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ptlng


Sep 27, 2007, 3:24 PM
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Extreme actuary, the deceleration is not constant. It increases linearly with rope stretch. That's why there is a peak force at the very end instead of a constant one. The correct answer is twice what you calculated.

An error of factor 2 is a pretty big one in actuarial work, is it not?


extreme_actuary


Sep 27, 2007, 3:56 PM
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Good point, I was assuming constant deceleration. (talking about nit picky!)
Does the force to stretch the rope increase linearly? That seems odd, you would think it would be closer to exponentially. But, I am no rope expert.

An error by a factor of two would mean our insurance company is holding double the amount of money in reserves for future claims, cutting our profits. Our stock price would go down a few points. Big deal, it would be years before they would find my mistake! Smile


sgauss


Sep 27, 2007, 4:05 PM
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Re: [extreme_actuary] Kilonewtons? a question for those who understand physics [In reply to]
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extreme_actuary wrote:
Just like engineers, throw around a bunch of equations without really knowing what's going on.Wink

Here is the way an actuary explains it:

I am going to keep this all in metrics so it is easier to follow.
Let's say your mass is 75 kg. (that is about 165 lbs here on earth).
Now, you suppose you fall 10 meters (about 30 ft).
Let's say you are caught by the rope, and with all of the slippage in the system and rope stretch, from when the rope first starts to catch you until you actually stop is 1 meter (about 3 ft.).

Now, let's look at the forces:

First, we have to figure out your final velocity during this big whipper.

We will use the equation:
(final velocity)^2 = (initial velocity)^2 + 2 X (accel.) X (distance)
initial velocity = 0
Accel. = 9.8 m/sec^2 is the acceleration due to gravity on earth.
Distance = 10 meters
so, (final vel)^2 = 2 X (9.8 m/sec^2) X 10m
Solving this gives us the final velocity = 14 meters/sec

Now, we need to figure out our decceleration when we stop. We will use the same equation above:
(final vel)^2 = (initial vel)^2 + 2 X (Decceleration) X distance
Now, the initial velocity is 14 m/sec and the final velocity is 0 m/sec. because we are stoppping.
The distance to stop is 1 meter (given at the beginning due to stretch and slippage)
so, our equation is:
0 = (14)^2 + 2 X (Decceleration) X 1
solving gives Decceleration = -98 m/sec^2 (which is about 10 g's, well within our tolerance)
Almost done!
Now, plugging this decceleration into our formula for force:
Force = Mass X Acceleration give us:
Force = 75 kg X -98 m/sec^2
= 7350 Newtons = 7.35 Kilonewtons (force is always positive)
So, this 30 foot fall by a 165 lbs. person where the rope/system stretches 3 feet causes about 7.35 Kilonewtons of force on our system.

Whew! All of this math knowledge and I am stuck pricing insurance?!?

I can't believe I'm about to spray about physics.

Your math is too messy, to hard, with too many intermediate results and nasty square roots. Just like an actuary to get overinvolved in the numbers, and ignore the underlying concepts.

Basic physics

1. Force = mass * acceleration
2. Work = Force * distance.

So
Work falling is mgd1.
Arresting the fall has to counter that energy.
Work arresting is F*d2

F*d2 = mgd1
F = mgd1/d2 : Yeah, I'm showing my work this time.

One problem, in order to stop you, the rope also has to counter the force of gravity. So

F = mgd1/d2 + mg or mg(1 + d1/d2)

So, for your ten meter fall, one meter arrest of a 75KG climber, the answer is 8.085 kN.

I will add that this naively assumes that the rope applies a constant force, which is naive. I don't know what the accepted model for rope behavior is, although I'll acknowledge ptIng's suggestion of 2:1.


extreme_actuary


Sep 27, 2007, 4:30 PM
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In reply to:
So, for your ten meter fall, one meter arrest of a 75KG climber, the answer is 8.085 kN.

Sure, after you've seen the answer.


ptlng


Sep 27, 2007, 4:46 PM
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Actuary, yes a simple rope model is like a spring. Force grows linearly with stretch.

You are also ignoring the additional energy in the fall that occurs while the rope is stretching. Sgauss accounted for that which is why his answer does not match yours.

You are fired.


jt512


Sep 27, 2007, 6:06 PM
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extreme_actuary wrote:
In reply to:
So, for your ten meter fall, one meter arrest of a 75KG climber, the answer is 8.085 kN.

Sure, after you've seen the answer.

It must be nice to have so much time on your hands that you can post lengthy analyses that are completely wrong. The constant braking force assumption is not even remotely accurate. The usual model of rope behavior is Hooke's Law, which states that the force is proportional to the relative stretch. Hasn't rgold already covered this? Back to school, boys.

That said, "Extreme_actuary" is the raddest username on the site.

Jay


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Sep 28, 2007, 5:34 AM
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Re: [ptlng] Kilonewtons? a question for those who understand physics [In reply to]
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ptlng wrote:
Extreme actuary, the deceleration is not constant. It increases linearly with rope stretch. That's why there is a peak force at the very end instead of a constant one. The correct answer is twice what you calculated.

Ah, that explains it! I didn't like E_A's solution, because I thought that was too little rope stretch to give a figure as low as 7kN. But when I checked the math, it was all correct.

Thanks PtIng!

GO


extreme_actuary


Sep 28, 2007, 9:57 AM
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I better stick to my actuarial tables. At least when I make a mistake there, nobody ever catches it.


extreme_actuary


Sep 28, 2007, 10:06 AM
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When I was in college, I was a pre-med student. One day, my math professor came to me and told me I should go into math instead of medicine. I was flattered. I asked him "Do you really think I am good enough at math?"
He responded "No, but you make so many mistakes you'd kill somebody if you went into medicine."


jt512


Sep 28, 2007, 3:09 PM
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extreme_actuary wrote:
When I was in college, I was a pre-med student. One day, my math professor came to me and told me I should go into math instead of medicine. I was flattered. I asked him "Do you really think I am good enough at math?"
He responded "No, but you make so many mistakes you'd kill somebody if you went into medicine."

I was a premed too originally, and for some reason I got hounded with recruitment mail from actuarial programs at other schools. I ended up going into epidemiology and then biostatistics, so I guess these actuarial schools had something about me figured out.

Jay


Partner rgold


Sep 29, 2007, 9:48 PM
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jt512 wrote:
Hasn't rgold already covered this?

Well, yes, in this .pdf posted about half a year ago on this site, but there are lots of folks out there having their own fun with mathematics. Extreme actuary is in good company; the error of assuming that deceleration is constant is, from what I've seen, the most common mistake among those who write with enough clarity to make it possible to identify errors.

The Hooke's law assumption itself is an idealization, of course. However, there is data suggesting it provides a good model for the extension phase of a dynamic rope arrest.


pastprime


Oct 3, 2007, 4:19 PM
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This thread is a good example of why so many sensible,intelligent people think they can't understand math and physics. The problem isn't that math, or physics, is difficult. It isn't. What is actually going on is about as basic, and understandable as any subject could be. The problem is that people in the field refuse to explain it in understandable terms.

Latch onto this concept: The principles; the reality; that math was invented to describe, existed exactly as they are for quite a few billion years before there were humans or language. The words mathematicions, and physicists, use to describe what is going on, are just noises made with the mouth, or weird markings on a paper. They have no intrinsic meaning in themselves.

Mass and force really are two separate things. There are times when speaking as if they are the same, or using the same unit titles to describe them, can cause confusion. This is particularly true for astrophysicists. Remember, whether or not we use the same word to describe a certain amount of mass, and or a certain amount of force, is up to us. It is something we just decided to do, or not do.
We seem to get along using the same word for different things, like boat that floats on the water, and gravy boat, that holds gravy; and using different words for pretty much the same thing, like cup and mug; but scientific academecians think if we use the same word for an amount of mass; or weight- that is, mass under the influence of gravity on earth; and the amount of force it takes to support that mass when it is on the earth, that we are going to get hopelessly confused. Because they care deeply about us, they decided to help us out of this confusion by introducing a new set of terms that make no sense to anyone who has not gone to some considerable effort to understand them.

Remember, the people who decided that the word pound, or kilogram, would absolutely not do to describe force, are the same people who consider it important , and worth arguing at length about, whether or not Pluto should be called a planet. Pluto does what it does, and is what it is, with no regard whatsoever to what anyone says about it. Forces, and weights, do what they do with no regard whatsoever to what terms are used to describe them.


Consider this: The word pound was used to describe force for many, many years, and the cars, and airplanes, and a whole lot of other things, designed using the word pound as a unit of force, worked just fine.
When torque readings for tightening bolts were given in foot pounds, a whole lot of people working on their cars without torque wrenches handy, knowing about how much force it took to lift 50 lbs, for instance, and knowing they had a 1 foot wrench, were able to come reasonably close to getting the torque right on bolt that specified 50 ftlbs. This worked just fine for many decades. Now torques are given in newtons, and pounds are no longer a unit of force, and somehow we are supposed to believe that if we use pounds as a unit of force, nothing will work and the engine will come apart.
I still have a torque wrench calibrated in foot pounds, and the engines I build hold together just fine.

In summary: 1kn=the force exerted by 225 pounds at rest, on earth, in a downward direction, and knowing this can give a pretty good idea of how strong something is, which is what we were concerned about in the first place.

If you fall, and after all the math, it in reality turns out that you exert the amount of force that we call 10 kn, then if your anchor will hold exactly 2260 pounds, hanging from it statically, then you are ok. If your anchor will hold only 2240 pounds, hanging from it without movement, then you are in trouble.

Thank you for allowing me to vent. I feel much better now.


Valarc


Oct 3, 2007, 6:50 PM
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pastprime wrote:
This thread is a good example of why so many sensible,intelligent people think they can't understand math and physics.

...

Consider this: The word pound was used to describe force for many, many years, and the cars, and airplanes, and a whole lot of other things, designed using the word pound as a unit of force, worked just fine.

...

Now torques are given in newtons, and pounds are no longer a unit of force, and somehow we are supposed to believe that if we use pounds as a unit of force, nothing will work and the engine will come apart.

Actually, you are an example of one of those people who have gotten confused. Pounds are a unit of force. Ever since the invention of newtonian physics, pounds have been a unit of force, and they always will be. Using pounds to describe mass is a hackneyed and confusing artifact of the history of the english system of units.

What you need to realize is, the unit of pounds existed LONG before mankind knew the difference between a weight and a mass. The concept that the pull of gravity could vary from place to place was completely unknown, and the measure was a practical one. When the math was developed to actually understand what a force was, it was determined that what they had really been measuring all these years was a force, and thus the pound was determined to be a unit of force.

However, people were still using pounds to describe how much of something they had, and so it was used as a unit of mass too. It's not REALLY a unit of mass, but since the Earth's gravitational field is relatively consistent across the surface of the Earth, it's good enough for anyone not trying to calculate the solutions to physics problems.

What I think is most completely wrong about your long tirade, though, is your blaming the confusion on educators. The confusion in the terminology is a result of historical usage, and has nothing at all to do with the way it's taught (*at least by physics teachers, and I'll touch on that one again in a second). When I teach the concepts of force and mass to undergraduate students, they have absolutely no problem understanding it - because we use units that were developed AFTER the discovery of newtonian physics - kilograms and newtons, where there is absolutely no historical ambiguity.

Which brings me back to another one of your points - pounds did not suddenly stop being a unit of force, and become replaced by kilonewtons. Instead, your wrenches were changed in a fruitless and half-assed attempt to convert form the ass-backwards and unwieldy english system to the more elegant metric system. Pounds are still a unit of force.



* There is a caveat to my statement that the way it's taught is not the source of the confusion. The way it's taught in physics courses is not confusing at all. However, engineers have this absolutely irritating habit of using pounds for both mass and weight, which is a big source of confusion, and I watched fellow students struggle with the concept for months at a time when I was forced to take a few engineering courses back in my undergrad days. Pounds are a force. Slugs are a mass. The english system of units SUCKS ASS, and their common usage sucks even MORE ass.


jt512


Oct 3, 2007, 9:20 PM
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pastprime wrote:
This thread is a good example of why so many sensible,intelligent people think they can't understand math and physics. The problem isn't that math, or physics, is difficult. It isn't. What is actually going on is about as basic, and understandable as any subject could be. The problem is that people in the field refuse to explain it in understandable terms.

Latch onto this concept: The principles; the reality; that math was invented to describe, existed exactly as they are for quite a few billion years before there were humans or language. The words mathematicions, and physicists, use to describe what is going on, are just noises made with the mouth, or weird markings on a paper. They have no intrinsic meaning in themselves.

Mass and force really are two separate things. There are times when speaking as if they are the same, or using the same unit titles to describe them, can cause confusion. This is particularly true for astrophysicists. Remember, whether or not we use the same word to describe a certain amount of mass, and or a certain amount of force, is up to us. It is something we just decided to do, or not do.
We seem to get along using the same word for different things, like boat that floats on the water, and gravy boat, that holds gravy; and using different words for pretty much the same thing, like cup and mug; but scientific academecians think if we use the same word for an amount of mass; or weight- that is, mass under the influence of gravity on earth; and the amount of force it takes to support that mass when it is on the earth, that we are going to get hopelessly confused. Because they care deeply about us, they decided to help us out of this confusion by introducing a new set of terms that make no sense to anyone who has not gone to some considerable effort to understand them.

Remember, the people who decided that the word pound, or kilogram, would absolutely not do to describe force, are the same people who consider it important , and worth arguing at length about, whether or not Pluto should be called a planet. Pluto does what it does, and is what it is, with no regard whatsoever to what anyone says about it. Forces, and weights, do what they do with no regard whatsoever to what terms are used to describe them.


Consider this: The word pound was used to describe force for many, many years, and the cars, and airplanes, and a whole lot of other things, designed using the word pound as a unit of force, worked just fine.
When torque readings for tightening bolts were given in foot pounds, a whole lot of people working on their cars without torque wrenches handy, knowing about how much force it took to lift 50 lbs, for instance, and knowing they had a 1 foot wrench, were able to come reasonably close to getting the torque right on bolt that specified 50 ftlbs. This worked just fine for many decades. Now torques are given in newtons, and pounds are no longer a unit of force, and somehow we are supposed to believe that if we use pounds as a unit of force, nothing will work and the engine will come apart.
I still have a torque wrench calibrated in foot pounds, and the engines I build hold together just fine.

In summary: 1kn=the force exerted by 225 pounds at rest, on earth, in a downward direction, and knowing this can give a pretty good idea of how strong something is, which is what we were concerned about in the first place.

If you fall, and after all the math, it in reality turns out that you exert the amount of force that we call 10 kn, then if your anchor will hold exactly 2260 pounds, hanging from it statically, then you are ok. If your anchor will hold only 2240 pounds, hanging from it without movement, then you are in trouble.

Thank you for allowing me to vent. I feel much better now.

Nice rant. Too bad you got a basic fact wrong. The pound is fundamentally a unit of force. So your bolded statements above are not very meaningful.

Jay


(This post was edited by jt512 on Oct 3, 2007, 9:22 PM)


pastprime


Oct 4, 2007, 8:08 AM
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valarc and j, thanks for the correction. I feel better now, knowing the world is in this small way somewhat less screwed up than I had thought. Seriously, I'm not being sarcastic.
It's been a long time since I took physics, and I'd gotten the impression something had changed.

So why are we stuck with strength of climbing gear being given in KNewwtons, instead of the much more relatable kg or lbs? I'm old enough to have been in the industry when those were the units on the hang tags and in the literature, and no one ever questioned what what they actually meant, as so many do with Kn.
My rant may have been misguided, but I'm still convinced Kn is a poor unit to use for conveying an important piece of information.


jt512


Oct 4, 2007, 8:34 AM
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pastprime wrote:
valarc and j, thanks for the correction. I feel better now, knowing the world is in this small way somewhat less screwed up than I had thought. Seriously, I'm not being sarcastic.
It's been a long time since I took physics, and I'd gotten the impression something had changed.

So why are we stuck with strength of climbing gear being given in KNewwtons, instead of the much more relatable kg or lbs? I'm old enough to have been in the industry when those were the units on the hang tags and in the literature, and no one ever questioned what what they actually meant, as so many do with Kn.
My rant may have been misguided, but I'm still convinced Kn is a poor unit to use for conveying an important piece of information.

I suspect that nearly all the people who don't understand what a kN is are Americans. You can graduate from college here without ever having even an introduction to physics or math beyond the elementary school level. People here can't calculate a 15% tip, never mind fathom a fearsome equation like F = ma.

As to why gear is now usually rated in kN, I don't know for sure. Like I said, it's likely only to be a problem for Americans, anyway. But the kN is the official international unit of force (whereas kg is the unit of mass), so, I imagine that the practice is becoming, or has become, standard worldwide. Or it simply might be required by the EN under which the gear is certified.

Jay


glytch


Oct 4, 2007, 9:18 AM
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pastprime wrote:
valarc and j, thanks for the correction. I feel better now, knowing the world is in this small way somewhat less screwed up than I had thought. Seriously, I'm not being sarcastic.
It's been a long time since I took physics, and I'd gotten the impression something had changed.

So why are we stuck with strength of climbing gear being given in KNewwtons, instead of the much more relatable kg or lbs? I'm old enough to have been in the industry when those were the units on the hang tags and in the literature, and no one ever questioned what what they actually meant, as so many do with Kn.[/email]
My rant may have been misguided, but I'm still convinced Kn is a poor unit to use for conveying an important piece of information.

I would contend that most people have absolutely no perspective on forces of the magnitude that gear can handle. The average person probably can't tell you if their car weighs 2000, 4000, or 6000 lbs. After a certain point (a few hundred pounds, say), any bodyweight intuition pretty much vanishes. Same for distances in space: How far is 93 million miles (distance to the sun)? Well, it's in miles, a unit we use all the time, but it's still impossible to comprehend. As you learn about gear and anchors, you have to recalibrate your intuition regarding the size of forces, no matter the units used; kilonewtons are good units for the task, giving manageable numbers (can you imagine buying carabiners rated to 5,723lbs?) - if you have to re-learn the sizes of things, might as well do it with a convenient unit.


sgauss


Oct 4, 2007, 9:23 AM
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jt512 wrote:

As to why gear is now usually rated in kN, I don't know for sure. Like I said, it's likely only to be a problem for Americans, anyway. But the kN is the official international unit of force (whereas kg is the unit of mass), so, I imagine that the practice is becoming, or has become, standard worldwide. Or it simply might be required by the EN under which the gear is certified.

Jay

Why is it in KN?

Valarc wrote:
The english system of units SUCKS ASS, and their common usage sucks even MORE ass.

When I took Physics, I think they gave us problems in AMERICAN units just to make us suffer. I agree with Valarc, and I'm glad most climbing equipment info is given in metric units. I find gear specs that give carabiner weight in ounces useless. An ounce is just too coarse a measurement at 28g/ounce, with carabiner weights starting to bottom out at 28g.

I just hope that the terrorists don't win if we use the metric system!


(This post was edited by sgauss on Oct 4, 2007, 9:36 AM)


Valarc


Oct 4, 2007, 10:09 AM
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pastprime wrote:
So why are we stuck with strength of climbing gear being given in KNewwtons, instead of the much more relatable kg...

Because kilograms are not a unit of force. A one kilogram hunk of styrofoam has a mass of one kilogram whether it's sitting on the ground exerting roughly ten newtons of force downward, or floating in water exerting a couple of newtons of force upward. Mass is an intrinsic quantity of an object.

Rating strength is a fundamentally force-based idea - you pull on an object with a certain force and see if it breaks. The mass of the object used to pull isn't necessarily connected. Think of it this way - a hydraulic ram, with a mass of a few kilograms, can exert hundreds or even thousands of newtons of force. Using a unit of mass when you really mean to use a unit of force is exactly why the weight versus mass discussion can get so confusing. Use the proper units to refer to things and it's a hell of a lot simpler.


whirbl


Oct 4, 2007, 10:38 AM
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if only all you americans would switch from your silly and backwards english system all this confusion would be avoided.


binrat


Oct 4, 2007, 10:59 AM
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whirbl wrote:
if only all you americans would switch from your silly and backwards english system all this confusion would be avoided.

Nice, but don't forget the old Canadians who flip back and forthCrazy

Binrat


pastprime


Oct 4, 2007, 11:41 AM
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Re: [Valarc] Kilonewtons? a question for those who understand physics [In reply to]
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You had me feeling better until you said Kg wasn't a unit of force. If pounds can be a unit of force, so can kg. All you have to do to make it so, is for people to agree that it is. The physics stays exactly the same.
1kg=2.20462lb . 1lb=.45359kg. The law of identity says that whatever is on one side of the equation can be substituted for whatever is on the other side. They are the same thing.
For those who say kg is not a unit of force, I say it can be used as such, and it works just fine.
Go back to may origional post, substutute ".45359kg" everywhere you read pounds, and I stand by it.
It's not that I don't understand what is being said. I think it is confusing to force people into acting as if there is some distinction that is only there in outer space.
All definitions of units of force that I know of go back to expressing it in terms of the effects of gravity on a certain mass.

To those who say weight does not equal force, I ask: How is weight measured? By a scale. What does a scale actually indicate? The downward force being applied to it by the object being weighed.
A scale, which measures weight, and, on earth, mass, does not scan the object, calculate the density of it's molecules, then count those molecules to come up with some figure. It measures the force being applied to it, and we know that that force is the same as the mass, or weight.


glytch


Oct 4, 2007, 11:50 AM
Post #48 of 85 (1742 views)
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Re: [pastprime] Kilonewtons? a question for those who understand physics [In reply to]
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pastprime wrote:
You had me feeling better until you said Kg wasn't a unit of force. If pounds can be a unit of force, so can kg. All you have to do to make it so, is for people to agree that it is. The physics stays exactly the same.
1kg=2.20462lb . 1lb=.45359kg. The law of identity says that whatever is on one side of the equation can be substituted for whatever is on the other side. They are the same thing.
For those who say kg is not a unit of force, I say it can be used as such, and it works just fine.
Go back to may origional post, substutute ".45359kg" everywhere you read pounds, and I stand by it.
It's not that I don't understand what is being said. I think it is confusing to force people into acting as if there is some distinction that is only there in outer space.
All definitions of units of force that I know of go back to expressing it in terms of the effects of gravity on a certain mass.

To those who say weight does not equal force, I ask: How is weight measured? By a scale. What does a scale actually indicate? The downward force being applied to it by the object being weighed.
A scale, which measures weight, and, on earth, mass, does not scan the object, calculate the density of it's molecules, then count those molecules to come up with some figure. It measures the force being applied to it, and we know that that force is the same as the mass, or weight.

A kilogram is defined as a specific quantity of mass. The conversion between pounds and kilograms is, you're right, a bit confusing. That said, a kilogram simply is NOT a unit of force, and no amount of twiddling can make it anything other than a unit of mass.

Here's an example of what you're doing, in a different context: Take a car that is traveling at an exactly constant speed (x miles/hour). If you want to know how far the car has traveled, the answer surely comes in miles. However, in this specific case, someone could say that the car has traveled 3 hours. Since you know that the car is traveling at exactly x mph, you know that the car has gone precisely 3*x miles. That obviously doesn't mean that in this scenario time and distance are now the same thing. There is a known relationship between time and distance when dealing with the car, just as on earth with our more-or-less constant gravity, there is a well known relationship between mass and force. That does not imply that mass and force are one in the same!

I hope that example clears things up, at least a bit.


pastprime


Oct 4, 2007, 12:20 PM
Post #49 of 85 (1732 views)
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Re: [glytch] Kilonewtons? a question for those who understand physics [In reply to]
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I fully realize that mass and force are not the same thing. In truth, I can't easily imagine anyone thinking they are, or why anyone ever thought it necessary to make such a big deal over the distinction.
My point (pointless point- no one is going to change anything because of this discussion) is that, on earth, which, to the best of my knowledge, is where everyone lives who might be reading this, the names we use for units of mass can be interchangably used as the names we use for units of force, and the physics works out the same.
There is no valid reason to complicate things by adding more terminology that is not easy to relate to.
The fact that pounds has been used for centuries as a unit of both without problem proves my point.
We don't need, and would create less confusion, without Kilonewtons. Kilograms would work better, and would better help some guy, even some guy in France or Norway, I'll bet, know whether this skinny cord, made of some material he's never heard of, is strong enough to be used for tying up his cow.


jt512


Oct 4, 2007, 12:33 PM
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Re: [sgauss] Kilonewtons? a question for those who understand physics [In reply to]
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sgauss wrote:
jt512 wrote:

As to why gear is now usually rated in kN, I don't know for sure. Like I said, it's likely only to be a problem for Americans, anyway. But the kN is the official international unit of force (whereas kg is the unit of mass), so, I imagine that the practice is becoming, or has become, standard worldwide. Or it simply might be required by the EN under which the gear is certified.

Jay

Why is it in KN?

Did you actually read what you quoted?

Jay

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