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Anonymous Poster #1

Help Find Center Of Gravity of Compound Body

05/17/2017 2:14 PM

Dear Gurus,

Please help me to find the C of G of the following combined bodies: it is drawn on a 1 foot grid

This is not a homework question: it is something that "came up" at work.

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#1

Re: Help find Center Of Gravity of compound body

05/17/2017 2:20 PM
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#2

Re: Help Find Center Of Gravity of Compound Body

05/17/2017 2:50 PM

For one thing, you show a 2 dimensional object.

The other thing what your really looking for is the Moment of Inertia. Or maybe the Centroid.

Thirdly, you give the density, but not the mass for unit of measurement... of course one could extrapolate...

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#3

Re: Help Find Center Of Gravity of Compound Body

05/17/2017 3:25 PM

which way is up, in your diagram? Are these free objects in space, or are we looking down on them as on a plane surface?

How high is each from surface? What do you mean when you say combined? Do you mean in the present positions, but linked, or do you mean all smashed and squished together? Are the objects drawn to the scale indicated in your opening statement?

Is this a normal 4 dimensional universe with space-time curvature?

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#4

Re: Help Find Center Of Gravity of Compound Body

05/17/2017 3:29 PM

1. find the mass of each region (two rectangles and circle), m1, m2, m3

2. find the center of each region, concentrate the mass at the center.

3. pick a reference point (e.g. left bottom corner) (0,0)

4. for each region masses m1, m2, m3, center point at (x1,y1), (x2,y2), (x3,y3)

5. total moment from reference point = (Mx, My)

Mx=m1*x1+m2*x2+m3*x3, My=m1*y1+m2*y2+m3*y3

6. center of gravity is located at (cx, cy)

cx = Mx/(m1+m2+m3) cy = My/(m1+m2+m3)

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#15
In reply to #4

Re: Help Find Center Of Gravity of Compound Body

05/17/2017 11:18 PM

Good. I think #s 1, 2, & 3 are overthinking it, or maybe (probably??) rabble rousing.

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#5

Re: Help Find Center Of Gravity of Compound Body

05/17/2017 3:29 PM

.

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#6
In reply to #5

Re: Help Find Center Of Gravity of Compound Body

05/17/2017 3:35 PM

Interesting, my numbers are slightly different.

X: 6.7414, Y: 3.7352

hey,... now they're really different...

How you get '.'?

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#8
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Re: Help Find Center Of Gravity of Compound Body

05/17/2017 3:51 PM

Without indicating the location of the origin, the numbers can be anything. Where is your origin?

ρ = 50:

mass = 8 * 50 = 400

CoM location: 3,4

.

ρ = 100:

mass = 12 * 100 = 1200

CoM location: 4,2

.

ρ = 400:

mass = pi (1.5^2) * 400 = 2827

CoM location: 10,5

.

Xcom = (400*3 + 1200*4 + 2827*10) / (400 + 1200 + 2827)

Xcom = (1200 + 4800 + 28270) / 4427

Xcom = 34270 / 4427

Xcom = 7.74

.

Ycom = (400*4 + 1200*2 + 2827*5) / (400 + 1200 + 2827)

Ycom = (1600 + 2400 + 14135) / 4427

Ycom = 18135 / 4427

Ycom = 4.09

.

Aggregate CoM = 7.74, 4.09

4427 pounds.

Check my math. I'm my own worst profreadr

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#7

Re: Help Find Center Of Gravity of Compound Body

05/17/2017 3:49 PM

What ever your job is,

I hope it is not in engineering, and

if you have to ask such a question of us, and

you do not figure this out for yourself,

then your employer is paying you too much...

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#9
In reply to #7

Re: Help Find Center Of Gravity of Compound Body

05/17/2017 4:15 PM

Was that really necessary?

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#11
In reply to #9

Re: Help Find Center Of Gravity of Compound Body

05/17/2017 5:53 PM

Apparently.

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#13
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Re: Help Find Center Of Gravity of Compound Body

05/17/2017 8:34 PM

Trying to pick up where Lyn left off.

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#14
In reply to #13

Re: Help Find Center Of Gravity of Compound Body

05/17/2017 11:14 PM

... same answer ..

-Mr.Guest... What possessed you to post such a reply?

.. Tho they do say the clock can write twice a day.

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#27
In reply to #13

Re: Help Find Center Of Gravity of Compound Body

05/18/2017 2:04 PM

Who's lyn?

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#28
In reply to #27

Re: Help Find Center Of Gravity of Compound Body

05/18/2017 3:06 PM

Now stop it, just stop it!

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#29
In reply to #28

Re: Help Find Center Of Gravity of Compound Body

05/18/2017 3:58 PM

Who put Sir Robin off topic.... I put 1 vote on topic...

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#30
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 4:23 PM

Sir Robin himself did. He originally posted off-topic. Now he has 5 GAs and nothing to show for it.

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#33
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 6:46 PM

Oh,... that happens to me all the time.

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#34
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 6:58 PM

Seems a lot of us are in that boat....

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#35
In reply to #34

Re: Help Find Center Of Gravity of Compound Body

05/18/2017 7:34 PM

Off topic, us? Never, the link is there (arguably tenuous as it may be sometimes).

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#36
In reply to #35

Re: Help Find Center Of Gravity of Compound Body

05/18/2017 7:51 PM

Speaking of off-topic, anybody know a way to search for the post with the highest off-topic count? Might be kind of amusing to see the "bottom ten".

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#37
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 8:22 PM

I don't think the site has that particular feature. I think we have to do it from memory, besides some of the highest have likely been deleted when the whole thread was deleted by the site moderators.

If you are interested try a search on CR4 for post histories of certain particularly <ahem> out of their element and entertaining CR4 users, if I remember correctly those are where the most off-topic flags reside.

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#38
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 8:38 PM

Some months I read where one of the mods (or maybe it was Savvy) who, as a joke, marked someone's comment at 10,000 OTs?

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#41
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 9:42 PM

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#52
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Re: Help Find Center Of Gravity of Compound Body

05/19/2017 10:05 AM

Come on, Jack, don't be timid, you can name me, I am almost certain it is me you refer to...hey man, love you one beer.

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#57
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Re: Help Find Center Of Gravity of Compound Body

05/21/2017 4:18 PM

Really, it didn't even cross my mind. Perhaps you are thinking of political discussion posts, I don't count those (far, far too easy).

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#39
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 8:46 PM

I think your answer lies with our new guru, gutmonarch and his predecessors

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#40
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 9:30 PM

Once upon a time, a moderator gave somebody 10,000 OT votes (in fun). IIRC, Merph to Doorman.

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#42
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 10:19 PM

Hahaha! How did he respond? Like, WTF????

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#43
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 11:14 PM

With good humor.

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#44
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 11:29 PM

I've employed a "click farm" to bring up my GA count, but it barely keeps me out of the bottom ten.

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#47
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Re: Help Find Center Of Gravity of Compound Body

05/19/2017 7:00 AM

I think its been hacked.

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#53
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Re: Help Find Center Of Gravity of Compound Body

05/19/2017 3:27 PM
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#54
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Re: Help Find Center Of Gravity of Compound Body

05/19/2017 4:10 PM

So that is where all the little cellulars live in the matrix before reality jolts them out in the virtually real world?

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#55
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Re: Help Find Center Of Gravity of Compound Body

05/20/2017 12:30 AM

Those sounds like two reasonable explanations..

I've read about lithium batteries dimensions a fraction of a mm too large for it's case and essentially 'squishing' them into combustion. (perhaps at some point)

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#56
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Re: Help Find Center Of Gravity of Compound Body

05/20/2017 8:40 AM

That looks like the "next-gen" massively parallel super computer config.

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#45
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Re: Help Find Center Of Gravity of Compound Body

05/19/2017 3:12 AM

In danger of getting into murky bath water...
Del

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#46
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Re: Help Find Center Of Gravity of Compound Body

05/19/2017 6:59 AM

Challenge accepted... that is for the most off topic post that is. I'll start if off.

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#48
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Re: Help Find Center Of Gravity of Compound Body

05/19/2017 8:19 AM

Start 'if' off?

Sounds iffy

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#49
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Re: Help Find Center Of Gravity of Compound Body

05/19/2017 9:30 AM

Now that was accidently appropriate, how convenient.

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#51
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Re: Help Find Center Of Gravity of Compound Body

05/19/2017 10:04 AM

Probably the post I have responded to the most. Just sayin'.

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#12
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Re: Help Find Center Of Gravity of Compound Body

05/17/2017 7:47 PM

Now, now, he/she never said what they do for a living. For all we know it came up at an accounting firm during the lunch break.

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Re: Help Find Center Of Gravity of Compound Body

05/17/2017 4:25 PM
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#16

Re: Help Find Center Of Gravity of Compound Body

05/18/2017 4:48 AM

Thanks all for the replies and sorry to put you all to so much trouble.

Didn't anyone follow my link to this weeks "caption this". I thought at least Phoenix911 would have recognised the configuration.

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#18
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 7:39 AM

I did, but how many times have I told you about copying other peoples work during the exam.

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#25
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 1:43 PM

Looking at this picture, shouldn't the (extremely lightweight for a forklift) forklift rectangle be rotated 90° with respect to the torpedo/bomb rectangle?

And what of that round thingo? If that represents the contents of the forklift operator's trousers after dropping that load, shouldn't it be in the driver's seat? Or was he wearing Spandex and landed nearby?

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#17

Re: Help Find Center Of Gravity of Compound Body

05/18/2017 4:53 AM

cut them out from thin sheet steel.
Use 1 thickness for the 50 lb/ft.
Use 2 for the 100 lb/ft
Use 8 for the 400 lb/ft
Fix them together on a sheet of stiff card or thin plywood.
Dangle it from point and draw a vertical. Repeat and the intersection of the verticals is the c of g.
No calculation required.
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#19
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 9:56 AM

Interesting answer, and clearly a pragmatic means.

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#20
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 10:07 AM

This basically how I did it. I changed it to a unitless measurement and used the ratios instead.

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#21

Re: Help Find Center Of Gravity of Compound Body

05/18/2017 10:34 AM

These are flat shapes and not bricks, cylinders or spheres, aren't they?

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#22

Re: Help Find Center Of Gravity of Compound Body

05/18/2017 12:30 PM

Impossible to solve as stated/shown. Density needs to be in mass/volume. You are showing density as mass/area which makes no sense!

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#23
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 12:36 PM

yes, it should have been in lbs/ft3

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#24
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 1:18 PM

OR it could be some new 2D universe someone is about to reveal?

I agree that knowing the weight per square foot and (assumption) having gravity facing into the page makes it possible to calculate an answer, but what does that have to do with reality? Don't ask me.

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#26
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 2:01 PM

Or he could've simply called it 'pressure' instead. Force/area.

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#31
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 5:39 PM

Mass/area is just fine with me. When I was working, some of which was designing floors, lb/sqft was the unit we used. Mass/sqft may not properly be called density, but it works just fine.

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#32
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Re: Help Find Center Of Gravity of Compound Body

05/18/2017 6:05 PM

Strictly-speaking, mass isn't a force, and so mass/area isn't a pressure. Weight/area is because it takes into account the acceleration of gravity. Unfortunately the units of mass and of weight have the same names and therein lies the confusion.

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#50
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Re: Help Find Center Of Gravity of Compound Body

05/19/2017 10:01 AM

That is where carpenters making a world sized room could and would run into problems.

In the limit where gravitation acceleration is not a "local" constant due to a change in effective radius, the weight density over the length of a floor would not be constant, although the mass density would in fact remain constant.

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#58
In reply to #31

Re: Help Find Center Of Gravity of Compound Body

05/22/2017 1:31 PM

Mathematically, ''lbs/ft2'' is unit-area-weight-density, and ''kg/m2'' is unit-area-mass-density, or if you prefer, weight-density-per-unit-area, and mass-density-per-unit-area, respectively, because:

w = m g (all in appropriately corresponding units)

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