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So here's a curious little thing...
I noticed the other day that some of the cars in the showroom were
parked on little metal ramps. Now here's the puzzling thing. My car is
only little, and that weighs 1.25 tonnes. Some of the bigger cars surely
weigh even more than this. So these ramps have multiple tonnes bearing
down on them... and they're made from 2mm steel.
Now obviously somebody far, far smarter than me has carefully calculated
how thick the steel needs to be to hold a given amount of weight. But
these things look so utterly flimsy, it looks like you could bend them
with your bare hands. And yet, you can park a car on them, and they
don't even distort slightly.
I am at a loss to explain this.
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> I noticed the other day that some of the cars in the showroom were parked
> on little metal ramps.
You mean like these:
http://members.iinet.net.au/~mmckenzie/files/VX_CHARGED_S/ramps.JPG
> Now here's the puzzling thing. My car is only little, and that weighs 1.25
> tonnes. Some of the bigger cars surely weigh even more than this. So these
> ramps have multiple tonnes bearing down on them... and they're made from
> 2mm steel.
The bigger cars are probably at most 2000 kg, worst case is say 70/30
front/rear weight distribution, so I'd say max 700 kg on each ramp (if you
put the front wheels on it).
> Now obviously somebody far, far smarter than me has carefully calculated
> how thick the steel needs to be to hold a given amount of weight.
Well it seems to me that there are 4 vertical columns supporting the weight,
so probably max 200 kg or a max force of 2000 N in each column.
There's a neat formula that Engineers use to determine the maximum load a
column can take without buckling, find it here:
http://en.wikipedia.org/wiki/Buckling
A bit of rearranging gives us a formula for I (the required area moment of
inertia):
I = F * (K*L)^2 / (pi^2 * E )
In this case we have:
F = 2000 N
K = 0.5
L = 0.3 m
E = 200 GPa
So I = 2.3 x 10^-11 m^4
This allows you to choose what shape and thickness to use.
For simplicity assume a cylindrical rod is used, the formula for the 2nd
moment of area is:
I = pi/4*r^4
Rearranging:
r = (4*I/pi)^(1/4) = 2.3 mm
So there you go, make it out of diameter 5 mm steel rod and you'll be fine!
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scott wrote:
> You mean like these:
>
> http://members.iinet.net.au/~mmckenzie/files/VX_CHARGED_S/ramps.JPG
Yeah.
> The bigger cars are probably at most 2000 kg, worst case is say 70/30
> front/rear weight distribution, so I'd say max 700 kg on each ramp (if
> you put the front wheels on it).
Does that really work? I mean, can you really just say "oh, this thing
has 4 wheels, so each one only takes 1/4th of the load"?
Also, something like a Prius is 3042 Kg (unloaded). I'm presuming they
make these ramps with a damned wide margin for safety.
> Well it seems to me that there are 4 vertical columns supporting the
> weight, so probably max 200 kg or a max force of 2000 N in each column.
But can you really do that? Can you really just say "there's 4 columns,
so divide the load by 4"? Wouldn't it depend on the angle of the force
being applied? And what about the horizontal elements? They need to not
bend at the points where they're unsupported as well.
> Rearranging:
>
> r = (4*I/pi)^(1/4) = 2.3 mm
>
> So there you go, make it out of diameter 5 mm steel rod and you'll be fine!
Looks thinner tham 5mm to me - but then again, it isn't cylindrical...
Just how strong is steel? I mean, obviously it varies by type, but how
much load can you typically put on steel without bending/shattering it?
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> Does that really work? I mean, can you really just say "oh, this thing has
> 4 wheels, so each one only takes 1/4th of the load"?
Well from experience most cars are pretty equal for left/right weight
distribution, and as I said worst case is probably 70% on the front wheels.
So yes, probably 35% of the total weight is the maximum on any single wheel.
> Also, something like a Prius is 3042 Kg (unloaded). I'm presuming they
> make these ramps with a damned wide margin for safety.
Usually when you buy a pair of those ramps they will be marked as supporting
a certain load. 2 ton per pair of ramps is common. If you go over that
then obviously there is a large risk they will break.
> But can you really do that? Can you really just say "there's 4 columns, so
> divide the load by 4"? Wouldn't it depend on the angle of the force being
> applied?
Of course, I was simplifying to get a rough estimate. In reality you would
have to take the worst case loading condition, which is probably with the
tyre directly on top of a single column.
> And what about the horizontal elements? They need to not bend at the
> points where they're unsupported as well.
You would obviously check for this if you were designing it, but I assume
this wouldn't happen as a tyre usually spreads out the load across an area.
The loading would be concentrated at the tops of the support columns as
these won't budge.
> Looks thinner tham 5mm to me - but then again, it isn't cylindrical...
Yes, something like an I beam or a hollow cylinder is a more efficient use
of the metal.
> Just how strong is steel?
It varies from about 250 - 750 MPa. That's the stress you need to apply to
it before it starts to deform plastically. As an example, my steel ruler
has a cross section of 1mm x 25mm, you'd need to pull on it with between
6-18 kN of force, that's the weight of a car.
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Shape is everything. Metals resist tension better than they do pure buckling.
And think of the keystone bridge. Put this all together and you have an
intuitive explanation for why those ramps are not perfect cubes.
Unfortunately, this IS what I studied in college. :/
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>> Does that really work? I mean, can you really just say "oh, this thing
>> has 4 wheels, so each one only takes 1/4th of the load"?
>
> Well from experience most cars are pretty equal for left/right weight
> distribution, and as I said worst case is probably 70% on the front
> wheels. So yes, probably 35% of the total weight is the maximum on any
> single wheel.
Hmm, interesting. I wouldn't have expected that to work.
> Usually when you buy a pair of those ramps they will be marked as
> supporting a certain load.
Sure. I just meant that they probably design them to easily support more
weight than any common car that somebody might try to put on them.
> Of course, I was simplifying to get a rough estimate. In reality you
> would have to take the worst case loading condition, which is probably
> with the tyre directly on top of a single column.
Isn't the worst-case when you drive the car onto the ramp and the
suspension jiggles it up and down over one support column?
>> And what about the horizontal elements? They need to not bend at the
>> points where they're unsupported as well.
>
> You would obviously check for this if you were designing it, but I
> assume this wouldn't happen as a tyre usually spreads out the load
> across an area. The loading would be concentrated at the tops of the
> support columns as these won't budge.
Looks to me like the tire would usually sit between the two horizontal
struts. One is directly over an upright, but the other is on the middle
of the beam. (Obviously that isn't a problem or they'd have added
another upright...)
>> Looks thinner tham 5mm to me - but then again, it isn't cylindrical...
>
> Yes, something like an I beam or a hollow cylinder is a more efficient
> use of the metal.
A few of those struts seem to be angled. But most of them are just flat.
>> Just how strong is steel?
>
> As an example, my steel
> ruler has a cross section of 1mm x 25mm, you'd need to pull on it with
> between 6-18 kN of force, that's the weight of a car.
Jesus, that's strong! o_O
So... what the hell is the thickness of a tin can then? Those seem to
deform pretty easily.
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>> Well from experience most cars are pretty equal for left/right weight
>> distribution, and as I said worst case is probably 70% on the front
>> wheels. So yes, probably 35% of the total weight is the maximum on any
>> single wheel.
>
> Hmm, interesting. I wouldn't have expected that to work.
What, that a car has more weight on the front wheels than the back? Most
front wheel drive cars on the roads are configured like this. Some rear
wheel drive cars have more 50/50 weight distribution, others (if they have
the engine in the back) can have more weight on the rear wheels than the
front. Of course the car's suspension and so-on is designed for this, so
you probably won't notice much when driving normally.
> Sure. I just meant that they probably design them to easily support more
> weight than any common car that somebody might try to put on them.
You would think so.
> Isn't the worst-case when you drive the car onto the ramp and the
> suspension jiggles it up and down over one support column?
Probably. But I really suspect in the design of these things that they just
make a few and test them. I highly doubt they do some computer simulation
or really complex calculation to figure out what size metal to use - it just
wouldn't be worth it because it's so quick to just make a few and test them.
> So... what the hell is the thickness of a tin can then?
0.2 mm or thereabouts.
> Those seem to deform pretty easily.
You mean by squeezing them on the sides? Well yes, I can bend my ruler too
pretty easily and that's 1mm thick! What you're doing there is essentially
using a huge lever, you are moving your fingers a few cm to cause a
contraction/expansion of a few microns in the surface of the material,
generating a huge stress which causes it to permanently distort. Now try to
permanently stretch a tin can by pulling on each end :-)
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>> Hmm, interesting. I wouldn't have expected that to work.
>
> What, that a car has more weight on the front wheels than the back?
Possibly, once you've got the back wheels up on a ramp. ;-)
I meant more that I wouldn't have expected to be able to just completely
disregard 3/4 the weight of the object just because I'm only looking at
one wheel.
>> Sure. I just meant that they probably design them to easily support
>> more weight than any common car that somebody might try to put on them.
>
> You would think so.
So it's probably rated to 5 tonnes or something.
>> Isn't the worst-case when you drive the car onto the ramp and the
>> suspension jiggles it up and down over one support column?
>
> Probably. But I really suspect in the design of these things that they
> just make a few and test them.
Oh, yeah, probably. More like they figure out approximately how much
load it's supposed to take, then design it to withstand 80% more or
something, and then go check whether it breaks or not.
>> So... what the hell is the thickness of a tin can then?
>
> 0.2 mm or thereabouts.
...my God. You can make metal that thin?? o_O
>> Those seem to deform pretty easily.
>
> You mean by squeezing them on the sides? Well yes, I can bend my ruler
> too pretty easily and that's 1mm thick! What you're doing there is
> essentially using a huge lever, you are moving your fingers a few cm to
> cause a contraction/expansion of a few microns in the surface of the
> material, generating a huge stress which causes it to permanently
> distort. Now try to permanently stretch a tin can by pulling on each
> end :-)
Heh, yeah, well, those horizontal beams may only be 5cm long, but they
have up to 2 tonnes pushing them sideways. That's a lot of force...
PS. Apparently human bones have a higher tensile strength than solid
copper. WTF?
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On Tue, 09 Feb 2010 15:37:05 +0100, Invisible <voi### [at] dev null> wrote:
>
> I meant more that I wouldn't have expected to be able to just completely
> disregard 3/4 the weight of the object just because I'm only looking at
> one wheel.
Why not? Try doing some one-handed push-ups and see if they are not harder
to do than two-handed ones.
>>> So... what the hell is the thickness of a tin can then?
>> 0.2 mm or thereabouts.
>
> ...my God. You can make metal that thin?? o_O
Surely you are joking.
http://en.wikipedia.org/wiki/Aluminium_foil
--
FE
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>> I meant more that I wouldn't have expected to be able to just
>> completely disregard 3/4 the weight of the object just because I'm
>> only looking at one wheel.
>
> Why not? Try doing some one-handed push-ups and see if they are not
> harder to do than two-handed ones.
When I become able to do two-handed push-ups, I'll let you know. ;-)
>>>> So... what the hell is the thickness of a tin can then?
>>> 0.2 mm or thereabouts.
>>
>> ...my God. You can make metal that thin?? o_O
>
> Surely you are joking.
>
> http://en.wikipedia.org/wiki/Aluminium_foil
Damn. I thought that stuff was plastic with a metal-powder coating...
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On Tue, 09 Feb 2010 15:49:55 +0100, Invisible <voi### [at] dev null> wrote:
>
> When I become able to do two-handed push-ups, I'll let you know. ;-)
Oh, come on. Even I can do push-ups, and I have arms like a little girl.
I have seen pictures of you; I know you are not obese. You can do push-ups.
>> http://en.wikipedia.org/wiki/Aluminium_foil
>
> Damn. I thought that stuff was plastic with a metal-powder coating...
http://en.wikipedia.org/wiki/Metallised_film
--
FE
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> I meant more that I wouldn't have expected to be able to just completely
> disregard 3/4 the weight of the object just because I'm only looking at
> one wheel.
Why not? A car has 4 wheels, the weight is (roughly) spread evenly between
the 4 wheels. If you want something to support one wheel it need only
support 1/4 of the total weight, plus a bit for safety.
> So it's probably rated to 5 tonnes or something.
As I said, it seems most common ones are rated to 2 ton for the pair, so
that would be 1000 kg per ramp/wheel. That should cater for most normal
passenger cars, plus quite a lot to spare.
>> 0.2 mm or thereabouts.
>
> ...my God. You can make metal that thin?? o_O
You've seen aluminium foil haven't you? That's probably 10x thinner. You
just force it through a pair of rollers that are very close together.
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>> When I become able to do two-handed push-ups, I'll let you know. ;-)
>
> Oh, come on. Even I can do push-ups, and I have arms like a little girl.
>
> I have seen pictures of you; I know you are not obese. You can do push-ups.
Not obese, no. Also not fit. My arms contain very little muscle, and
attempting to lift 100 Kg using only my arms operating in an unusual
direction is pretty much beyond my current capabilities.
>>> http://en.wikipedia.org/wiki/Aluminium_foil
>>
>> Damn. I thought that stuff was plastic with a metal-powder coating...
>
> http://en.wikipedia.org/wiki/Metallised_film
Oh, I see... So *that's* why that stuff is so indestructable.
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Invisible wrote:
> Not obese, no. Also not fit. My arms contain very little muscle, and
> attempting to lift 100 Kg using only my arms operating in an unusual
> direction is pretty much beyond my current capabilities.
You make it sound harder than it is :-)
First off you are probably not lifting 100kg when you do pushups,
because a good part of your weight is supported by your feet. I think
less than 70% of your weight is more accurate. Even less if you do them
on your knees (which you should probably try).
And the arms are not in an unusual position when you do that exercise.
They are very well made to operate in front of your torso :-) For a more
unusual position try the reverse push ups, with the belly facing up
instead of down...
Read this book for more fun :-D
http://www.lulu.com/product/t%C3%A9l%C3%A9chargement/the-little-book-of-push-ups/6102671
--
Vincent
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>> Not obese, no. Also not fit. My arms contain very little muscle, and
>> attempting to lift 100 Kg using only my arms operating in an unusual
>> direction is pretty much beyond my current capabilities.
>
> You make it sound harder than it is :-)
No, actually putting it in writing makes it sound significantly *easier*
than it is.
> First off you are probably not lifting 100kg when you do pushups,
> because a good part of your weight is supported by your feet. I think
> less than 70% of your weight is more accurate. Even less if you do them
> on your knees (which you should probably try).
Well, just for giggles, I did have a go at a pushup a little earlier
today. I can get my head a few milimeters off the floor, but that's
about it. My neck and shoulders can't take much more than that, never
mind the unability of my arms to supply sufficient power. (And ignoring
the increased blood pressure to my head...)
> And the arms are not in an unusual position when you do that exercise.
> They are very well made to operate in front of your torso :-)
Sure. And I can lift fairly heavy loads in an *upwards* direction. But
pushing forwards is a pretty unusual configuration.
> Read this book for more fun :-D
>
>
http://www.lulu.com/product/t%C3%A9l%C3%A9chargement/the-little-book-of-push-ups/6102671
"Fortunately, it is almost impossible to injure yourself while doing
basic pushups."
LMAO! WTF?
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Invisible wrote:
> Well, just for giggles, I did have a go at a pushup a little earlier
> today. I can get my head a few milimeters off the floor, but that's
> about it. My neck and shoulders can't take much more than that, never
> mind the unability of my arms to supply sufficient power. (And ignoring
> the increased blood pressure to my head...)
You're doing it wrong. You should start at the up position, then go down
as far as you can, then go back up. Trying to start from lying flat on
the ground is quite a bit harder and won't train you to succeed...
>> And the arms are not in an unusual position when you do that exercise.
>> They are very well made to operate in front of your torso :-)
>
> Sure. And I can lift fairly heavy loads in an *upwards* direction. But
> pushing forwards is a pretty unusual configuration.
What about all this time you spent on all fours as a child? What about
all those doors you've pushed?
If you prefer pushing upward you can try vertical pushups, but they are
not the easiest kind ;-)
--
Vincent
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Vincent Le Chevalier wrote:
> You're doing it wrong. You should start at the up position, then go down
> as far as you can, then go back up. Trying to start from lying flat on
> the ground is quite a bit harder and won't train you to succeed...
Oh. I see.
>>> And the arms are not in an unusual position when you do that
>>> exercise. They are very well made to operate in front of your torso :-)
>>
>> Sure. And I can lift fairly heavy loads in an *upwards* direction. But
>> pushing forwards is a pretty unusual configuration.
>
> What about all this time you spent on all fours as a child?
Mass rises as the cube of size, but muscle power rises as the square of
size. (This is why ants can lift 1,000 times their own weight, but
elephants can only lumber along.)
Besides, you can move on all fours with your elbows locked. That doesn't
take much muscle power. ;-)
> What about all those doors you've pushed?
A door isn't nearly as heavy as a person.
I did, however, move a piano up a spiral staircase one time... Jesus,
THAT was fun! o_O
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Invisible wrote:
> Well, just for giggles, I did have a go at a pushup a little earlier
> today.
If you can't do that, then lean against the edge of a table, so you're at a
45-degree slant or so, and do some. Then use a lower table, or the edge of
your matress, or some such. Do one more of that type every day.
When you can get to doing pushups on the floor, do one more every day. It
really only takes like 5 minutes a day to get a basic amount of fitness.
In three months, you'll be doing 100 pushups in a row.
You might not be able to do one more every day if the day has been
particularly tiring, but it doesn't sound like you have particularly tiring
days. Or if that'sa a problem, do them in the morning.
--
Darren New, San Diego CA, USA (PST)
Forget "focus follows mouse." When do
I get "focus follows gaze"?
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scott wrote:
>> ...my God. You can make metal that thin?? o_O
> You've seen aluminium foil haven't you? That's probably 10x thinner.
And one of the benefits of gold is that you can squash it down to literally
one atom thick and it'll still stick together in sheets.
--
Darren New, San Diego CA, USA (PST)
Forget "focus follows mouse." When do
I get "focus follows gaze"?
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> Well, just for giggles, I did have a go at a pushup a little earlier
> today. I can get my head a few milimeters off the floor, but that's about
> it. My neck and shoulders can't take much more than that, never mind the
> unability of my arms to supply sufficient power. (And ignoring the
> increased blood pressure to my head...)
You can start off with your hands on a raised platform to make it easier.
For example, feet on ground, hands on table, should be very easy. Then try
hands on a chair, etc., eventually you will be able to do it with your hands
on the ground. Then start to lift your feet up, until finally you can do a
press-up with your body vertical :-)
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Invisible wrote:
>>> Hmm, interesting. I wouldn't have expected that to work.
>>
>> What, that a car has more weight on the front wheels than the back?
>
> Possibly, once you've got the back wheels up on a ramp. ;-)
>
> I meant more that I wouldn't have expected to be able to just completely
> disregard 3/4 the weight of the object just because I'm only looking at
> one wheel.
>
The suspension of the car does play a part here. They are designed to
keep all four wheels on the ground, and as flat as possible, when going
through a corner. If the weight of the car started shifting around every
time you moved the center of mass on the interior or went into a banked
corner just a bit too fast, the car would not be very stable at all.
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"Invisible" <voi### [at] dev null> wrote in message
news:4b717a62@news.povray.org...
> Not obese, no. Also not fit. My arms contain very little muscle, and
> attempting to lift 100 Kg using only my arms operating in an unusual
Then don't lift your body; push the earth down.
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>> Not obese, no. Also not fit. My arms contain very little muscle, and
>> attempting to lift 100 Kg using only my arms operating in an unusual
>
> Then don't lift your body; push the earth down.
Mass of the Earth = 5.9742 × 10^24 Kg o_O
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Invisible wrote:
> Vincent Le Chevalier wrote:
>
>> What about all those doors you've pushed?
>
> A door isn't nearly as heavy as a person.
>
Some of the ones we had offshore weighed half a ton.
--
Best Regards,
Stephen
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>> A door isn't nearly as heavy as a person.
>
> Some of the ones we had offshore weighed half a ton.
Short or long?
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> Mass rises as the cube of size, but muscle power rises as the square of
> size.
I would have thought the strength of a muscle depends on its volume, why do
you say is rises with the square of size?
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scott wrote:
>> Mass rises as the cube of size, but muscle power rises as the square
>> of size.
>
> I would have thought the strength of a muscle depends on its volume, why
> do you say is rises with the square of size?
Muscle power is [apparently] proportional to cross-section area, not volume.
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>>> Mass rises as the cube of size, but muscle power rises as the square of
>>> size.
>>
>> I would have thought the strength of a muscle depends on its volume, why
>> do you say is rises with the square of size?
>
> Muscle power is [apparently] proportional to cross-section area, not
> volume.
I guess that makes sense if you assume each cell in the muscle fibre can
only exert a certain force, a chain of them can still only exert that same
force no matter how long it is. It's having more fibres in parallel that
help to increase the force.
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>> Muscle power is [apparently] proportional to cross-section area, not
>> volume.
>
> I guess that makes sense if you assume each cell in the muscle fibre can
> only exert a certain force, a chain of them can still only exert that
> same force no matter how long it is. It's having more fibres in
> parallel that help to increase the force.
Precisely.
Also of note is that [apparently] if all the fibers were to contract
simultaneously, the muscle would be ripped from the bone (assuming
there's any load on it). Apparently the fibers are actually programmed
to twitch a few at a time, so that they have time to recover between
contractions, while the muscle as a whole maintains constant force.
You know how when you try to lift something too heavy and you start
shaking? That's apparently because there aren't enough fibers fiting at
once...
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Invisible a écrit :
>>> Not obese, no. Also not fit. My arms contain very little muscle, and
>>> attempting to lift 100 Kg using only my arms operating in an unusual
>>
>> Then don't lift your body; push the earth down.
>
> Mass of the Earth = 5.9742 × 10^24 Kg o_O
That's nothing, but the guys at the antipods are giving you some trouble
(as they push down too... to your side!)
--
A: Because it messes up the order in which people normally read text.<br/>
Q: Why is it such a bad thing?<br/>
A: Top-posting.<br/>
Q: What is the most annoying thing on usenet and in e-mail?
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Invisible wrote:
>>> A door isn't nearly as heavy as a person.
>>
>> Some of the ones we had offshore weighed half a ton.
>
> Short or long?
About half a ton.
--
Best Regards,
Stephen
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On 2/9/2010 9:49 AM, Invisible wrote:
>>> I meant more that I wouldn't have expected to be able to just
>>> completely disregard 3/4 the weight of the object just because I'm
>>> only looking at one wheel.
>>
>> Why not? Try doing some one-handed push-ups and see if they are not
>> harder to do than two-handed ones.
>
> When I become able to do two-handed push-ups, I'll let you know. ;-)
>
>>>>> So... what the hell is the thickness of a tin can then?
>>>> 0.2 mm or thereabouts.
>>>
>>> ...my God. You can make metal that thin?? o_O
>>
>> Surely you are joking.
>>
>> http://en.wikipedia.org/wiki/Aluminium_foil
>
> Damn. I thought that stuff was plastic with a metal-powder coating...
You ever try to stand on an empty coke can?
Just set it on level ground and place your foot on it. Then gently
shift all your weight to that foot without losing you balance. The can
should be able to hold you up. It might take a few tries.
Then when on the can, tap the side with your other foot. The can will
flatten nicely.
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"Invisible" <voi### [at] dev null> wrote in message
news:4b728aed$1@news.povray.org...
> >> Not obese, no. Also not fit. My arms contain very little muscle, and
> >> attempting to lift 100 Kg using only my arms operating in an unusual
> > Then don't lift your body; push the earth down.
> Mass of the Earth = 5.9742 × 10^24 Kg o_O
Makes failure feel a little better, no?
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Invisible wrote:
> Just how strong is steel? I mean, obviously it varies by type, but how
> much load can you typically put on steel without bending/shattering it?
Strong enough to hold up hundreds of floors above it when used in buildings.
I think a piddly little car won't give it too much trouble ;)
...Chambers
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