lot, even for a decent size tree.  You
certainly wouldn't want to do that to a tree you liked.


********************************************************************
Embed Inc, Littleton Massachusetts, http://www.embedinc.com/products
(978) 742-9014.  Gold level PIC consultants since 2000.

2010\05\19@092624 by BOB

picon face
Why is the truck even needed?  Just secured the blue line to the base
of  the tree.

OLD BOB





Olin Lathrop wrote:
{Quote hidden}

2010\05\19@112005 by Russell McMahon

face picon face
>> I want to pull the container down an incline that drops about 1 rod
>> per 100 feet.

> There is no need to deliberately use obscure units just because you can.
> No, I'm not going to look up how long a rod is so that I can compare it to
> 100 feet.

I said:

>> Presumably you mean 40 millifurlong per 100 feet.

but I transposed some brain cells.
In fact 1 rod* = 25 millifurlongs.

>> That's a ramp angle of about 160 milliradian, which is usefully steep.

I think I got that right.
A man can never have enough milliradians - especially when rolling
heavy containers downhill.



    R


* Rods, I'm pleased to say, have never made it out here to the
beginning of every day and the edge of the Empire that the sun never
sets on. Except, perhaps, for cleaning drains. Arguably some people
have hot ones, but we are blessed to not have acquired the 25
millifurlong variety.

2010\05\19@120944 by Alan B Pearce

face picon face
> * Rods, I'm pleased to say, have never made it out here to the
> beginning of every day and the edge of the Empire that the sun never
> sets on. Except, perhaps, for cleaning drains. Arguably some people
> have hot ones, but we are blessed to not have acquired the 25
> millifurlong variety.

And here was me believing that surveyors used to use them in that part of
the world, as in 'rod, pole or perch' all being the same unit of different
names, when measuring out the dimensions of real estate.

2010\05\19@160157 by YES NOPE9

flavicon
face
>
> On May 19, 2010, at 7:26 AM, BOB wrote:
>
> Why is the truck even needed?  Just secured the blue line to the base
> of  the tree.
>
> OLD BOB

The truck provides power for the winch

2010\05\19@203420 by BOB

picon face
But even so does it need to be connected to the cables or ropes.

Also where I grew up in Southern Minnesota all farm boys knew that a ROD
was 16.5 feet long.
the survey of my property also has rod measurements.  Many lots are 66
feet (4 rods) wide. and that is in the city.

OLD BOB


YES NOPE9 wrote:
{Quote hidden}

2010\05\20@081444 by Lee Jones

flavicon
face
>> Why is the truck even needed?  Just secured the blue line
>> to the base of  the tree.
>>
>> OLD BOB

> The truck provides power for the winch

>From your drawing, it appears that the winch & 4-fold force
multiplier pulley arrangement is anchored to the truck.

Recall -- For each action, there is an opposite reaction.

How heavy is the truck?  A light pickup truck could easily
weigh less than an 8000 lbs container.  And the truck could
have much less friction sitting on 4 smallish round tire
contact patches than the break-away friction of the flat
surface of the bottom of a large container.

                                               Lee Jones

2010\05\20@085321 by Dave Tweed

face
flavicon
face
Lee Jones wrote:
> And the truck could have much less friction sitting on 4 smallish round
> tire contact patches than the break-away friction of the flat surface of
> the bottom of a large container.

Non-issue. If you work it out, you'll see that contact area cancels out.
The available lateral force is simply the weight of the truck multiplied
by the coefficient of friction between the rubber and the earth. Same
thing for the container.

Yes, there are generally two different numbers (static vs. sliding
coefficients of friction) for each pair of materials, so you need to
verify all of the combinations.

-- Dave Tweed

2010\05\20@105037 by Lee Jones

flavicon
face
>From piclist-bouncesspamKILLspammit.edu Thu May 20 05:55:57 2010
Received: from pch.mit.edu (PCH.MIT.EDU [18.7.21.90])
       by frumble.claremont.edu (8.9.3/8.9.3) with ESMTP id FAA21108
       for <.....leeKILLspamspam.....frumble.claremont.edu>; Thu, 20 May 2010 05:55:55 -0700
Received: from pch.mit.edu (pch.mit.edu [127.0.0.1])
       by pch.mit.edu (8.13.6/8.12.8) with ESMTP id o4KCrNq8015750;
       Thu, 20 May 2010 08:53:23 -0400
Received: from mailhub-dmz-2.mit.edu (MAILHUB-DMZ-2.MIT.EDU [18.7.62.37])
       by pch.mit.edu (8.13.6/8.12.8) with ESMTP id o4KCrLbb015747
       for <EraseMEpiclistspam_OUTspamTakeThisOuTPCH.mit.edu>; Thu, 20 May 2010 08:53:21 -0400
Received: from dmz-mailsec-scanner-4.mit.edu (DMZ-MAILSEC-SCANNER-4.MIT.EDU
       [18.9.25.15])
       by mailhub-dmz-2.mit.edu (8.13.8/8.9.2) with ESMTP id o4KCqnFH015364
       for <piclistspamspam_OUTmit.edu>; Thu, 20 May 2010 08:53:21 -0400
X-AuditID: 1209190f-b7b20ae000003f85-a5-4bf530c1f53a
Received: from elasmtp-masked.atl.sa.earthlink.net
       (elasmtp-masked.atl.sa.earthlink.net [209.86.89.68])
       by dmz-mailsec-scanner-4.mit.edu (Symantec Brightmail Gateway) with
       SMTP id F5.0C.16261.1C035FB4; Thu, 20 May 2010 08:53:21 -0400 (EDT)
Date: Thu, 20 May 2010 08:53:21 -0400
Received: from [68.162.216.100] (helo=localhost.localdomain)
       by elasmtp-masked.atl.sa.earthlink.net with esmtpa (Exim 4.67)
       (envelope-from <@spam@picKILLspamspamdtweed.com>) id 1OF5FY-0000Xm-VY
       for KILLspampiclistKILLspamspammit.edu; Thu, 20 May 2010 08:53:21 -0400
MIME-Version: 1.0
References: <RemoveME201005201216.FAA20790TakeThisOuTspamfrumble.claremont.edu>> To: <spamBeGonepiclistspamBeGonespammit.edu>
From: Dave Tweed <TakeThisOuTpicEraseMEspamspam_OUTdtweed.com>
Organization: Embedded Computer Engineering
Subject: Re: [TECH] The theory of pulleys
Message-ID: <RemoveMEE1OF5FY-0000Xm-VYspamTakeThisOuTelasmtp-masked.atl.sa.earthlink.net>> X-ELNK-Trace: 5507fdf0269a8d2672cc1e1b0924a179239a348a220c2609fcc95578a5499375a57a3d2ff50fa56e350badd9bab72f9c350badd9bab72f9c350badd9bab72f9c
X-Originating-IP: 68.162.216.100
X-Brightmail-Tracker: AAAAAA==
X-Topics: [TECH]
X-BeenThere:
piclistEraseMEspam.....mit.edu
X-Mailman-Version: 2.1.6
Precedence: list
Reply-To: "Microcontroller discussion list - Public." <EraseMEpiclistspammit.edu>
List-Id: "Microcontroller discussion list - Public." <piclist.mit.edu>
List-Unsubscribe: <mailman.mit.edu/mailman/listinfo/piclist>,
       <RemoveMEpiclist-requestEraseMEspamEraseMEmit.edu?subject=unsubscribe>> List-Post: <RemoveMEpiclistspam_OUTspamKILLspammit.edu>
List-Help: <RemoveMEpiclist-requestTakeThisOuTspamspammit.edu?subject=help>> List-Subscribe: <mailman.mit.edu/mailman/listinfo/piclist>,
       <
EraseMEpiclist-requestspamspamspamBeGonemit.edu?subject=subscribe>> Content-Type: text/plain; charset="us-ascii"
Content-Transfer-Encoding: 7bit
Sender:
RemoveMEpiclist-bouncesKILLspamspammit.edu
Errors-To: piclist-bouncesSTOPspamspamspam_OUTmit.edu
Status: R

Lee Jones wrote:
>> And the truck could have much less friction sitting on 4 smallish
>> round tire contact patches than the break-away friction of the
>> flat surface of the bottom of a large container.

> Non-issue. If you work it out, you'll see that contact area
> cancels out.  The available lateral force is simply the weight
> of the truck multiplied by the coefficient of friction between
> the rubber and the earth. Same thing for the container.

I agree with your mathematics & physics.  And we may be talking
about a truck that weighs 1/3 of the container's dead weight.

Now let me posit a possible scenario based on items that have
been mentioned in previous posts.

one end of rope -- 8000 lb square cornered container caught on
a tree root in soft earth road.

other end of rope -- 2500 lb smallish pickup truck sitting on
4 round wheels (i.e. no corners to dig in) of which only the
rear two are locked into a non-rotational state (i.e. parking
brake on); front wheels are free to rotate.

Maybe you think this won't happen.  And maybe you're right.

Personally, I would want to be a safe distance away from such
a light truck when the winch is turned on.

                                               Lee Jones

2010\05\20@105219 by Lee Jones

flavicon
face
[ Oops, I apologize, I forgot to trim headers before sending. ]

Lee Jones wrote:
>> And the truck could have much less friction sitting on 4 smallish
>> round tire contact patches than the break-away friction of the
>> flat surface of the bottom of a large container.

> Non-issue. If you work it out, you'll see that contact area
> cancels out.  The available lateral force is simply the weight
> of the truck multiplied by the coefficient of friction between
> the rubber and the earth. Same thing for the container.

I agree with your mathematics & physics.  And we may be talking
about a truck that weighs 1/3 of the container's dead weight.

Now let me posit a possible scenario based on items that have
been mentioned in previous posts.

one end of rope -- 8000 lb square cornered container caught on
a tree root in soft earth road.

other end of rope -- 2500 lb smallish pickup truck sitting on
4 round wheels (i.e. no corners to dig in) of which only the
rear two are locked into a non-rotational state (i.e. parking
brake on); front wheels are free to rotate.

Maybe you think this won't happen.  And maybe you're right.

Personally, I would want to be a safe distance away from such
a light truck when the winch is turned on.

                                               Lee Jones


2010\05\21@030719 by Marechiare

picon face
> I want to pull the container down an incline that drops
> about 1 rod per 100 feet. I am going to assume the
> incline won't make much difference..... it may assist
> me a bit.

Wrong assumption, 1 to 7 incline would assist you greatly. If you cut
the container loose, it would do the job on its own.

> I will put some logs under it to reduce the drag friction.

Some grease instead would be better and don't forget about placing a
lot of sand at the end of the path.

WARNING: USE CERTIFIED PROFESSIONALS TO DO THE ABOVE. DOING IT ON YOUR
OWN YOU ARE UNDER THE RISK OF YOUR AND OTHERS HEALTH/PROPERTY DAMAGE.

You've been warned.
Good Luck.

More... (looser matching)
- Last day of these posts
- In 2010 , 2011 only
- Today
- New search...