Weight Calculation

Steps-

1. By using basic geometry to find the volume (Class 6 mathematics provided the tyre/wheel are not having tread or profiles on outside)

2. Multiply by density to get the weight.

I see.so how do you calculate the volume and density to get the weight given the data in my previous question? I`m really sorry cause I`m really having a hard time figuring it out.Thanks.

Area of ring = area of outer circle- area of inner circle

volume = cross-section x height

"height" ?

Am I missing something here, sb? Don't you mean cross section x radius of revolution ?

<edit- can't be bothered to delete- your'e quite right, sb, he said 'height'. Go with working out toroidal volume by following the manner shown in the link below>

The size given sounds more like a roller than a tyre .

If he means a tyre, I'm not even sure if it's solid or not. Ah well, perhaps Arnold can figure it out from the answer given by mathsguy here.

Since Arnold is not just weighing the thing, it sounds like homework . Trouble is, not long ago there was a thread all about helping students. I'm soooo confused !

Arnold : Could you bit a little clearer about the shape you're trying to work out, and why you want to know. I don't mind occasionally trying to help a student (if that's what you are) - the link may give you something to go on.

Well height can be the third dimension didn't want to sppon feed. In fact already spoonfed enough.

Interestingly the dimensions almost looked that of a 1/2" machined washer.

can not be metric (at least not of preferable size M14 is not much in use it is M12 or M16)

But then washers weights are given any of the catalogues (Though mostly in terms weight/100 pcs or 1000 pcs) we can however divide can we ? not sure.

Yes I caught it:

Washer M14 as per DIN 9021/ ISO 7093 - ID 15mm, OD 44mm - but thickness is 3mm not 4

Well that makes life easier if it's a washer; He can way a zillion of them and divide by a zillion.

He mentioned wheel and tire. Maybe a model airplane wheel, which would make sense to know its weight.

He needs to calculate cross sectional area of the tire, assuming pretty much circular, times the mean circumference of the tire to get the volume of the tire, times the density of the tire material. He's on his own there.

The wheel, being multi-contoured, needs to be dipped into a vessel filled to the top with water with a pan underneath to catch the overflow. The volume of the overflow can be measured and multiplied by the density of the wheel material. Actually, the same can be done with the tire, particularly if the cross section of the tire is not circular.

Doh, I just read post 7.

Weight = Mass x Gravity Acceleration

Mass = Volume x Density

• To find th volume: immerse the tire/wheel into a scaled tank filled with a liquid, then find the difference in two volumes (before immerse and after) which represents the actual volume of tire/wheel.

• To find the density: ask the supplier.

• To find the acceleration of gravity: open any physics book.

• Note: If the scaled tank is not available, try to buy one. And this procedure is the the best one, and don't try to measure the weight directly by using any means or scale.

why not just weigh it on scales

It sounded like the excercise was to do it without the luxury of a scale.

V (annulus) = pi (t) (outer radius^2 - inner radius^2)

= pi (4) (22^2 - 7.5^2).

~ 5375 mm^3

Then, multiply by the density of the material to get the weight.

Alternatively, V (solid of revolution) = pi (mean diameter of rotation) (area of cross-section) = pi [(44+15)/2] (4) [(44-15)/2] ~ 5375 mm^3.

Hello Arnold,

Can you tell me if this is 'homework' please?

Is this 'wheel' flat, or does it have a small rim with a plastic 'tire'?

With a wheel so small, it would be pretty easy to mark a glass jug or bowl, measure the water in the container and then measure the expelled water. Just as advised by Mr Galala.

If this cannot be done try calcs as 'sb' suggested.

If this wheel is just a flat disc you should know how to work this out with basic math. Please be honest. Things you need to know is: the stuff the wheel is made from, Is it pressed steel? Is it all the same metal or does it have a plastic rim.

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If you do as advised by Mr Galala yo will find the volume but maybe not the exact weight. You can search for the weight of mild steel which is probably what is it.

But then who marked hiim OT?

Let me correct it back there is nothing OT on a home work (except the thread itself)

Hello sb,

Hope you are well?

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Here it the part from the 'Faqs' list with reference to:

'Homework".

Do your own homework. CR4 is not a homework cheat site. While some here might relish the opportunity to sharpen up old rusty skills by working the homework problem, consider this and consider it well.

If you cheat on your homework by using someone else's answers, you are only cheating yourself, because the purpose of any homework or other college assignments is to help you learn - by practice, repetition, and self-discovery. (thanks STL Engineer)

Take care................bb

Hi bb,

I don't disagree with the official line, but.....Arnold has not yet clarified the questions asked of him, and also thing are not quite so clear cut;

DAG : Now for the question, would users of CR4, in general, mind receiving questions (some may seem elementary or not well thought out) from high school students?

Chris Leonard : I am very supportive of the idea and think we can provide a lot of value through it.

You'll have to read the linked thread to see the full context, and I don't think Arnold is one of DAG's students. However, I see no harm in pointing him to a link to calculate volume of a toroid. I've suggested links to many members on topics that might be viewed as more basic. In general I wouldn't do sums for somebody, though I'd be happy to suggest the direction to go or tools to use.

Where did STL go ? He was always fun and informative, especially on the Challenge Questions.

Very well said, YesMam !

I'm of the opinion that Arnold's stuck on the geometry, but your second paragraph contains comment just as good/valid as the first.

Hello YesMAM,

You get a thumbs up from me.

GA to you Sir.

The OP has enough sense to find CR4 and all they need is here on the 'sponsors' area. If they can find this they should be able to find the other info' they need.

As the OP is still 'at school', which seems the case anyway, they should know or have at their 'finger tips' answers to any Math, Volume, or area equations needed. In fact all they need by way of 'tools' to solve this problem are likely to have been dealt with in the Math or Engineering studies, in which they were asked to solve this problem.

It is called 'studying', and not for nothing.

Here for this problem to be solved and throughout their life, the OP will need to solve any number of these types of problems. Learning the basics now, getting those hammered well in place, will make any future solving a piece of cake................. Or it will if the OP studies and actually takes it, absorbs, the basic 'laws' and 'rules'.

If, the OP is trying to find an answer by using some 'converter' or similar method they will not learn anything. They should have the knowledge already, but if they have to search out a site or book which gives an explanation, then they are on the correct course!................. There will be a time when a computer or calculator is not 'at hand' so the need to figure this out with pen and paper is the only really reliable way. It is the way we all work things out as we work, if that is, the answer is not already in our heads as we work?

The OP may not know the kind of metal, but, in that case they should get answers based on all the basic metals it is 'likely' to be.

There is not many, it is probably either mild steel, cast white metal, cast aluminium, cat iron, or possibly stainless. Not hard work really.

I wish you luck Arnold. Can you tell us if you are a boy or bloke? I will not have to refer you as 'they/OP' then.

Take care.

Hi bb,

This is slightly off-topic, but we have sort of come to an interesting point ; over-dependence on the internet, and the nature of teaching/learning. Schools (UK) seem to be driven by bottom line results (not just exam results, but ongoing SAT type evaluations of school/pupils). The answer is usually deemed more important than the process of finding it (). When I venture to the libraries, I rarely see youngsters now (unless they are using the free internet access).

I harbour a secret fantasy - to be in charge of a class for 1 term. I'd et assignments and not allow any internet use. Give the students as much access to books as they want. Somebody who didn't get the exact answer to a specific problem would get marks for demonstrating the approaches to solution they had taken. My justification for that would be the value of applying original thought, and research via books. A computer link may not be available in a real-life situation, and often it's the knowledge gained along the path of solving a specific problem that has as much (if not more) value as the solution. Not quite a return to the dark ages, but a bit of practice in using methods that are not hi-tech. I'd expect solutions to be written up from first principles, and would add complications such as tred-pattern to a question such as the example asked about by the OP. Students who added additional blab about tyres, mathematical history, historical citations etc would get extra marks. Anybody attempting cut 'n' paste would be locked in the cellar with nothing more than pen and paper (with perhaps straight edge and compass).

Hello Kris,

Sounds just the way I would go about teaching for a term. I know exactly what you mean about bok knowledge as well. There is always times when you do not have access to a computer or the net. Often a book is more direct as well. Searching is an acquired skill. Where as having a set of encyclopaedia and you can find as many references to the subject you want to know about, as you have time or can be bothered to read.

On a computer often a search result seems to have no relation to what you typed! It all depends on the search Engine and whether it is Meta? I have learned almost all I know from books. Looking at one reference you notice something else on the opposite page and before you know it you have spent three hours doing research.

Though one of my friends belittles searches and computing, they are the first to want me to research something and they want to know 'yesterday'! And when I call it research I am told I am just 'playing. Makes me angry sometimes. Still I am busy enough without searching for people who do not give a damn. Like me working on research for a day or more then they say "oh, I have changed my mind now"!

Hey, take care..............bb

Hi again bb,

Yep, I much agree with what you say.

The internet is a fantastic tool, but I think it's easy for people to become overdependent on it for problem solving. In the rush to make youngsters IT savvy, some fundamental learning skills are being marginalized. Not just technical and research, but social skills and communication. Perhaps the world could have a 'no-tech' day/week at schools, just to see what happened. It would be interesting if nothing else. It's good that youngsters learn how to use the internet, but there should be balance between doing so and using more traditional methods/resources.

Hello Kris,

Perhaps the world could have a 'no-tech' day/week at schools,/

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You may have said it 'tongue in cheek', but I think it would be a seriously good idea. There could be a disaster or a major electrical fault which could not be remedied in less the say a week? What would the Teachers and Pupils do then?

I note a pretty balanced use of the several Libraries I use, with older pupils perhaps on 'day-release' and already at work, using a computer to verify information for 15 minutes, then they go back to the tables and Encyclopaedia to continue their projects.

I wonder if the schools Minister would be brave enough to close the electronic super highway down for a day or week as you say? I have a feeling you would get at most a wry grin? As you said though, it would be a chance to consolidate and prove they bot Teachers and Pupils are capable of using pen and paper......I wonder???

Take care my friend.............bb

I think your mind was reading mine ! When writing it, I was slightly tongue-in-cheek, but by the time I finished I did actually think it would be quite a good exercise. It would probably need 1-week for whatever conclusions to begin to sink in, but I'm sure some valuable lessons could be learned by all.

Hello Kris,

Agreed, it does seem as if we were thinking the same thoughts!

Take care..............

bb

Why we all think the same thing (have I started invading the brains too?)

Two things I find problem with the net searching.

1. The data very often (and you will or may be will not be surprised) conflict as you said already.

2. The searching is too easy. And without the hard work, you forget even before you have learnt it. And these forums are the worst offender for students. I tell my children again and again (when-ever they ask for some meaning) to refer the dictionery. And for clarifications, I usually never as far as possible give the answer, just show the method. And after I posted my mail #1, I asked my son (class 6) to tell me crossection area, he didn't know area of circle formula so I just tried on rectangle that he knew, and he solved it without any hint. For volume, he needed hint but then I asked how to calculate volume of cube from the base square and he could do the rest.

The problem what I have founs (and I have mentioned some times back too) the students of today don't like to toil, they love the answers readymade and they do not visualise the problems.

The responsibility is with the education system and the peer pressure.

I remember in my long back school days- (<sob> the reminisces are always accompanied with it) there used to be a few questions amounting to some 30% marks where you have to solve by first principles some equation. All those have disappeared with objective type questions (select the correct answer) and what i have seen that due to this the total basic understanding and the foundations have collapsed.

There was time (and the questions papers gave ample time) for one to even calculate a bit of formulae if you do not remember and you know the principles. But now no more, the answer to be marked in one minute flat or less. So either you know the answer or don't. Method immaterial. And that's the thing mirrorred in CR4 too.

What about the edu systems elsewhere?

Hello sb,

I echo what you say in every respect.

In the UK and similarly in the U.S. some of the lack of learning enjoyment, if that is the way to phrase it, is down to 'one Parent Families'. Certainly in the UK one person cannot be certain to have enough time to realise 'homework' should be done....... Not later! But as soon as the kid/s come in from school. That is if the kid/s do

come in from school and do not go to a friend's or play football away from the house. It is one mad rush to get the homework finished, or that should be 'acceptable', 'it will do' kind of attitude, is prevalent.

I know of at least one Family where the Sons homework was done by the Mother. Because, I imagine, it was easier to do that, and halfway expect a 'B', than to let the child take the responsibility of the undone homework. This became a habit, so after a few days of starting in high school, the child did not expect to have to complete THAT homework. So they 'knew' nothing of the effort and anguish, (quite natural when accomplishing a project anyway) the single parent went through. This included the complete lack of what was expected of a child in high school, and the fact that the school 'process' should be to gradually put more pressure on a child as part of the 'growing up' and being ready for anything system. I have no idea how this child ever learned anything at all! Of course in that situation there was no 'pressure', common sense, order, and any sense that homework was the child's 'job' went out the window. There was little routine past that which 'had' to be done.

It became ridiculous when the Mother allowed the child to leave the homework on the coat rack as they collected the football and trainers to go out and play football for a couple of hours and to 'hang around with friend's for most of the rest of the time before it was bed time. This was never before 23:30. Almost needless to say this child never even thought of University.

That whole situation is down not only to the single parent and the child. It is also down to both Parents not taking Marriage seriously enough to stay together long enough to raise the kids!

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Quite how this child, now adult, ever manages his real work I cannot imagine. Would they go home after a mundane days of packing boxes and or loading shelves expecting others to clear up after them?

As you may have realised this makes me extremely angry.

All it would have taken to do a halfway decent job of bringing this single child up, would have been the drumming into the child that school work/homework yes, can get encouragement and help, from the Parent, but the work was the child's to do and if they did not do it they take the consequences. Simple as that.

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This is just one Family and admittedly unusual in the homework being done by the Parent. I also know of two others where the grown up 'kids' cannot read and understand what they try to read, and they get Mum to write CV's and any correspondence at all.

This is far longer than I had planned for a reply. Forgive me sb.

Take care...............

I wrote letters all the time when I was at school. Did they not learn?

I did the same thing with my daughter in the beginning (never with home work rather with class project).

Then stopped it and told her that please get a C in your project but with your own effort. What other kids parents are doing are none of our concern.

The son automatically (being junior) had to do it from first.

The funnier thing is in class 2 or 3 they expected them to make the model with cardboard of an ambulance. last year (class 5) they were supposed to make the model with electric motor, battery etc of a wind mill.

He did it, not artistic of course , got a C. But do they really want these to be done by kids?

I wonder.

BTW we are already totally off topic and on a new topic (of the squirrel's subject).

Should we ask the admin to change the name or cut a part of it and paste as a new topic "Education system maladies".

can not keep on talking the same thing again.

Hello sb,

Hope you are well?

With ref' to my post,............. The problem is this child was not giving enough time to allow the homework to be done. This is why the Mother started to do the homework. It carried on and became the 'norm'!

With regard to your son having to do homework with motors etc, I think any homework is done to 'prove' the previous learned subject is fully understood? But if kids are not 'pushed' using their own methods, they will not ever find 'what' they are good at or, come to that, what they actually like doing? Which could mean the way they go when it comes to finding a Job?

Thanks for the post my friend.

Kris, bb,..

I think we are way OT on this, but still a very stimulating and meaningful dialogue, if you ask me. I wonder how many others in CR4 are thinking the same way. There was a push on to teach elementary students math skills with calculators instead of the old addition/subtraction tables. Saves time, is more accurate, and the abundance of inexpensive calculators made them accessible to every student. (Again, the emphasis is on quick and right instead of on the how and technique.) Good until the battery dies. I agree with both of you that there is too much dependence on internet answers (I can say I'm as guilty as the next person) and not enough pure research done. Emphasis in manufacturing companies (except pharmaceuticals) is to get away from research/development and into cheap production techniques. Same is for time spent. Quicker to do an internet search to find a simple answer than to dig out the old textbooks. But by eliminating those low tech skills we somehow lose something. Keep the faith and stick with what you know works.

It's a very interesting digression (and not entirely off-topic). I suspect that most CR4 people would echo the views we all have here.

This would make for an interesting wider debate if any of you were to post it up as a thread in it's own right. I'm going away for a week soon, so can't do so with the attention it deserves. Whilst we might share concern about the current state of things, it would be good to hear more input about possible ways to address some of the issues raised. Any takers ? As said, I can't make much further input for a while, but it's a worthy topic to initiate wider discussion on.

Hello YesMAM,

Many thanks for your post.

Perhaps we have been OTT on this. But we said what I feel needed saying. And with regard to your reference to the rest of CR4 I would not be surprised to hear they feel the same way.

As I left school I knew how to fathom the area and volume of anything 'with right-angled corners'. But knew nothing of how to figure out the areas of circles, etc. I bought some books and taught myself that. I had a terrible schooling with little care by the Teachers. But, I did do my own homework. The fact I went through three years of the same classes, being taught the same subject repeatedly seems to have wrung no bells at all with anyone who should have been checking!

Take care...............

Hello YesMAM,

Just to say I pretty much fully agree with what you say.

I do not understand how these people (now adult) cannot be ashamed by having to ask their Mother (and me) to write letters and fill in Forms etc?

For various reasons I had a terrible education, I have to say 95% is down to being taught the same things in almost all lessons apart from History and Geography, for three terms.

Most of the stuff I 'know', especially the science based stuff, I have learned myself from a book, because I realised early on that though I knew the basics of the three R's, I did not know enough to run my life, and so bought books and just studied in my own time. Sooner that than ask my Parents about Math and English!

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Take care my friend...................

One of the most important lessons I learned in college oh so many years ago was not to know all the answers but where to find them.

Boy, does that remind me of my undergraduate P Chem final. We were given a sheet with 3 problems on it, choose 1 and answer it fully. 3 days to complete it, total access to textbook, class notes, and library. Solution written up in Journal format with footnotes and references. Just work individually, no collaboration. As we compared notes later, we found that it had actually been a test of our ability to search the library, since each problem required its own specific piece of data that could only be found in a published research paper in one of the journals in the library.

Glad I could bring back memories. Hope they are good ones. But I guess that depends on how well you did on the exam, doesn't it. Keep your comments to CR4 coming.

Hello Kris,

Have only just read you post sorry, just soooo busy catching up on emails.

I will come back to your links latter, and I would be interested in the thoughts of Chris Leonard, and the clear cut views of CR4 admin!

I looked through "Faqs", and you can see what they say in my post just above your I think? But they seem to say something different to what Chris says.

I have no qualms in pointing the possible school kids to a site or explaining a way to find an answer at all. I have never thought it a good idea to give someone an answer though, because it will be of no future use. They will always rely on others instead of being self reliant, which the schools, and homework seems to want to achieve? Can't forever go ask mummy can we?

Besides which, if or when they asked others and out of spite the wrong answer was given it could have more serious consequences.

I will read the links Kris, but I don't have time right now. Whatever chris says should be echoed in the Faqs though!!!!!!!

Take care............

Hello again Arnold,

Firstly, please stay in contact with this thread.

It will 'test' your searching 'skill', but all the answers are actually on CR4 or I should say "Globalspec.com". All the various things like the Metal weight are listed somewhere on this site. Do some work in searching and using the stuff you find to find the answer. I have the answer based on the weight of stainless steel.

The weight will not be very much different from 'mild steel' which it is more likely to be.

Good luck and let us know when you have an answer please.

Arnold. I agree with those that have said you need to know an answer, or how to find it. GlobalSpec sponsors this fine site. Try this. Look for wheels that match the dimensions that you have given. Then look at the shipping weights for the wheels that closely match. That is a no math method to find your answer. Good luck, and try to think of who has done your work for you already.

Hello bob c,

Just to say the shipping weight will not necessarily give the wheel weight. I would imagine he may also have to show his method?

Take care OK?

Hi Arnold,

It's my pleasure to help you.

You haven't given much information, but let's assume you're speaking of a simple disk of the dimensions you mentioned. The only thing missing is the material the disk or tire is made of, but since tires are often made of rubber, let's make that assumption, too.

On the internet, you can search for the "specific gravity" of materials. Specific gravity is a number comparing the density of a material to the density of water. The number always is in grams per cubic centimeter.

Take a look at the following, and I hope this will help you to understand ...

Please understand that this makes a lot of assumptions. If your tire has round edges, the volume will be different. If it is made of another material, you must multiply by the specific gravity of that material.

If you want to explore more about Solid Geometry, you might check out ...

http://www.onlinemathlearning.com/solid-geometry.html

I hope this helps.

Kind regards ...