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Re: the famous formula

From Odd Bodkin <bodkinodd@gmail.com>
Newsgroups sci.physics.relativity
Subject Re: the famous formula
Date 2018-12-12 16:27 +0000
Organization Aioe.org NNTP Server
Message-ID <purcte$1tqu$2@gioia.aioe.org> (permalink)
References (12 earlier) <g77moqF8191U1@mid.individual.net> <pummhj$vf2$2@gioia.aioe.org> <g7a3hoFoc5dU1@mid.individual.net> <puovcb$1mbf$1@gioia.aioe.org> <g7co0oFbh39U1@mid.individual.net>

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Thomas Heger <ttt_heg@web.de> wrote:
> Am 11.12.2018 um 19:24 schrieb Odd Bodkin:
> 
>>>>>>> 
>>>>>>> We have a similar problem with 'speed' and 'velocity'.
>>>>>>> 
>>>>>>> Both have units like m/s , but one is a vector quantity (velocity) and
>>>>>>> one is not (speed).
>>>>>>> 
>>>>>>> Speed is the magnitude of velocity.
>>>>>>> 
>>>>>>> https://examples.yourdictionary.com/examples-vector-scalar-quantity-physics.html
>>>>>>> 
>>>>>>>> The acting force has direction.
>>>>>>>> The path along which the force is acting has direction as well
>>>>>>>> But the work as integral of scalar product of these 2 vectors is a
>>>>>>>> scalar, without direction.
>>>>>>> 
>>>>>>> work is NOT 'forth times path'
>>>>>>> 
>>>>>>> but ' force times distance'.
>>>>>> 
>>>>>> No, it is not that either. It is the integral of the scalar product between
>>>>>> two vectors, the force and the differential displacement.
>>>>> 
>>>>> 
>>>>> 'Work' is the name of a quantity in physics.
>>>> 
>>>> As is velocity.
>>>> 
>>>>> 
>>>>> It relates to the real world, hence is not a product of either one or
>>>>> two vectors.
>>>> 
>>>> I disagree. There are LOTS of real world quantities that are related in
>>>> some way to other real world quantities. Velocity (a vector) is related to
>>>> differential displacement and differential time. Momentum is related to
>>>> mass and velocity.
>>> 
>>> This is correct. But I had something against this statement:
>>> 
>>> ".. It is the integral of the scalar product between two vectors..."
>>> 
>>> I said: no, it is not, since a vector is a mathematical construct.
>> 
>> I disagree. A vector is a way to characterize a physical quantity. Velocity
>> is a vector, momentum is a vector, force is a vector. All of those are
>> real.
> 
> There is still a difference between 'vector' and 'physical quantity 
> characterized by a vector'.

Not in a physics discussion, normally. 
When I talk about velocity, I can refer to it as a vector and that means
the physical quantity characterized as a vector. The two are synonymous and
understood. Maybe not by you. 

> 
> A vector is a mathematical construct, while quantities have units and a 
> physical meaning.
> 
> You may characterize that quantity by an appropriate vector, but this 
> does not make a vector a quantity.
> 
> 
>>> 
>>> A number is also a mathematical construct. And you cannot multiply two
>>> brainchilds and hope to get something real.
>>> 
>>> 
>>> First statement: a quantity in physics (work) is defined as being the
>>> product of one quantity (force)and some sort of length.
>> 
>> “the product” is too vague. Given that the two things you are multiplying
>> are vectors, you have to be precise about what you mean by “product”. In
>> this case “product” means scalar- or dot-product.
> 
> 
> I was trying to show, that the product of a force and a path is not the 
> right idea.

If you want to redefine work, using the same term that has been used with a
particular understanding for centuries, good luck with that. 

So many amateur hacks come into this group with a lack of background
reading and understanding of basic concepts, and then they make mistakes
because the concepts do not mean what they think those mean. And then they
complain, “Well, it SHOULD mean what I think it means.” 

No, it should not. What SHOULD happen is that amateur hacks should educate
themselves on the meaning of basic concepts before discussing them. 

> 
> You are correct, since it is always done that way.
> 
> But it is wrong, in my opinion. So let me tell you, why work should be a 
> vectorial quantity:
> 
> 
> Force is a quantity (represented by a vector) with a direction (in space).
> 
> This vector contains enough information about the direction.
> 
> A path is actually a construct composed out of points in Euclidean 
> space, which the object in question reaches at certain points in time.
> 
> First problem: the points are unimportant and do not belong into the 
> calculation.
> 
> IOW: if you lift a heavy stone by one meter, the work should be equal, 
> if you lift the same stone a little bit later at a different position 
> (same gravity assumed).
> 
> So the location does not belong into the equation and also time 
> (absolute time) does not belong there neither.
> 
> If we kick that out of the equation, we have got left 'distance' (in the 
> direction of the movement), which is something we need.
> 
> This distance is a scalar.
> 
> If we multiply the scalar value of distance with a vector for force, 
> then we get a good and satisfying result.
> 
> 
> The benefit is, that the quantity would match to the usual understanding 
> of the term 'work'.
> 
> It is also matched by a counterpart, similar to Newton's actio equals 
> reactio.
> 
> The work is then done by the active part (in case of the stone: by you) 
> and balanced by the passive part (the stone).
> 
> 
> If work is a scalar quantity, you cannot easily do this,
> 
> Instead it would require to invent something like 'working stuff'.
> 
> But work is not a substance, but an activity (done by e.g. material 
> objects).
> 
> 
> ...
> 
> 
> TH
> 



-- 
Odd Bodkin — Maker of fine toys, tools, tables

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