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### The Weight Lifter: CR4 Challenge (02/16/10)

Posted February 15, 2010 5:01 PM

This week's Challenge Question:

You are a weight lifter at the Olympic games and you are about to break a record. Your lift consists of a barbell and disks weighting 255 kg. It takes you 6 seconds to lift the weights to a height of 2.1 meters. How much energy you need to perform this feat?

And the Answer is...

Treat the barbell and the disk as one solid object. To lift this object you must apply a force that will produce work to overcome the work done by the gravitational force F = mg = (255 kg)(9.8 m/s^2) = 2,499 Newton (N). Now, as you know from your introductory Physics you took in high school, the work done on an object is equal to the product of the weight (or force) and the displacement in the direction of the force. For the gravitational work done on this object we have,

Therefore the amount of energy (equal to the work) that you must supply 5247.9 Joules.

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#1

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/16/2010 11:38 AM

Work = Force x Distance

Force = mass x Acceleration

Therefore:

Work = Mass x Acceleration x Distance

= 225 x 9.81 x 2.1

= 4635.225 J*

Since the time has been given, we can calculate overall Power too.

Power = Work / Time

Power = Energy / Time

= 772.5375 J/s ... or Watts

This calculation is based on statics, and I haven't included the acceleration imparted over the lifted ... off to brush up my calculus...or wait for Fyz

* This assumes the lift is straight up, since the vector of the acceleration must be in line with the direction of movement.

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#2
In reply to #1

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/16/2010 11:41 AM

It's interesting to note that 4635 J = 1.1 kcal.....

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#4
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/16/2010 2:58 PM

I also don't trust those values on the weights.

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#5
In reply to #1

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/16/2010 3:38 PM

Hmm.
It's a GA - minor misreading of the question (225 vs 255 kg, and giving mean power as well as energy) excepted. I certainly can't add anything substantive in terms of answers - though I still have several (pedantic) questions:

Given the stated weight, and that you are about to break an Olympic record, I assume that this must be the 105-kg class "clean and jerk" (if it was the heavyweight "snatch" you would have broken the record on a previous attempt). So 'you' are unlikely to be more than 175-cm tall, which would mean that the bar will be reaching 2.1-m; the base of the weights would be rather lower than this. Maybe we have overestimated the amount of work performed on the barbells?

But then, is this meant to be a question about the increase in the potential energy of the barbells? It says the amount of energy you need, and you are also raising yourself, dissipating energy in jerks (please restrain yourselves), and then there is the efficiency of your muscles and the energy expended in support - so the efficiency is less than about 25% if you are starting from food, or 60% if you are starting from ATP.

Fyz

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#7
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/16/2010 4:13 PM

"It says the amount of energy you need, and you are also raising yourself, dissipating energy in jerks (please restrain yourselves), and then there is the efficiency of your muscles and the energy expended in support - so the efficiency is less than about 25% if you are starting from food, or 60% if you are starting from ATP."

True, but by introducing additional-but-unstated parameters into the problem we preclude any possibility of our answering the question in a meaningful way. Once we open Pandora's Box, Pandora herself may jump out and begin to speculate further that while our weightlifter was about to break a record he was, at that moment, lifting these weights with the aid of a machine, possibly by means of a control pendant in one hand and a beer in the other. Now, about that machine's hydraulic efficiency - or does it use muscle wire? ...

SR

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#35
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 7:46 AM

introducing additional-but-unstated parameters into the problem

That's half* the fun

*I am willing to debate that value

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#37
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 7:55 AM

Thanks Fyz, but why a demerit for giving additional information (the power)? I was just drawing attention to the fact that the time wasn't needed to answer the energy question.

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#39
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 8:06 AM

Maybe the time was a ?

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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 8:32 AM

And a very bony one, too.

My point (rapidly losing any hint of humour ) was that I'd spotted it...it just seemed a shame to leaving lying about. We're supposed to be advocates for recycling aren't we?

Now where's that darned Cat...I have a fishy tale (and head) for him....

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#43
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 11:18 AM

Though I say it myself, I'm sure my abandonment of apostrophe's and commas is having an effect here. Next mission is the full stop

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#42
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 10:33 AM

It was a reservation rather than a demerit. Two items prompted the remark: the first being that I didn't feel that "as well" was quite explicit enough for this community; and the second being that "peak power" would be more illustrative of the difference between impulse activities and long-term work than the 6-second average (as we didin't have the data to calculate it, I'd have gone for the comment without the number).

But you could with equal justification put it down to "having got out of bed on the wrong side".

Fyz

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#45
In reply to #42

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 11:48 AM

Comments duly noted.

Will try harder

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#54
In reply to #5

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/23/2010 9:23 PM

Applying reductio ad absurdum then we also need to include the energy expended during training, since without that the lifter wouldn't be able to lift the weight; also the energy required to create the conditions to create the lifter, etc etc.

Therefore: The energy required equals the total amount of energy in the Universe.

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#6
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/16/2010 3:46 PM

"* This assumes the lift is straight up, since the vector of the acceleration must be in line with the direction of movement."

The path taken by the mass does not contribute to the final energy so long as it terminates at an elevation 2.1 meters higher than the starting point (in the reference frame of the gravitational field, which we assume is uniform here). No work is done on the mass in moving it horizontally and so motion along the horizontal component of the path vector does not contribute at all to the final energy. Only in the vertical direction is work done. This means that the path can zig-zag through space, dip below the starting point and even rise above it*. The path endpoint need not even be directly above the start point so long as the mass arrives at its relative target elevation of 2.1 meters.

* Our confused and exhausted weightlifter may disagree with these remarks, naturally.

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#16
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 6:12 AM

Exactly. To put it in vector calculus terms, gravity is a curl-free field.

Cheers.........Codey

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#36
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 7:48 AM

You have elegantly and exactly explained what I was trying to say...

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#3

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/16/2010 12:14 PM

"How much energy you need to perform this feast?"

Feat.

Mass, m = 255 kg

Force, f = mg = 255 kg * 9.80665 m/s2 = 2501 N

Distance, d = 2.1 m

Potential Energy, EP = f * d

EP = 2501 N * 2.1 m = 5251 J

Note: The amount of time required to accomplish this feat, namely 6 seconds, is irrelevant because the question does not ask about power - i.e., the rate at which the energy is expended.

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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 1:09 AM

Sonos, clear concise and correct - worth a coveted GA

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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 3:33 AM

GA from me too. In fact this is true in ideal conditions i.e. in a frictionless system. Even the human body is not frictionless. Also, you should add the weight of your own hands (about 2Kg more... you need energy in order just to raise your own hands...) Hence, in fact you need sth more than 5251J.

(However, this was such an easy "question".)

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#26
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 11:19 PM

1. In an ideal world (which we have to assume for lack of better information) the time is indeed irrelevant. Whatever energy is expended in accelerating the mass will be recovered as it slows to a stop at the top of the lift. A well placed red herring!

2. I am inclined to support the intent if not the results from those who try to analyze the energy expended by the lifter (chemical as well as mechanical) in a muscle system which is not 100% efficient. And carrying the analysis all the way back to the food ingested to produce the calories expended is clearly supported by the (Freudian?) typo referring to accomplishing this FEAST.

3. When you are not sure what you are talking about, always number your paragraphs. (Old essay test taking wisdom.)

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#8

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/16/2010 9:01 PM

Just to add my two cents, the height of the lift I'm assuming would be taken from the centre of the bar? Now this means, that since the bar sits with the weights on the ground (not the bar itself) we need the geometry of the weights and the bar to determine the bars starting height, this will reduce the work required by the weight lifter, compared to a weight starting at ground level.

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#9

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/16/2010 11:18 PM

How much energy you need to perform this feast?...

Depends on how hungry you are! :)

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#10

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/16/2010 11:50 PM

Sonos Research, with the qualifier by guest re starting height, is the perfect answer.

This is that energy is simply the mass x 9.8 x height lifted -time is irrelevant.

9.8 is or course an approximation to any of the more accurate values for converting Mass in Kg to force in N (on this planet), and gives the result 5247.9 joules, or watt-sec, if 2.1m is the lifted distance.

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#12

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 1:29 AM

The question is poorly written and irrational, but assuming the question is referring to the amount of work done (not by the lifter) on a 255 kg object raised 2.1 m (change in height of the object's center of gravity) at sea level (no altitude or which Olympic games was given).

Potential Energy = (mass)(gravity)(change in height) = (255 kg)(9.81 m/s2)(2.1 m)

Potential Energy = 5253 kg m2/s2 = 5253 joules (only 2 S.F. allowed) =

Answer = 5300 J

Respectfully Dave

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#34
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 7:33 AM

Hello Prof,

I thought the definition is kg m /s2, (not kg m2 / s2)

Otherwise, a quite good answer, I find.

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#41
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 10:18 AM

Thanks Floram ~ PE = mgh did you remember to multiple g (m/s2) by h (m) which gives m2/s2

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#53
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/19/2010 11:32 AM

Sorry Dave, I do owe you an apology. Looks like I am getting quite rusty.

I thought of the definition of N. You are correct regarding energy. There must have something in my coffee that morning.

Thanks for straightening me out.

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#58
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/24/2010 1:10 PM

Apology not needed...we all slip up once in a while...but thank you any way...shows you are a "stand up guy"! I'm just an old retired prof. trying to keep his mind active. I left out a zero on an answer a few posts ago (7 cm/min instead of 70 cm/min).

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#56
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/24/2010 12:40 PM

When an object is displaced 2.1 m, it implies that the center of mass (or gravity ~ indicative of my military experience) is moved that distance. Selecting arbitrary locations on the object as the starting point and another for the end point (as some have apparently done ~did the shape of the object changed?) does not appear correct. Maybe, I'm missing something, but I do not understand how the distance became smaller than 2.1 m. Can someone help me understand this calculation? Could be my neurons are not firing appropriately again...nursing a migraine. One of those "dog" days!

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#57
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/24/2010 1:06 PM

It seems to me that the problem is that some people do not make the simplifying assumption, common in physics problems and even in the real world, that lifting an object "to a height of N meters" means moving the CG of that object upward N meters from its starting position rather than ending up with the CG at a height of N meters.

Failure to interpret the statement of the problem in this sense turns a simple problem into an insoluble one, which appears to be the fundamental goal of some of the posters!

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#59
In reply to #56

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/25/2010 7:36 AM

Although I would give the calculation for 2.1-m an "adequate answer" rating, the problem is posed as relating to a quasi-real-world situation.

The challenge states 2.1-metres as being the height to which the bar is raised. In the absence of additional information, you could read this as being either the final height or the displacement. But we have additional information - that the weight being lifted approaches the highest of the Olympic records, and that these are standard Olympic weights being correctly lifted under Olympic conditions. As competitive weight-lifters are not exceptionally tall, there is no way that the final height could be the ~2.325-m that would be required for a 2.1-metre displacement. So we should know that 2.1-metre displacement is incompatible with the terms of the challenge.

It may well be that "the answer" conforms to your viewpoint. However, this is an engineering forum, not a "high-school abstract-question" forum. Please respect the desire of practicing/retired engineers to treat it as such.

So, we've established that we can't exactly answer the challenge as posed - but we've also established a range.

To my mind, the correct answer is 4.7-kJ (or 4.7x103-J)
(N.B. not 4700-J etc., as this is unnecessarily ambiguous)

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#60
In reply to #59

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/25/2010 2:51 PM

Would you explain how your answer (4.7 kJ or 4.7X103 J) is less ambiguous or different from the "ambiguous" answer 4700 J (Also, 4.7-kJ actually means 4.7/kJ). I don't know who is correct you or other posts, but the principles of mathematics and physics apply to all of us even in a "quasi-real world".

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#61
In reply to #60

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/25/2010 5:43 PM

You can't be certain what resolution (Significant fuigures) 4700 Joules is intended to denote. Is it just 2 significant figures (4.7 kJ) or three S.F. (4.70 kJ would be clear for this) or...

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#62
In reply to #61

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/25/2010 6:43 PM

All three values are identical...each expression has two significant digits and the same range of accuracy: 4.65 kJ to 4.75 kJ.

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#63
In reply to #62

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/26/2010 6:07 AM

I'd like to know how you would propose to indicate that 4700 is actually accurate to 3 SF?
FYI, the convention* is that trailing zeros to the right of a decimal point are used to denote the number of significant digits (though you might under some circumstances be suspicious about correctness of usage if there are two or more).

Fyz

*Can someone explain why many contributors are dogmatic about things that can so easily be shown incorrect with a trivial check?

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#64
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/26/2010 1:34 PM

Comment #62 is correct ~ 4700 has two significant digits just like your values and a range of 4650 to 4750 (range numbers often have one more digit). Range numbers are not specific, for they are just stating that the correct answer falls somewhere between those numbers.

1 has one SD range 0.5 to 1.5

11 has two SD's range of 10.5 to 11.5

111 has three SD's range of 110.5 to 111.5

Respectfully Dave

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#65
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/26/2010 4:44 PM

He's right about 4700, but wrong about 4.70x103. Hence my question about how he proposed to indicate that 4700 was accurate to 3SF.

But maybe you didn't actually read either the posts or the context before sounding off?

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#68
In reply to #65

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/26/2010 9:16 PM

I never stated 4700 was accurate to 3 SF!

"4700" has two SF

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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/26/2010 10:20 PM

I never implied that you said 4700 was accurate to 3-SF. I asked how you would present 4700 in order to show it was accurate to this level. My point is that, even in a context where the presentation implies the precision, 4700 only tells you that the number is accurate to at least 2-SF; it does not imply that it is not accurate to 3-SF (or even to 4-SF.

So please read the wikipedia article, and particularly the section entitled "Identifying significant digits". It correctly states what I have been saying - only it does the job rather better than ever I could.

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#73
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/26/2010 10:45 PM

Dave

Please ignore the first phrase of post #65. It's a consequence of careless editing (I should be ashamed of myself - nothing new there).

You will have gathered that at best I consider the use of the "significant digit" convention to be too crude for serious work. But it could have application for this sort of thing - but only if used with care.
The position is that trailing zeros before a decimal point have no significance either way in terms of precision. This means both that the mere presence of such a zero does not mean the precision is tight - and also that its (mere) presence does not imply the precision is lax. To my mind, the wikipedia article on the topic handles this rather well (and far more clearly than ever I could); the section entitled "Identifying significant digits" is particularly relevant.

So, even in a context where the significant digit convention is to expected, 4700 expressed without additional information would tell you that you had precision to at least 2-SF. On the other hand, 4.7x103 would usually be taken to imply 2-SF.

You will appreciate that this is not in line what you and a couple of even more dogmatic guests have been saying. But Wikipedia is not infallible, even(?) when it happens to agree with me. I would be prepared to eat my words on what the conventions actually are if you can cite a coherent and authoratitive source to support your view. On the other hand, I would continue regard a convention that forces 4700 to have a lower precision than 4690 and 4710 (rather than being ambiguous) as being somewhat perverse.

Regards

Fyz

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#75
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/26/2010 11:32 PM

In scientific work, most numbers are measured quantities and thus are not exact. All measured quantities are limited in significant figures (SF) by the precision of the instrument used to make the measurement. The measurement must be recorded in such a way as to show the degree of precision to which it was made-- no more, no less. Calculations based on the measured quantities can have no more (or no less) precision than the measurements themselves. The answers to the calculations must be recorded to the proper number of significant figures. To do otherwise is misleading and improper.

Conclusion:

The precision of the instruments used in collecting data determines the degree to which your results are accurate. Significant figures provide an easy way of indicating that accuracy. Using these guidelines assures that the data resulted from your procedures is not only reproducible, but also allows an observer to understand the degree to which your data is accurate.

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#80
In reply to #73

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/27/2010 1:18 PM

4700 has two (and only two) sig. digits. and is identical to 4.7 X 103

I would really like to know why engineering students are taught to use SF (and are in our text) if they are "crude", and why are they are widely used in science and mathematics. I am a fairly intelligent student, and have yet to find a uniform process that is better . The key here is accuracy of reporting data because if our data is not accurate then calculations with that data will compound the error. I want to be a good engineer and provide my employer with correct answers based on the good logic, mathematics, and precision of instrument available. I have several members of my project group that don't apply SF appropriately, and we always get the wrong answer (or less accurate based on measurements from a more precise instrument that the instructor applies). I respect your opinions, but frankly a few of your arguments are not correct or applicable over a broad spectrum. My instructor who has a Ph.D and experience in engineering frequently states that good answers come from appropriate logic, measurements, and mathematics, but unfortunately most of us lack two of them. Then I find this site where comments or answers are not any better than my classmates. I don't have parental support and need a "B average" this semester to keep my scholarship. I wish I could tell who of you were educated and had appropriate engineering experience. There are also excellent answers by some, and I try to follow them. Thanks for your time and don't give up on us.

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#82
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/27/2010 2:09 PM

If you really must use significant figures (and, God, I dislike 'em!), use "modified scientific notation" where it is unambiguously clear what is meant. By "modified", I mean to not be hamstrung by that idiotic rule (left over from the days of Smoley's Tables - which you probably don't have a copy of anyway - where the mantissa has to be between 1.000000... and 9.9999999...

Also, if you're going to use sig figs, avoid the common pitfalls and use radians rather than degrees, make sure you're always talking about ΔΘ rather than Θ, and use series expansions for anything that isn't obvious.

Also, keep in mind that any decent engineer always carries a "guard digit" in intermediate steps.

As to what gets used, you'll have to use judgement.

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#83
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### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/27/2010 2:23 PM

By the by, here's an interesting reference.

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#84
In reply to #83

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/27/2010 3:23 PM

Finally found someone who is not elitist, arrogant, and impatient. and who does not kick you in the face and call you a 7th grader for trying to learn something that is not taught at my level. Although, I did learn something from his first paragraph.

We do obviously use the scientific notations (with applied sig. fig.) but it was slightly different in physics than chemistry.

Thank you so much for this source (strange that it was from the Chinese although several citations were American) for it cleared up several points for me (gave you a GA for this and previous post). This really helped me understand better about the precision factor +/- X not always equal to 0.5 of the last SD. Am I wrong to assume that this does not discount SF but improves that method, and that I will experience these new methods in more advanced engineering courses. Thanks again for the information...you represent a positive spirit of this site. I assume it is for people like me. If not I will disappear!

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#85
In reply to #84

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/27/2010 3:40 PM

Of course this site is for people like you. You are the future and we owe you all the guidance we can give. However, many of us love to argue and are often irreverent. We usually add emoticons when we're not being serious. Please stay around if you can stand the crowd. This is, at many levels, the absolute best engineering site there is. One of the outstanding features about this is that you can jump into any discussion with post 1 just as easily as with post 5000. Nobody will put you down for being a newbie. Almost all insults are equal opportunity and are meant in good sport. Hope you sign up and stay.

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#90
In reply to #83

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/27/2010 4:31 PM

No, why does this remind me of the fact that the values 1-to-2 pages of log tables were always more worn than the rest of the books?

Perhaps because the core of the article seems to be the recognition that 9.9 (2SF) is almost identical in accuracy to 1.01 (3SF)?
Perhaps also because, for multiplication and division, my high-school teacher taught us to calculate the implied error level as a fraction of the element value (regardless of whether the error was defined via S.F. or via explicit tolerance), and state the final SF on the same basis? (I had thought this would be the norm).

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#91
In reply to #90

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/27/2010 4:52 PM

I don't know if there is a norm. I wish there were. I see all kinds of stuff; in fact, sometimes I contribute to that when I don't stop and think. I work with a guy who's in love with statistics and he has been known (I swear on my Machinery Handbook this is true!) to calculate the standard deviation and error of three measurements of a quantity. It would help if we had some kind of Bible for error. There's a guy at NIST, whose name escapes me, who has written pretty extensively on all this but I swear I can't make heads nor tails of half his stuff - I'm just not quite that bright in maths.

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#92
In reply to #91

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/28/2010 4:41 PM

I do statistical calculations only when necessary - and then it's crucial to get things clear and correct. [However, most of the complexities seem to me unnecessary for most applications (though I'm not above plagiarising tools and methods) - a little physical insight generally leads to the required result - and in my opinion in a way that is rather safer than following guidelines. The only "downside" is that it will sometimes be expressed differently.]

You say "guy". The only NIST statistical (not both statisticians as such) names I remember are Mary Natrella (for her contribution to "handbook 91", which sounds like something from Heller) and Dave Allan (of "Allan variance").
But there's a whole department at NIST devoted to statistical analysis. Scary but true.

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#93
In reply to #92

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/28/2010 4:51 PM

Nah, they ain't the name. I'm no big fan of statistics, but I do like standards and guidelines. I worked quite a bit as a design draftsman and them that don't follow the standards screw it up for everybody else. Come to think of it, maybe that's why I'm so pedantic about things.

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#94
In reply to #93

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/28/2010 5:23 PM

Point taken and agreed, standards and guidelines are essential. I expressed myself badly.

The case you cite is where we need unambiguous communication between people with different backgrounds. So if I need a drawing for parts manufacture or assembly I get a draftsman to do two things: check for opportunities to standardise (which needs his/her early involvement), and translate my sketches into a form that conforms with the guidelines. I can then check that a part manufactured to drawing will do what I intended. (The method works - as many are the times that a skilled practitioner of the art can save a generalist from his ignorance).
To labour my point - you really need to know the guidelines very well to get this right, and jacks-of-all trades such as myself can't know them all.
I have done the equivalent with statistical presentation - derived the result from first principles, and then translated them as necessary for the use to which they were put. (I suppose that the proof of the pudding would be if results as presented were later confirmed by measurement specialists)

What I was trying to say - and failing (maybe still doing so) - was that if I tried to work from my initial results to the final version by literally following guidelines, I would need to know them really well before starting, as I would otherwise doubtless either misinterpret them or make some silly mistake on the way. (But once think I know what I'm doing, I ensure that the final method/presentation is consistent with guidelines)

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#95
In reply to #94

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/28/2010 6:58 PM

Yeah, I see your point. We all could, in fact, make use of some sort of "good little book" about this subject, maybe 35 or 40 pages, plainly written, with examples. It makes me crazy when I have to spend twenty minutes reading just to figure out how to show an error bar.

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#96
In reply to #95

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

03/01/2010 6:10 AM

The Natrella book may be just what you need. Although it is considerably longer than you say, this is partly because it contains stuff you will never want; however, it is arranged so that you can easily skip this. The other reason it is relatively long is that it presents worked examples, again skippable, but very helpful for clarification for those cases where the basic explanation appears insufficient. It's in print again - the downside is US\$35 (or thereabouts).

N.B. The NIST/SEMATECH e-Handbook of Statistical Methods (Croarkin and Tobias - I looked it up) is said to be closely based on Natrella - but I would have trouble using it because the internet format is not readily scannable. [It also concerns me that several users who send me data seem to duplicate the formats of examples line-for-line and quantity-for-quantity, when it would appear that the examples were only intended to clarify the ideas.]

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#97
In reply to #96

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

03/01/2010 7:06 AM

I wish you would sign in. I'd give you two GAs for that reference! (I'd have to go up to the library and register as English Moose so they'd let me have two votes, but I would.) The linked list of references was a gold mine. Thank you!

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#98
In reply to #97

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

03/01/2010 10:50 AM

Give a GA to the posting anyway (it will work - although guests cannot give GAs, their postings can receive them). So far as I am concerned, the purpose of GAs is to help other technical victims (analogous to style victims) to identify useful postings.

One reason I don't log in is aggressive system protection. (In any case, you'll be able to recognise my postings until such time as someone with better technical expertise takes the trouble to spoof my style)

*I could override it - but I won't do that while using someone else's system

Fyz

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#99
In reply to #98

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

03/01/2010 12:49 PM

Wait a %%\$# minute! I knew I was talking with you, but I thought there were also two other guests that I was talking to also. Were you the only one there?

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#100
In reply to #99

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

03/01/2010 1:18 PM

I rather assumed you knew - including that the Natrella and Sematech references were mine.

Regarding others, it depends how far back you track. Ignoring the ignorant dogmatists (my opinion), there was the "welcome student" and at least one other (yes, it could have been two).

Fyz

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#101
In reply to #100

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

03/01/2010 7:20 PM

Hey Fyz - you got a Shiny number!

(Visit www.Shinys-on-BBT.cum for more disinformation).

Anonymous Poster
#102
In reply to #101

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

03/02/2010 5:27 AM

Thanks Kris

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#103
In reply to #102

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

03/02/2010 6:42 AM

Dunno who #101 was, but not moi (not that I'm saying a link to BBT is bad).

Fyz : I've read some of the recent stuff - please log on when posting. I'm not suggesting/implying you have any connnection to above post, but just wanted to take this opportunity to ask. We had this chat, a long time ago. CR4 has been a bit frictional of late, and logging in can help to stop any misunderstanding. Thanks. As said, I'm just saying this here as a by-the-by. No inuendo about other posts inteneded. Kris

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#104
In reply to #103

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

03/02/2010 8:39 AM

OK - I'll put my hand up to it.

I was logged on, but posted anon. in a moment of pranksterishness.

I got some sackcloth - anyone e-mail me some ashes?

(Also forgot to off-topic it ).

(But it was kinda sorta my unbirthday-ish ).

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#106
In reply to #104

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

03/02/2010 9:43 AM

Ask early, or I fear you'll need to ask an Aussie

Fyz

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#107
In reply to #106

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

03/02/2010 9:44 AM

Who are you kiddin'?

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#105
In reply to #103

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

03/02/2010 9:41 AM

The reply (#102) to room 101 was indeed moi - I didn't think it necessary to say. I'll post using the approved method when I'm posting from a computer where either the "protection" is not paranoid, or I don't consider it too unethical to over-ride it (e.g my own machine). In the meantime, I'll try to leave more clues that it is I.

Fyz

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#108
In reply to #105

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

03/02/2010 10:32 AM

OK, thanks to you and John for responding. I somewhat disagree with the not logging in bit, though it's no big deal. If John has got latex glooves on, it will be a very big deal - the folk at Dover Port will testify that I find such thing's to be no laughing matter. Being told to 'relax', just doesn't work.. Thanks, guys - issue sorted.

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#109
In reply to #93

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

03/30/2010 8:40 PM

Pedantic....damn I wished that thesaurus feature worked during these replys!

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#88
In reply to #80

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/27/2010 4:12 PM

On the subject of significant digits:
i) The defined accuracy changes in factors of 10 (crude)
It should be obvious to you that this alone is enough to mean that significant digits are inappropriate for serious work.
ii) Presentation as 4700 is not universally recognised as meaning 2 SF, and neither should it be, because that would make it impossible to show matters accurately. If you have to use significant digits, either use scientific notation with trailing digits after the decimal point, or use an an overscore to denote the final SF if the medium you are working in allows it (otherwise use an underscore).
If your examiners are fixated on this method, this should keep you as clean as practical without incurring their wrath. At the time of writing, the Wikipedia article I referenced earlier is by far the best resource on this topic I have seen.

If you want to do the tolerancing properly, state the number to a convenient number of digits (exceeding the actual accuracy), and state the uncertainty explicitly - either as "σ=" if the difference is statistical, or as "+/-value pk-pk" if that is more appropriate to the situation. That may not be standard in your field, but is generally understood, and it is both both clear and concise. If appropriate, you may also segregate the different sources of error.
NIST TN1297 is accessible on line, and will show you how the professionals do it; unfortunately, not everything there is appropriate for every situation, but only because some things are not routinely stated (being "motherhood" in the standards community).

Regarding this forum: it is completely open to anyone, so you should expect to see some people here who couldn't remotely make it onto your course; a lot of these people are very vocal. You will also find some very knowledgeable people, maybe even the (very) odd highly regarded engineer or teacher, though some who make such claims anonymously will prove to be fraudulent. Checking facts and approaches out for yourself is a wonderful way to learn. (And, if in doubt, collar the lecturer you most respect and ask her)

Good luck

Fyz

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#66
In reply to #64

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/26/2010 7:12 PM

Just to chuck in a thought or two:

"1 has one SD range 0.5 to 1.5"
...
Accepted.

"11 has two SD's range of 10.5 to 11.5" ...
and so 10 has two SD's range of 9.5 to 10.5

"111 has three SD's range of 110.5 to 111.5" ...
and so 110 has three SD's range of 109.5 to 110.5
and so 100 has three SD's range of 99.5 to 100.5

And the pattern continues.

Just because a digit within a number happens to be zero doesn't mean it's not significant.

Suppose you counted the number of playing cards in two packs, with all the jokers and red aces removed. Write down your answer.

Now we can all be absolutely sure that the number of cards is between 50 and 150??

I concede that counting cards is not the same thing as measuring some continuously variable quantity; but without knowledge of the capabilities of the measuring instruments, you cannot arbitrarily impose a measurement uncertainty - specifically not by basing it on the number of trailing zeros in the result presented.

If a 3½ digital meter, calibrated and known to be accurate up to the full scale displayed number (1999 ±0.5) reads "1000" - what range would you put on the value of the quantity measured?

Sorry to whitter on, but my goat was got and my gears were ground. Blame Ruddles.

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Anonymous Poster
#67
In reply to #66

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/26/2010 9:09 PM

10 has one SD and a range of 5 to 15

Anonymous Poster
#69
In reply to #66

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/26/2010 9:19 PM

110 has two SF and a range of 105 to 115

Anonymous Poster
#70
In reply to #66

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/26/2010 9:24 PM

100 has one SF and a range of 50 to 150

I'm out of here ... go and review...I've got better things to do!

Anonymous Poster
#74
In reply to #70

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/26/2010 10:47 PM
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#71
In reply to #66

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/26/2010 10:12 PM

Thanks John, you are writing sensibly. But these people are writing about a convention in representing precision - something that instruments don't attempt.

Now, even used "as intended", the use of significant digits to denote precision is a pretty crude indicator, and therefore any self-respecting professional would wish to discourage it's use where the level of precision is important. However, the convention has a long history, so I can't be totally cavalier about it.

The "proper" convention for significant digits (or significant figures) is that, if data is presented by a human, trailing zeros after a decimal point are assumed to imply precision - unless there is an accompanying statement to deny this. Fair enough so far. However, standard format numbers may need trailing zeros (e.g. 4700), and (to clarify that is is only trailing zeros that imply such precision) many texts state that "trailing zeros before a decimal point do not imply increased precision". Unfortunately, many people interpret this "do not imply increased" to mean that the precision will be the minimum possible for such a presentation - and this too is false. The wikipedia article on this matter is about as good presentations on the topic get:

• The significance of trailing zeros in a number not containing a decimal point can be ambiguous. For example, it may not always be clear if a number like 1300 is accurate to the nearest unit (and just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundred due to rounding or uncertainty. Various conventions exist to address this issue:
• A bar may be placed over the last significant digit; any trailing zeros following this are insignificant. For example, has three significant figures (and hence indicates that the number is accurate to the nearest ten).
• The last significant figure of a number may be underlined; for example, "20000" has two significant figures.
• A decimal point may be placed after the number; for example "100." indicates specifically that three significant figures are meant.
However, these conventions are not universally used, and it is often necessary to determine from context whether such trailing zeros are intended to be significant. If all else fails, the level of rounding can be specified explicitly. The abbreviation s.f. is sometimes used, for example "20 000 to 2 s.f." or "20 000 (2 sf)". Alternatively, the uncertainty can be stated separately and explicitly, as in 20 000 ± 1%, so that significant-figures rules do not apply.

Regards Fyz
Anonymous Poster
#76
In reply to #66

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/27/2010 12:06 AM

(1999 +/-0.5) would be 1999 and has four SF's (the last SF is always in doubt)

range 1998.5 to 1999.5

Anonymous Poster
#77
In reply to #76

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/27/2010 6:24 AM

One convention is to write such things as this as "1999". If the result was 1999 ±0.7, reading "1999" as being ±0.5 would be an overstatement of the accuracy, and to write 2000 would both introduce a systematic error that exceeds the tolerance, and (according to what I take to be other postings by yourself) to state that the tolerance is ±500. Even writing 1999 would be to imply an error that is a factor of seven greater than the actual.

Conclusion: not only is the SF method of implying tolerance generally unsuitable for serious work, but your insistence on ignoring presentation conventions means that you cannot even exploit such capabilities as it does possess.
If you have anything substantive to add I'd be grateful to read it. Otherwise, please refrain, as 7th-grade partial-use of a system with limited capability does not properly belong in an engineering forum.

Fyz

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#78
In reply to #66

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/27/2010 8:16 AM

Your point is clear and correct.

In the US, our version of the Royal Society for the Checking of Butcher's Dishonest Scales is the National Institute of Standards and Technology (NIST). NIST has established, and published, some almost absolutely clear guidelines. I say "almost" because NIST has thrown up their hands at the ambiguity of significant figures (which almost nobody gets right anyway - try getting a typical college student to tell you the correct number of significant figures for a trig function!) and advises in SP811 that the use of significant figures is controlled by many things.

"These include: — the need to indicate which digits of a numerical value are significant,
— the need to have numerical values that are easily understood, and
— the practice in a particular field of science or technology."

In NIST TN1297, which describes the accepted ways of stating uncertainty, they essentially recommend moving away from significant figures altogether and, instead, stating uncertainty (some call this error) in a way that reflects accuracy.

So, a typical meter reading (on my all too cheap DMM), if the meter has been properly calibrated will give a dc voltage reading of, let's say, 16.74 V. The accuracy of my meter, for that reading, is given to be +/-(0.8% of the reading + 5 digits). Thus my reading is best described as 16.74 V +/- 0.19 V. Those who check my math will see I have rounded up rather than rounded off; errors are usually done that way. Because this is a single measurement, the best way to express it is as worse case and the accuracy will thus be one significant figure or

16.7 V +/- 0.2 V

If maths are to be done, i.e., propagation of error, then the 16.74 V +/- 0.19 V should be expressed as relative error or 16.74 V +/- 1.1% and the standard rules for error propagation should be followed rather than the ones for significant figures. Note that maths should be done before any rounding (I used +/- 0.184 V instead of +/- 0.19 V) and the use of "guard" digits for intermediate steps is recommended.

So, you, in your case (obviously you have paid more than 10 EU for your meter!) would be correct in saying your reading is 1000.0 V +/- 0.5 V. At least here in the colonies. There is a slightly more detailed standard used, I understand, in Europe - the ISO GUM, but that costs even more than a good meter so I don't have a copy at the moment.

Cheers.

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#79
In reply to #78

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/27/2010 12:39 PM

That's interesting additional material.

I wasn't aware of SP811. Although the presentation seems a mite haphazard to me, I find that their recommendation in B7.2 (that if there is a conflict you should retain precision at the expense of implying lower than actual rounding errors) accords with my experience. (In any event, I would specify the errors separately if their value was important.)

I'm curious as to where you identified the TN1297 recommendation to "move away from significant figures".
Is there a codicil that I have missed, or are you relying (correctly in my view) on the firm instruction that explicit tolerance values must always be provided?
I also like the drive to distinguish between error types- but I suppose that could be because my potty-training was carried out by standards professionals.

Regards

Fyz
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#81
In reply to #79

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/27/2010 1:50 PM

God only knows where I saw that. Please note that I said they "essentially recommend". I don't believe there is anything like a "thou shall not..". If you're wondering, I'm in a different location from my copy of 1297. I'll look through next week if and when infrastructure returns here to the frozen artic rust belt and let you know.

Yes, 811 is a bit "catch as catch can". We're very fragmented in the US. Chemists use a different approach than physicists. Some people use ASTM, some use ISO, all too many use sig figs. In the default, and because I think I no longer have enough remaining years to wait for a unified standard, I specify errors anytime it's important. You can't go wrong with that (unless you consider my habit of rounding up and error in an error).

This whole topic would make a heck of a good blog. Would you be willing to sort of moderate one since you're the most knowledgeable (I think) on here about the subject?

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#86
In reply to #81

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/27/2010 3:45 PM

I think that, like you, I sort of know what is "best practice", and even sometimes manage to implement it. I can't see that this has changed since my technical nappies were changed in the '60s.

But the evidence so far is that you actually know far more about the practical variety of implementation.

Maybe a sort of joint effort in excess? (moderation not being a major one of my vices)

BTW, in common with many NIST manuals, the main text of TN1297 (1994) and SP811 are both freely (truly!) available on line.
And, while on this sort of subject, this relative openness is one of quite a few reasons that many Brits prefer the IEEE to our own national "equivalent" (I wish).
But at least the Royal Society is a different matter...

Regards

Fyz

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#87
In reply to #86

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/27/2010 4:07 PM

For the most part, we residents of "The land of round door knobs" don't know how to sort out foreign standards and agencies. Perhaps a primer on the English ones?

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#89
In reply to #87

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/27/2010 4:19 PM

My opinion (may not be true in all areas)
In practice we just negotiate to try and ensure we can both understand and use ISO (god, that's a tedious activity - albeit necessary), and then use ISO or US standards depending on the customer. Sometimes one or both of these is/are reissued with a British stamp on it.

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#13

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 1:42 AM

Alot.

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#15

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 6:06 AM

Just looking at the weight itself, energy = 5.25 kJ. The time doesn't come into calculating the energy, but it's needed to get the power. This comes to (average) 0.875 kW.

That's ignoring things like air resistance, lifting part of your own body mass etc, which posters might mention.

Cheers.........Codey

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#17

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 7:32 AM

Which lift? Some lifts consist of more than one stage, with energy lost at the shifts.

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#18

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 7:40 AM

Bit early for pedantry, but I'd need to bend over to pick the thing up. My arms aren't fat, but I'd ned to add that into the equation. Still trying to figure how time relates to energy in this. 'Power' sounds nearer the mark. I'll go hide, before I get butchered

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#23
In reply to #18

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 12:07 PM

8143 J ROFPMSLing at the prospect of a squirrel lifting a 255 kg barbell 2.1 m in 6 sec!

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#24
In reply to #23

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 1:58 PM

We only got liggle arms. Make up for it in nautighness, though

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#38
In reply to #24

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 7:56 AM

There must be something in the KrisDel™ Catalogue that would allow a squiggle to do this...if not, drag that Cat away from his bells and bows and get him to make one. He can use some of that mountain of tangled string he's accumulated.

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#19

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 7:55 AM

Of course, the official physics answer is work done = energy needed = mgh.

Nevertheless, it seems to me that biologically speaking, just to hold the weight in any position, much less lift it from position A to position B will surely require the significant expenditure of extra metabolic energy by the tissues - particularly by the skeletal muscles, brain and heart.

How would that be calculated?

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#20

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 10:16 AM

It requires more energy than I have!

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#21

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 11:24 AM

Feat or Feast,

I am sure a weight lifter exudes a lot of energy during a feast.

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#22

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 11:26 AM

about .25 horsepower.........

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#25

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 3:45 PM

Note that the problem asks how much energy you need, not how much work is done on the weight. Since the human body operates at an efficiency of ~20% - 25%, I'll pick the lower and say you need at least 25 kJ.

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#27
In reply to #25

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/17/2010 11:28 PM

WOW

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#28

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 2:07 AM

Olympics? Weights are 450 mm dia and thicknessed for increments

So lift is 1.875 m so;

1.875 x 9.81 x 255 = 4690.4 J

(it's in the question)

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#29
In reply to #28

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 2:13 AM

P.s that makes ER 55 J off and Sonos 560 off.

Or ER is 10 times as accurate.

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#30
In reply to #28

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 4:14 AM

If the weights are lifted to a height of 2.1 meters, then what is their height before they're lifted? 225 mm?

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#31
In reply to #28

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 5:07 AM

I didn't know the diameter of the weights was fully standardised. Do you have a reference?
But shouldn't we subtract the radius of the bar from the radius of the weights?

Fyz

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#32
In reply to #31

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 6:04 AM

It shouldn't matter so long as you're not consistent.

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#33
In reply to #31

### Re: The Weight Lifter: CR4 Challenge (02/16/10)

02/18/2010 6:39 AM

Yeah it's tragic Fyz, but everything in Olympics is 'standard', 'formulated', 'tabulated', 'unified'.

For reference? they only needed to google "Olympic standard+weights"

It was a huge clue to the start height.

But Hey - you did allude to that factor, quite early in the piece, and no one took notice!!!!

Ummmm - "radius of the bar"?

I think not; as the sex of the lifter is unspecified (but could be researched on weight division!!!!!)

But, if we were meant to factor anything but the finished height of the C of G - there would also be a deflection number as the different bar diameters have different 'droop', which also depend on such as grip spacing in different lifts.

Or conceivably, due to bar flex, the lifters hands may be higher than 2.1 m, the center of mass is at 2.1m, therefore "at the stated value".

Got a new "1 pearl, 1plain" crop near harvest?

(thanks Fyz - I was about to tear a few new.....pratt holes)

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