Where is the Extra Force Coming From in this Over-Unity Pulley System?

[lamina]

Over Unity Efficient Pulley?

Hi, I have a problem regarding a simple pulley system which seems to have an efficiency of over 100% and I just can't figure out what is going on.

Scenario:

I have a 5N mass vertically suspended using high tensile flexible steel wire from a simple spring gauge which measures force. The force measured is 5N. As expected.

I now place the steel wire over a plastic pulley with solid steel supports - and measure the force shown on the spring gauge to lift the 5N mass - this is shown as 4.5N. If I carefully lift the pulley so that it is not touching the wire, the force shown on the spring gauge goes back up to 5N.

If I replace the pulley with a polished solid steel bar, the force is always above 5N - frictional effects I suppose.

So I am lifting a 5N mass with a force of 4.5N - efficiency 111%

Assuming that I am not being REALLY daft ( always a possibility) where has the 0.5N come from?

I have tried smaller masses, different wires and just about anything I can think of.

This is driving me nuts and any help would be appreciated.

I would add that I have tried more than a single pulley system and have acheived efficiencies approaching 200%.

Regards

Richard

 

[Shooting Star]

I now place the steel wire over a plastic pulley with solid steel supports - and measure the force shown on the spring gauge to lift the 5N mass - this is shown as 4.5N. If I carefully lift the pulley so that it is not touching the wire, the force shown on the spring gauge goes back up to 5N.

If I replace the pulley with a polished solid steel bar, the force is always above 5N - frictional effects I suppose.

The picture is not at all clear to me. What do you mean by placing the wire over the pulley? And lifting the pulley? Give a diagram or please explain again.

 

[russ_watters]

It is either friction, the weight of the wire, or the stiffness of the wire absorbing the rest of the weight.

 

[lamina]

Hi,
Thanks for the replies.

The setup is very simple. I have a plastic pulley wheel with steel supports. When the 5N mass is lifted vertically without the pulley in the system, the force measured on the spring gauge is 5N. If I put the wire round the pulley, the same mass requires 4.5N to move it. If I then move the spring gauge vertically so that the wire is not touching the pulley, the force required to life the 5N mass is again 5N. So, as soon as the pulley enters the system I get a force reduction of 0.5N. How is this possible?
I can't see friction, the mass of the wire (which is about 0.02N) or the wire stiffness actually reducing the force - as far as I can see those factors would all increase the force required.
Hope that clarifies - sorry about lack of a drawing. This is about as simple as it gets but doesn't make sense - to me anyway.

Richard

 

[russ_watters]

Sounds like friction - when you measure the 4.5 N is the mass actually moving or sitting still?

 

[Doc Al]

Are you able to raise the 5 N mass with 4.5 N of force, or just support it? (A slightly different phrasing of what Russ just asked.)

 

[lamina]

Hi,
I can lift the 5N mass with a force of 4.5N when using the pulley - this force is the MAXimum reached when lifting and it gets nowhere near 5N - this can't be friction, this would increase the force required surely?

Richard

 

[HallsofIvy]

Sounds to me like you have the makings of a perpetual motion machine there!

 

[lamina]

HallsofIvy - haha - I plan to make a larger version and hook it up to a generator - any idea where I can get a flux-capacitor - ebay are all out :-))
Richard

 

[DaveC426913]

I'd like to see a diagram of this so we can rule out some assumptions.

 

[russ_watters]

How about the weight of the spring scale. You are pulling down with it, right? What does it read when you have it inverted but nothing is connected to it?

 

[lamina]

As a matter of interest, this all started as a simple demonstration which I suggested to my wife, a seconday school teacher to show to her students. I am a Chartered Engineer, a member of the Institution of Mechanical Engineers, have a PhD in engineering and thought that a simple pulley would exhibit a reasonable efficiency and then the group could move on to more complex pulley systems.

Haha - can I explain the results? They are simply ridiculous but I can't think of why they are. Pulleys cannot be 110% efficient - its just that my one, in front of me, is.

Baffled.

 

[lamina]

Hi,
I have attached a simple sketch of this simple set-up - The spring gauge is a good one and shows a zero reading when there is no force either horizontally or vertically

Richard

 

[Shooting Star]

I think this is due to friction between the wire and the pulley. Do one experiment. Wrap the wire tightly twice around the pulley. I think the gauge will show much less than 4.5 N. The whole weight will be supported by the pulley.

 

[lamina]

Hi Shooting Star,
I have wrapped the wire round the pulley twice and the 5N mass is lifted with a reading of 4.8N on the spring gauge. This is up from 4.5N with one turn. Tricky to do, but I will try to do three turns.
Gee, I'm glad we haven't progressed beyond a single pulley :-))

 

[Doc Al]

Also try raising different masses and comparing the measurements.

Also try changing the angle that the scale rope makes with the horizontal.

 

[lamina]

Three turns of tightly wrapped wire round the pulley - back to 4.5N.

 

[Shooting Star]

Is the mass moving when it's showing 4.8 N? Now you are driving everybody nuts.

Give it a sharp and sudden jerk, when the wire is around the pulley, and see how the reading goes. It should show a vey high reading, indicating that the gauge is all right.

 

[lamina]

Hi, Doc Al. I have tried masses from 1 to 5N and angles from 10 to 90 to the vertical. The only time that I get a force which is not less than the mass being raised is if the wire does not touch the pulley. As soon as the wire starts to 'wrap' round the pulley then the force required to raise the mass drops. I have tried wire, string, cotton, if my hair was longer I'd try that.
This is so simple and must have been done billions of times - on the point of looking for a warp in the space-time continuum - mind you my coffee just separated into two distinct layers of black coffee and milk :-))

 

[lamina]

Yep gauge is fine - if I use a straight steel bar instead of a pulley the force required goes way up to 7-10N. The mass is still when I measure the force to hold it, but I am moving it so gently that the gauge doesn't change much. Maybe I need a Video crew?

 

[stewartcs]

I would expect slightly less required force (tension applied from the right in your diagram) to hold the mass in static equilibrium. This is due to the static frictional force of the pulley opposing the force of gravity acting on the mass. That is to say that the force of gravity will try to pull the mass down and the pulley's static frictional force will try to oppose it (hold it up). Hence the net force or tension required to support the mass (applied from the right in your diagram) would be less than the weight of the mass (5N).

If the mass is moving up (being lifted) I would expect you to have to apply more force than that of the 5N mass. More force is required to overcome the now opposing frictional force of the pulley and any acceleration effects you are adding by moving it (if not at a constant velocity).

So, you should be seeing an increase in force from the scale on the right if you are lifting the mass, and you should see a decrease on it if you are holding it steady.

I would add that I have tried more than a single pulley system and have acheived efficiencies approaching 200%.

Well this makes sense. If you increase the number of pulleys in your system, then the ideal mechanical advantage is increased. Hence, less force (applied tension) is required to lift the load.

 

[stewartcs]

Well this makes sense. If you increase the number of pulleys in your system, then the ideal mechanical advantage is increased. Hence, less force (applied tension) is required to lift the load.

I suppose I should clarify this. This of course depends on the arrangement of the pulleys when you add them to the system!

 

[Shooting Star]

(Correction on my previous post:

I meant that give the gauge a sharp tug, not the mass.)

Hi Lamina,

The force need not be 5 N in a system of multiple pulleys, which is why we use pulleys, to gain mechanical advantage. But your results are peculiar even with a single pulley.

Please answer two simple questions.

When you are using one pulley, and the wire coming from the pulley and connecting to the gauge is horizontal, and there is no movement, what is the reading? (It is expected to be less than 5 N or at most 5 N.)

When you are using one pulley, and the wire coming from the pulley and connecting to the gauge is horizontal, and you are pulling the wire by pulling at the gauge horizontally, what is the reading? (It is expected to be more than 5 N.)

 

[TVP45]

What do you get when the mass is slowly moving up?

 

[minorwork]

I don't know much here but it looks like that the wire supporting the weight from the instant it hits the pulley is transferring force to the pulley axle. the scale is not lifting the non vertical portion of the wire. The pulley is leveraging and transferring weight to the axle. The pulley's radius is somehow gonna' be mathematically related to your force drop difference.