| Topic: |
Science > Physics |
| User: |
"Chris W" |
| Date: |
03 Jun 2007 07:38:37 PM |
| Object: |
How high will a tennis ball go? |
I have a problem that I need a little help with. If I could remember
much from my calculus classes in college I could probably figure it out
but I need help now.
I want to know how high an object will go when launched vertically at a
known speed. If we ignored wind resistance that would be easy but in
the case I am looking at, it would also make it far to inaccurate.
However to make it a reasonable problem we will assume the height isn't
going to be enough to significantly change the air pressure. So we can
use this simple formula for wind resistance...
http://upload.wikimedia.org/math/0/5/7/0575ba81da9b81c4856c9500d1d1574d.png
that can be found in context here...
http://en.wikipedia.org/wiki/Drag_(physics)
and assume a "standard day" at sea level which gives us an air density
of.. 1.293 kg/m^3
For the gravity part we can use the standard formula....
S = .5*a*t^2+Vi*t
where. . .
s = distance
a = acceleration of gravity (9.8m/s^2)
t = time
Vi = initial velocity
in this case a is going to be negative but we also have to add in the
constantly changing negative acceleration due to the force of drag so
somewhere in there we will need to also use another famous physics
formula...
f=m*a
where ...
f = force
m = mass
a = acceleration
As a bonus I would also like to try and solve for Vi and height if I
know how long it takes to go up and come back down. I'm not 100% sure
that is even possible but I think it can be done since we can figure the
terminal velocity it will reach on the way back down. However I think
to solve this one you may need differential equations and I don't
remember anything from that class.
The specific case I am looking at right now is for a tennis ball
launched from an air cannon. I don't currently know how fast it is
going when it leaves the air cannon, which is why I want the second part
finding Vi and height just from knowing how long it takes for the round
trip. Eventually I intend on using a chronograph that is commonly used
for ballistics to measure how fast the tennis ball is leaving the air
cannon.
Keeping it all in metric here are the numbers..
Tennis ball Dia = .0651 m
Tennis ball Mass = .0567 kg
Tennis ball Cd = .4 (that is just a guess from a chart that listed that
as the Cd for a rough sphere.
I also plan on finding how the height changes when I weight the tennis
ball down to 2 and 4 times it's initial mass.
I wonder if the height won't be effected as much as you might initially
expect. While the heavier ball isn't going to leave the air cannon as
fast, it also will have a lot higher kinetic energy to aerodynamic drag
ratio.
--
Chris W
KE5GIX
"Protect your digital freedom and privacy, eliminate DRM,
learn more at http://www.defectivebydesign.org/what_is_drm"
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| User: "Gib Bogle" |
|
| Title: Re: How high will a tennis ball go? |
03 Jun 2007 10:31:59 PM |
|
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Chris W wrote:
I have a problem that I need a little help with. If I could remember
much from my calculus classes in college I could probably figure it out
but I need help now.
I want to know how high an object will go when launched vertically at a
known speed. If we ignored wind resistance that would be easy but in
the case I am looking at, it would also make it far to inaccurate.
However to make it a reasonable problem we will assume the height isn't
going to be enough to significantly change the air pressure. So we can
use this simple formula for wind resistance...
http://upload.wikimedia.org/math/0/5/7/0575ba81da9b81c4856c9500d1d1574d.png
that can be found in context here...
http://en.wikipedia.org/wiki/Drag_(physics)
and assume a "standard day" at sea level which gives us an air density
of.. 1.293 kg/m^3
For the gravity part we can use the standard formula....
S = .5*a*t^2+Vi*t
where. . .
s = distance
a = acceleration of gravity (9.8m/s^2)
t = time
Vi = initial velocity
in this case a is going to be negative but we also have to add in the
constantly changing negative acceleration due to the force of drag so
somewhere in there we will need to also use another famous physics
formula...
f=m*a
where ...
f = force
m = mass
a = acceleration
As a bonus I would also like to try and solve for Vi and height if I
know how long it takes to go up and come back down. I'm not 100% sure
that is even possible but I think it can be done since we can figure the
terminal velocity it will reach on the way back down. However I think
to solve this one you may need differential equations and I don't
remember anything from that class.
The specific case I am looking at right now is for a tennis ball
launched from an air cannon. I don't currently know how fast it is
going when it leaves the air cannon, which is why I want the second part
finding Vi and height just from knowing how long it takes for the round
trip. Eventually I intend on using a chronograph that is commonly used
for ballistics to measure how fast the tennis ball is leaving the air
cannon.
Keeping it all in metric here are the numbers..
Tennis ball Dia = .0651 m
Tennis ball Mass = .0567 kg
Tennis ball Cd = .4 (that is just a guess from a chart that listed that
as the Cd for a rough sphere.
I also plan on finding how the height changes when I weight the tennis
ball down to 2 and 4 times it's initial mass.
I wonder if the height won't be effected as much as you might initially
expect. While the heavier ball isn't going to leave the air cannon as
fast, it also will have a lot higher kinetic energy to aerodynamic drag
ratio.
You won't be able to solve for the dynamics analytically. You need a
numerical ODE solver, e.g. Matlab or one of the free equivalents, or the
ability to program in C or Fortran.
.
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| User: "Narasimham" |
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| Title: Re: How high will a tennis ball go? |
04 Jun 2007 02:42:45 AM |
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On Jun 4, 8:31 am, Gib Bogle <b...@ihug.too.much.spam.co.nz> wrote:
Chris W wrote:
I have a problem that I need a little help with. If I could remember
much from my calculus classes in college I could probably figure it out
but I need help now.
You won't be able to solve for the dynamics analytically. You need a
numerical ODE solver, e.g. Matlab or one of the free equivalents...
which free equivalents, you mean Maple/Mathematica?
.
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| User: "Gib Bogle" |
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| Title: Re: How high will a tennis ball go? |
04 Jun 2007 04:12:05 AM |
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Narasimham wrote:
On Jun 4, 8:31 am, Gib Bogle <b...@ihug.too.much.spam.co.nz> wrote:
Chris W wrote:
I have a problem that I need a little help with. If I could remember
much from my calculus classes in college I could probably figure it out
but I need help now.
You won't be able to solve for the dynamics analytically. You need a
numerical ODE solver, e.g. Matlab or one of the free equivalents...
which free equivalents, you mean Maple/Mathematica?
The only one I know of is Octave (I assume, maybe wrongly, that it has
an ODE solver), but there may be others. Mathematica is far from free,
I don't know how much Maple costs.
I'd install g95 and a free ODE solver from Netlib.
.
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| User: "Z" |
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| Title: Re: How high will a tennis ball go? |
08 Jun 2007 03:49:18 AM |
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"Gib Bogle" <bogle@ihug.too.much.spam.co.nz> a écrit dans le message de
news:f40kf1$h74$1@lust.ihug.co.nz...
Narasimham wrote:
On Jun 4, 8:31 am, Gib Bogle <b...@ihug.too.much.spam.co.nz> wrote:
...
numerical ODE solver, e.g. Matlab or one of the free equivalents...
...
which free equivalents, you mean Maple/Mathematica?
The only one I know of is Octave (I assume, maybe wrongly, that it has
an ODE solver), but there may be others. Mathematica is far from free,
I don't know how much Maple costs.
I'd install g95 and a free ODE solver from Netlib.
Scilab is free, AFAIK.
Z
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| User: "" |
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| Title: Re: How high will a tennis ball go? |
03 Jun 2007 09:02:58 PM |
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On Jun 3, 5:38 pm, Chris W <1qaz...@cox.net> wrote:
I have a problem that I need a little help with. If I could remember
much from my calculus classes in college I could probably figure it out
but I need help now.
I want to know how high an object will go when launched vertically at a
known speed. If we ignored wind resistance that would be easy but in
the case I am looking at, it would also make it far to inaccurate.
However to make it a reasonable problem we will assume the height isn't
going to be enough to significantly change the air pressure.
Are you sure? Even a small child's helium-filled balloon floats up
because of the pressure difference in air at the bottom and top of the
balloon---and that is for an object a few tens of cm in size. Perhaps
the safest approach is to first solve the problem neglecting pressure
differences, then estimate the pressure differences a posteriori. If
they are "significant" you should try again, now putting in the
effects of decreasing pressure with altitude, or perhaps perform a
"perturbation" computation about the original solution.
R.G. Vickson
So we can
use this simple formula for wind resistance...
http://upload.wikimedia.org/math/0/5/7/0575ba81da9b81c4856c9500d1d157...
that can be found in context here...http://en.wikipedia.org/wiki/Drag_(physics)
and assume a "standard day" at sea level which gives us an air density
of.. 1.293 kg/m^3
For the gravity part we can use the standard formula....
S = .5*a*t^2+Vi*t
where. . .
s = distance
a = acceleration of gravity (9.8m/s^2)
t = time
Vi = initial velocity
in this case a is going to be negative but we also have to add in the
constantly changing negative acceleration due to the force of drag so
somewhere in there we will need to also use another famous physics
formula...
f=m*a
where ...
f = force
m = mass
a = acceleration
As a bonus I would also like to try and solve for Vi and height if I
know how long it takes to go up and come back down. I'm not 100% sure
that is even possible but I think it can be done since we can figure the
terminal velocity it will reach on the way back down. However I think
to solve this one you may need differential equations and I don't
remember anything from that class.
The specific case I am looking at right now is for a tennis ball
launched from an air cannon. I don't currently know how fast it is
going when it leaves the air cannon, which is why I want the second part
finding Vi and height just from knowing how long it takes for the round
trip. Eventually I intend on using a chronograph that is commonly used
for ballistics to measure how fast the tennis ball is leaving the air
cannon.
Keeping it all in metric here are the numbers..
Tennis ball Dia = .0651 m
Tennis ball Mass = .0567 kg
Tennis ball Cd = .4 (that is just a guess from a chart that listed that
as the Cd for a rough sphere.
I also plan on finding how the height changes when I weight the tennis
ball down to 2 and 4 times it's initial mass.
I wonder if the height won't be effected as much as you might initially
expect. While the heavier ball isn't going to leave the air cannon as
fast, it also will have a lot higher kinetic energy to aerodynamic drag
ratio.
--
Chris W
KE5GIX
"Protect your digital freedom and privacy, eliminate DRM,
learn more athttp://www.defectivebydesign.org/what_is_drm"
Gift Giving Made Easy
Get the gifts you want &
give the gifts they want
One stop wish list for any gift,
from anywhere, for any occasion!http://thewishzone.com
.
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| User: "Puppet_Sock" |
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| Title: Re: How high will a tennis ball go? |
04 Jun 2007 11:19:08 AM |
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On Jun 3, 10:02 pm, "C...@shaw.ca" <C...@shaw.ca> wrote:
[snip]
Are you sure? Even a small child's helium-filled balloon floats up
because of the pressure difference in air at the bottom and top of the
balloon---and that is for an object a few tens of cm in size.
Absolutely not. A balloon floats because of the difference in
density between the inside and outside, not top and bottom.
Socks
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| User: "me" |
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| Title: Re: How high will a tennis ball go? |
04 Jun 2007 11:48:04 AM |
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On Jun 4, 12:19 pm, Puppet_Sock <puppet_s...@hotmail.com> wrote:
On Jun 3, 10:02 pm, "C...@shaw.ca" <C...@shaw.ca> wrote:
[snip]
Are you sure? Even a small child's helium-filled balloon floats up
because of the pressure difference in air at the bottom and top of the
balloon---and that is for an object a few tens of cm in size.
Absolutely not. A balloon floats because of the difference in
density between the inside and outside, not top and bottom.
Socks
Probably a bit of semantics. The net force vector is "up" because
of the pressure difference between the air at the bottom of the
balloon
and the top. You can bear this out with a simple experiment.
Take that balloon in your car and tether it in the center of the air
mass. Drive at a constant speed and then apply the brakes.
The ballon will move aft, even as everything else tries to move
forward. The reason is that the air mass inside the car is also
pushing forward and the pressure of the air at the front of the
car is higher than the aft. The density of the air is different
because air is a compressible fluid. The same thing will happen
in incompressible fluids however.
.
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| User: "" |
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| Title: Re: How high will a tennis ball go? |
04 Jun 2007 11:39:32 AM |
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On Jun 4, 9:19 am, Puppet_Sock <puppet_s...@hotmail.com> wrote:
On Jun 3, 10:02 pm, "C...@shaw.ca" <C...@shaw.ca> wrote:
[snip]
Are you sure? Even a small child's helium-filled balloon floats up
because of the pressure difference in air at the bottom and top of the
balloon---and that is for an object a few tens of cm in size.
Absolutely not. A balloon floats because of the difference in
density between the inside and outside, not top and bottom.
Wrong. If the pressure is uniform all around the balloon, all
"pressure" forces cancel, and the balloon will fall, because only the
gravitational force will be left. To have it rise, or even hover, you
need a pressure difference.
R.G. Vickson
Socks
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| User: "" |
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| Title: Re: How high will a tennis ball go? |
04 Jun 2007 12:45:02 PM |
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In sci.physics <> wrote:
On Jun 4, 9:19 am, Puppet_Sock <puppet_s...@hotmail.com> wrote:
On Jun 3, 10:02 pm, "C...@shaw.ca" <C...@shaw.ca> wrote:
[snip]
Are you sure? Even a small child's helium-filled balloon floats up
because of the pressure difference in air at the bottom and top of the
balloon---and that is for an object a few tens of cm in size.
Absolutely not. A balloon floats because of the difference in
density between the inside and outside, not top and bottom.
Wrong.
Right.
If the pressure is uniform all around the balloon, all
"pressure" forces cancel,
You got this part almost right and it is why balloons are round.
AND the balloon will fall, because only the
gravitational force will be left. To have it rise, or even hover, you
need a pressure difference.
This is utter nonsense.
The balloon rises or falls because of its density.
Fill it with cold air, it falls.
Fill it with hot air, it rises.
Fill it with helium, it rises.
Fill it with hydrogen, it rises.
Fill it with nitrogen, it falls.
--
Jim Pennino
Remove .spam.sux to reply.
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| User: "" |
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| Title: Re: How high will a tennis ball go? |
04 Jun 2007 01:27:58 PM |
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On Jun 4, 10:45 am, wrote:
In sci.physics <> wrote:
On Jun 4, 9:19 am, Puppet_Sock <puppet_s...@hotmail.com> wrote:
On Jun 3, 10:02 pm, " " <> wrote:
[snip]
Are you sure? Even a small child's helium-filled balloon floats up
because of the pressure difference in air at the bottom and top of the
balloon---and that is for an object a few tens of cm in size.
Absolutely not. A balloon floats because of the difference in
density between the inside and outside, not top and bottom.
Wrong.
Right.
If the pressure is uniform all around the balloon, all
"pressure" forces cancel,
You got this part almost right and it is why balloons are round.
No, some of them are shaped like Snoopy the dog or Mickey Mouse. I
have seen pictures of some that are cubic, etc.
The point is that the buoyancy force equals the weight of the gas
excluded by the balloon's mantle (Archimedes' Law?), but this is a
_consequence_ of integrating the pressure forces over the balloon's
surface, which happens to come out in the end as a nice, simple
formula. The formula is a *consequence* of pressure differences, not a
statement of some fundamental, underlying law.
AND the balloon will fall, because only the
gravitational force will be left. To have it rise, or even hover, you
need a pressure difference.
This is utter nonsense.
No, it is actually the underlying physical reason.
The balloon rises or falls because of its density.
So, how does the balloon know which way is "up"? Presumably, it is
smart enough to know that it is opposite to the direction of the pull
of gravity. OK, so how, exactly, does the pull of gravity go about
producing an opposing buoyant force? What is the actual MECHANISM?
Fill it with cold air, it falls.
Right, because the force of bouyancy does not overcome the weight of
the gas inside + the weight of the rubber.
Fill it with hot air, it rises.
Right. Because the air inside is lighter---having a lower density. The
temperature is high, so the inside pressure can be the same (the
balloon stays expanded) but the density, hence the weight, is lower.
Fill it with helium, it rises.
Exactly. Weight of helium is small enough, so the bouyancy forces are
not swamped.
Fill it with hydrogen, it rises.
Ditto.
Fill it with nitrogen, it falls.
Ditto.
R.G. Vickson
--
Jim Pennino
Remove .spam.sux to reply.
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| User: "" |
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| Title: Re: How high will a tennis ball go? |
04 Jun 2007 01:55:02 PM |
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In sci.physics <> wrote:
On Jun 4, 10:45 am, wrote:
In sci.physics <> wrote:
On Jun 4, 9:19 am, Puppet_Sock <puppet_s...@hotmail.com> wrote:
On Jun 3, 10:02 pm, " " <> wrote:
[snip]
Are you sure? Even a small child's helium-filled balloon floats up
because of the pressure difference in air at the bottom and top of the
balloon---and that is for an object a few tens of cm in size.
Absolutely not. A balloon floats because of the difference in
density between the inside and outside, not top and bottom.
Wrong.
Right.
If the pressure is uniform all around the balloon, all
"pressure" forces cancel,
You got this part almost right and it is why balloons are round.
No, some of them are shaped like Snoopy the dog or Mickey Mouse. I
have seen pictures of some that are cubic, etc.
Big deal and point totally missed.
The point is that the buoyancy force equals the weight of the gas
excluded by the balloon's mantle (Archimedes' Law?), but this is a
_consequence_ of integrating the pressure forces over the balloon's
surface, which happens to come out in the end as a nice, simple
formula. The formula is a *consequence* of pressure differences, not a
statement of some fundamental, underlying law.
No, the point is the weight of the balloon equals the weight of the
contained gas plus the weight of the balloon.
The density of the balloon equals the total weight divided by the
volume.
If the density of the balloon is less than the surrounding air, it
goes up.
If the density of the balloon is greater than the surrounding air, it
goes down.
That's it. Pressures around the balloon have nothing to do with the
balloon going up or down.
<snip nonsense>
--
Jim Pennino
Remove .spam.sux to reply.
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| User: "arvee" |
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| Title: Re: How high will a tennis ball go? |
04 Jun 2007 02:16:08 PM |
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On Jun 4, 11:55 am, wrote:
In sci.physics <> wrote:
On Jun 4, 10:45 am, wrote:
In sci.physics <> wrote:
On Jun 4, 9:19 am, Puppet_Sock <puppet_s...@hotmail.com> wrote:
On Jun 3, 10:02 pm, " " <> wrote:
[snip]
Are you sure? Even a small child's helium-filled balloon floats up
because of the pressure difference in air at the bottom and top of the
balloon---and that is for an object a few tens of cm in size.
Absolutely not. A balloon floats because of the difference in
density between the inside and outside, not top and bottom.
Wrong.
Right.
If the pressure is uniform all around the balloon, all
"pressure" forces cancel,
You got this part almost right and it is why balloons are round.
No, some of them are shaped like Snoopy the dog or Mickey Mouse. I
have seen pictures of some that are cubic, etc.
Big deal and point totally missed.
Just a reply to your remark about balloons being round, which YOU
said, not me. They don't have to be round, they will still float
anyway.
The point is that the buoyancy force equals the weight of the gas
excluded by the balloon's mantle (Archimedes' Law?), but this is a
_consequence_ of integrating the pressure forces over the balloon's
surface, which happens to come out in the end as a nice, simple
formula. The formula is a *consequence* of pressure differences, not a
statement of some fundamental, underlying law.
No, the point is the weight of the balloon equals the weight of the
contained gas plus the weight of the balloon.
Exactly. The less the weight of the contained gas, the less the weight
of the balloon. A "vacuum balloon" (discussed in some web pages) would
have the highest possible buoyancy. Fill it with a lightweight gas (at
1 atm pressure) and it still might float. Fill it with a heavier gas,
and it will sink. The upward buoyancy force is not changed at all,
just the weight of the inside contents. It equals the weight of the
the contents, if those are the same as the surrounding air. That is
the expression of the numerical value of the buoyancy force. The
reason there is a buoyancy force at all is *because of pressure
differences*. We have learned a bit since Archimedes' time.
R.G. Vickson
The density of the balloon equals the total weight divided by the
volume.
If the density of the balloon is less than the surrounding air, it
goes up.
If the density of the balloon is greater than the surrounding air, it
goes down.
That's it. Pressures around the balloon have nothing to do with the
balloon going up or down.
<snip nonsense>
--
Jim Pennino
Remove .spam.sux to reply.
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| User: "" |
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| Title: Re: How high will a tennis ball go? |
04 Jun 2007 03:25:01 PM |
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In sci.physics arvee <C6L1V@shaw.ca> wrote:
On Jun 4, 11:55 am, wrote:
In sci.physics <> wrote:
On Jun 4, 10:45 am, wrote:
In sci.physics <> wrote:
On Jun 4, 9:19 am, Puppet_Sock <puppet_s...@hotmail.com> wrote:
On Jun 3, 10:02 pm, " " <> wrote:
[snip]
Are you sure? Even a small child's helium-filled balloon floats up
because of the pressure difference in air at the bottom and top of the
balloon---and that is for an object a few tens of cm in size.
Absolutely not. A balloon floats because of the difference in
density between the inside and outside, not top and bottom.
Wrong.
Right.
If the pressure is uniform all around the balloon, all
"pressure" forces cancel,
You got this part almost right and it is why balloons are round.
No, some of them are shaped like Snoopy the dog or Mickey Mouse. I
have seen pictures of some that are cubic, etc.
Big deal and point totally missed.
Just a reply to your remark about balloons being round, which YOU
said, not me. They don't have to be round, they will still float
anyway.
The point was that if you make a balloon out of something "stretchy"
like most common balloons are and do nothing to influence the shape,
it will tend to go round because all the pressure around it is the
same.
For the nit-pickers, the standard rate of change in pressure due
to altitude is about 1" Hg per 1000 feet.
Since 30" Hg is roughly 15 psi, that's a change of .5 psi per 1000 feet.
So a 100 foot balloon has a pressure difference of 0.05 psi between
the top and the bottom since the top and bottom are at different
altitudes.
Have we beaten this to death yet?
--
Jim Pennino
Remove .spam.sux to reply.
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| User: "PD" |
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| Title: Re: How high will a tennis ball go? |
04 Jun 2007 05:04:54 PM |
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On Jun 4, 1:55 pm, wrote:
No, the point is the weight of the balloon equals the weight of the
contained gas plus the weight of the balloon.
The density of the balloon equals the total weight divided by the
volume.
If the density of the balloon is less than the surrounding air, it
goes up.
If the density of the balloon is greater than the surrounding air, it
goes down.
That's it. Pressures around the balloon have nothing to do with the
balloon going up or down.
This is just plain wrong, Jim. If you immerse a cinderblock in water
by a rope, it will still go down, but its apparent weight (the tension
you feel in the rope) will decrease. This decrease is not because
gravity has changed (it hasn't). It is because there is a NEW force
acting on the block, and that is the buoyancy force upwards. Now,
where the hell did the buoyancy force come from? What could be acting
on the cinderblock to produce the buoyancy force? There is only one
thing available, and that's the surrounding water. But the only way
that water can exert a force on the brick is through its pressure
acting on the block, and the fact that this pressure results in a
buoyancy force UPWARDS tells you that there MUST be a gradient in the
pressure of the water on the cinderblock.
If you have a can of Campbell's Cream of Buckshot Soup, and a can of
Campbell's Cream of Styrofoam Soup, there is NO difference whatsoever
in the buoyancy force between the two cases. (How could it be
different? The water can't see the contents of the can.) However, the
downward gravitational force on the Cream of Buckshot Soup is greater
than this buoyancy force (and so it goes down), and the gravitational
force on the Cream of Styrofoam Soup is less than this same buoyancy
force (and so that can goes up).
PD
<snip nonsense>
--
Jim Pennino
Remove .spam.sux to reply.- Hide quoted text -
- Show quoted text -
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| User: "" |
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| Title: Re: How high will a tennis ball go? |
04 Jun 2007 05:35:03 PM |
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In sci.physics PD <TheDraperFamily@gmail.com> wrote:
On Jun 4, 1:55 pm, wrote:
No, the point is the weight of the balloon equals the weight of the
contained gas plus the weight of the balloon.
The density of the balloon equals the total weight divided by the
volume.
If the density of the balloon is less than the surrounding air, it
goes up.
If the density of the balloon is greater than the surrounding air, it
goes down.
That's it. Pressures around the balloon have nothing to do with the
balloon going up or down.
This is just plain wrong, Jim. If you immerse a cinderblock in water
by a rope, it will still go down, but its apparent weight (the tension
you feel in the rope) will decrease. This decrease is not because
gravity has changed (it hasn't). It is because there is a NEW force
acting on the block, and that is the buoyancy force upwards. Now,
where the hell did the buoyancy force come from? What could be acting
on the cinderblock to produce the buoyancy force? There is only one
thing available, and that's the surrounding water. But the only way
that water can exert a force on the brick is through its pressure
acting on the block, and the fact that this pressure results in a
buoyancy force UPWARDS tells you that there MUST be a gradient in the
pressure of the water on the cinderblock.
If you have a can of Campbell's Cream of Buckshot Soup, and a can of
Campbell's Cream of Styrofoam Soup, there is NO difference whatsoever
in the buoyancy force between the two cases. (How could it be
different? The water can't see the contents of the can.) However, the
downward gravitational force on the Cream of Buckshot Soup is greater
than this buoyancy force (and so it goes down), and the gravitational
force on the Cream of Styrofoam Soup is less than this same buoyancy
force (and so that can goes up).
So, by that logic, if take a 10 foot round balloon, fill it with
hydrogen, tie it off, then attach a short hose to the static port
of an altimeter and stick the hose next to the bottom, then the
top of the balloon, I will see something other than a 10 foot
difference in altitude because the buoyancy force increases the
air pressure on the bottom of the balloon?
Now I take a 10 lead sphere and hang it from a support and do the same
thing with the altimeter. Does the altimeter now the top of the lead
sphere much lower than the bottom of the sphere because of the
negative buoyancy force increasing the air pressure at the top?
--
Jim Pennino
Remove .spam.sux to reply.
.
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| User: "PD" |
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| Title: Re: How high will a tennis ball go? |
04 Jun 2007 08:29:22 PM |
|
|
On Jun 4, 5:35 pm, wrote:
In sci.physics PD <TheDraperFam...@gmail.com> wrote:
On Jun 4, 1:55 pm, wrote:
No, the point is the weight of the balloon equals the weight of the
contained gas plus the weight of the balloon.
The density of the balloon equals the total weight divided by the
volume.
If the density of the balloon is less than the surrounding air, it
goes up.
If the density of the balloon is greater than the surrounding air, it
goes down.
That's it. Pressures around the balloon have nothing to do with the
balloon going up or down.
This is just plain wrong, Jim. If you immerse a cinderblock in water
by a rope, it will still go down, but its apparent weight (the tension
you feel in the rope) will decrease. This decrease is not because
gravity has changed (it hasn't). It is because there is a NEW force
acting on the block, and that is the buoyancy force upwards. Now,
where the hell did the buoyancy force come from? What could be acting
on the cinderblock to produce the buoyancy force? There is only one
thing available, and that's the surrounding water. But the only way
that water can exert a force on the brick is through its pressure
acting on the block, and the fact that this pressure results in a
buoyancy force UPWARDS tells you that there MUST be a gradient in the
pressure of the water on the cinderblock.
If you have a can of Campbell's Cream of Buckshot Soup, and a can of
Campbell's Cream of Styrofoam Soup, there is NO difference whatsoever
in the buoyancy force between the two cases. (How could it be
different? The water can't see the contents of the can.) However, the
downward gravitational force on the Cream of Buckshot Soup is greater
than this buoyancy force (and so it goes down), and the gravitational
force on the Cream of Styrofoam Soup is less than this same buoyancy
force (and so that can goes up).
So, by that logic, if take a 10 foot round balloon, fill it with
hydrogen, tie it off, then attach a short hose to the static port
of an altimeter and stick the hose next to the bottom, then the
top of the balloon, I will see something other than a 10 foot
difference in altitude because the buoyancy force increases the
air pressure on the bottom of the balloon?
Now I take a 10 lead sphere and hang it from a support and do the same
thing with the altimeter. Does the altimeter now the top of the lead
sphere much lower than the bottom of the sphere because of the
negative buoyancy force increasing the air pressure at the top?
--
Jim Pennino
Remove .spam.sux to reply.
No, you still didn't get it quite right. A 10 ft radius balloon has a
volume of 4200 cubic feet or 119 cubic meters.
The density of air is 1.3 kg/cubic meter. From the top to the bottom
of either the hydrogen balloon or the lead balloon, the pressure
difference is
(1.3 kg/m^3)(9.8 m/s^2)(6.1 m) = 78 N/m^2, about 7.7E-4 atm.
If you integrate the pressure difference over the surface of the
balloon, you find that the buoyant force upwards is 1500 N. This
buoyant force is the *same* for the lead balloon and for the hydrogen
balloon and points upwards in both cases. [This integral is left as an
exercise for the reader.]
Now, the graviational weight of the hydrogen in a 10 ft radius balloon
is 105 N. The weight of the lead balloon is 13E6 N. It is pretty easy
to see that 1500 N > 105 N, which is why the hydrogen balloon rises.
It is also pretty easy to see that 1500 N < 13E6 N, which is why the
lead balloon falls.
As I said, the gravitational forces acting on the 10 ft hydrogen and
lead balloons are dramatically different. The buoyant force, due to
the small atmospheric pressure gradient from top to bottom of both
balloons, is the same.
PD
.
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| User: "" |
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| Title: Re: How high will a tennis ball go? |
04 Jun 2007 09:15:03 PM |
|
|
In sci.physics PD <TheDraperFamily@gmail.com> wrote:
On Jun 4, 5:35 pm, wrote:
In sci.physics PD <TheDraperFam...@gmail.com> wrote:
On Jun 4, 1:55 pm, wrote:
No, the point is the weight of the balloon equals the weight of the
contained gas plus the weight of the balloon.
The density of the balloon equals the total weight divided by the
volume.
If the density of the balloon is less than the surrounding air, it
goes up.
If the density of the balloon is greater than the surrounding air, it
goes down.
That's it. Pressures around the balloon have nothing to do with the
balloon going up or down.
This is just plain wrong, Jim. If you immerse a cinderblock in water
by a rope, it will still go down, but its apparent weight (the tension
you feel in the rope) will decrease. This decrease is not because
gravity has changed (it hasn't). It is because there is a NEW force
acting on the block, and that is the buoyancy force upwards. Now,
where the hell did the buoyancy force come from? What could be acting
on the cinderblock to produce the buoyancy force? There is only one
thing available, and that's the surrounding water. But the only way
that water can exert a force on the brick is through its pressure
acting on the block, and the fact that this pressure results in a
buoyancy force UPWARDS tells you that there MUST be a gradient in the
pressure of the water on the cinderblock.
If you have a can of Campbell's Cream of Buckshot Soup, and a can of
Campbell's Cream of Styrofoam Soup, there is NO difference whatsoever
in the buoyancy force between the two cases. (How could it be
different? The water can't see the contents of the can.) However, the
downward gravitational force on the Cream of Buckshot Soup is greater
than this buoyancy force (and so it goes down), and the gravitational
force on the Cream of Styrofoam Soup is less than this same buoyancy
force (and so that can goes up).
So, by that logic, if take a 10 foot round balloon, fill it with
hydrogen, tie it off, then attach a short hose to the static port
of an altimeter and stick the hose next to the bottom, then the
top of the balloon, I will see something other than a 10 foot
difference in altitude because the buoyancy force increases the
air pressure on the bottom of the balloon?
Now I take a 10 lead sphere and hang it from a support and do the same
thing with the altimeter. Does the altimeter now the top of the lead
sphere much lower than the bottom of the sphere because of the
negative buoyancy force increasing the air pressure at the top?
--
Jim Pennino
Remove .spam.sux to reply.
No, you still didn't get it quite right. A 10 ft radius balloon has a
volume of 4200 cubic feet or 119 cubic meters.
The density of air is 1.3 kg/cubic meter. From the top to the bottom
of either the hydrogen balloon or the lead balloon, the pressure
difference is
(1.3 kg/m^3)(9.8 m/s^2)(6.1 m) = 78 N/m^2, about 7.7E-4 atm.
If you integrate the pressure difference over the surface of the
balloon, you find that the buoyant force upwards is 1500 N. This
buoyant force is the *same* for the lead balloon and for the hydrogen
balloon and points upwards in both cases. [This integral is left as an
exercise for the reader.]
Now, the graviational weight of the hydrogen in a 10 ft radius balloon
is 105 N. The weight of the lead balloon is 13E6 N. It is pretty easy
to see that 1500 N > 105 N, which is why the hydrogen balloon rises.
It is also pretty easy to see that 1500 N < 13E6 N, which is why the
lead balloon falls.
As I said, the gravitational forces acting on the 10 ft hydrogen and
lead balloons are dramatically different. The buoyant force, due to
the small atmospheric pressure gradient from top to bottom of both
balloons, is the same.
So, you spent 5 paragraphs to say that air pressure changes by
about 1" Hg per 1000 feet?
I believe I said that about 3 or 4 posts ago.
And you spent several posts to say there are no "magic" pressure
differentials due to the force of buoyancy and the only pressure
change is that due to altitude?
I believe I also said that about 3 or 4 posts ago.
--
Jim Pennino
Remove .spam.sux to reply.
.
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| User: "PD" |
|
| Title: Re: How high will a tennis ball go? |
05 Jun 2007 06:06:06 AM |
|
|
On Jun 4, 9:15 pm, wrote:
In sci.physics PD <TheDraperFam...@gmail.com> wrote:
On Jun 4, 5:35 pm, wrote:
In sci.physics PD <TheDraperFam...@gmail.com> wrote:
On Jun 4, 1:55 pm, wrote:
No, the point is the weight of the balloon equals the weight of the
contained gas plus the weight of the balloon.
The density of the balloon equals the total weight divided by the
volume.
If the density of the balloon is less than the surrounding air, it
goes up.
If the density of the balloon is greater than the surrounding air, it
goes down.
That's it. Pressures around the balloon have nothing to do with the
balloon going up or down.
This is just plain wrong, Jim. If you immerse a cinderblock in water
by a rope, it will still go down, but its apparent weight (the tension
you feel in the rope) will decrease. This decrease is not because
gravity has changed (it hasn't). It is because there is a NEW force
acting on the block, and that is the buoyancy force upwards. Now,
where the hell did the buoyancy force come from? What could be acting
on the cinderblock to produce the buoyancy force? There is only one
thing available, and that's the surrounding water. But the only way
that water can exert a force on the brick is through its pressure
acting on the block, and the fact that this pressure results in a
buoyancy force UPWARDS tells you that there MUST be a gradient in the
pressure of the water on the cinderblock.
If you have a can of Campbell's Cream of Buckshot Soup, and a can of
Campbell's Cream of Styrofoam Soup, there is NO difference whatsoever
in the buoyancy force between the two cases. (How could it be
different? The water can't see the contents of the can.) However, the
downward gravitational force on the Cream of Buckshot Soup is greater
than this buoyancy force (and so it goes down), and the gravitational
force on the Cream of Styrofoam Soup is less than this same buoyancy
force (and so that can goes up).
So, by that logic, if take a 10 foot round balloon, fill it with
hydrogen, tie it off, then attach a short hose to the static port
of an altimeter and stick the hose next to the bottom, then the
top of the balloon, I will see something other than a 10 foot
difference in altitude because the buoyancy force increases the
air pressure on the bottom of the balloon?
Now I take a 10 lead sphere and hang it from a support and do the same
thing with the altimeter. Does the altimeter now the top of the lead
sphere much lower than the bottom of the sphere because of the
negative buoyancy force increasing the air pressure at the top?
--
Jim Pennino
Remove .spam.sux to reply.
No, you still didn't get it quite right. A 10 ft radius balloon has a
volume of 4200 cubic feet or 119 cubic meters.
The density of air is 1.3 kg/cubic meter. From the top to the bottom
of either the hydrogen balloon or the lead balloon, the pressure
difference is
(1.3 kg/m^3)(9.8 m/s^2)(6.1 m) = 78 N/m^2, about 7.7E-4 atm.
If you integrate the pressure difference over the surface of the
balloon, you find that the buoyant force upwards is 1500 N. This
buoyant force is the *same* for the lead balloon and for the hydrogen
balloon and points upwards in both cases. [This integral is left as an
exercise for the reader.]
Now, the graviational weight of the hydrogen in a 10 ft radius balloon
is 105 N. The weight of the lead balloon is 13E6 N. It is pretty easy
to see that 1500 N > 105 N, which is why the hydrogen balloon rises.
It is also pretty easy to see that 1500 N < 13E6 N, which is why the
lead balloon falls.
As I said, the gravitational forces acting on the 10 ft hydrogen and
lead balloons are dramatically different. The buoyant force, due to
the small atmospheric pressure gradient from top to bottom of both
balloons, is the same.
So, you spent 5 paragraphs to say that air pressure changes by
about 1" Hg per 1000 feet?
I believe I said that about 3 or 4 posts ago.
I agreed with you that the pressure difference (and hence the buoyancy
force) is too small to affect the flight of a tennis ball in any
significant way.
You also said that the gradient in pressure had nothing whatsoever to
do with why a balloon rises, and I've just spent 5 paragraphs
explaining to you why what you said is a load of hooey.
And you spent several posts to say there are no "magic" pressure
differentials due to the force of buoyancy and the only pressure
change is that due to altitude?
No, I didn't say anything of the kind. I said that the force of
buoyancy is due *precisely* to pressure differentials, though no magic
of any kind is required.
I believe I also said that about 3 or 4 posts ago.
--
Jim Pennino
Remove .spam.sux to reply.- Hide quoted text -
- Show quoted text -
.
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| User: "" |
|
| Title: Re: How high will a tennis ball go? |
05 Jun 2007 10:25:04 AM |
|
|
In sci.physics PD <TheDraperFamily@gmail.com> wrote:
On Jun 4, 9:15 pm, wrote:
In sci.physics PD <TheDraperFam...@gmail.com> wrote:
On Jun 4, 5:35 pm, wrote:
In sci.physics PD <TheDraperFam...@gmail.com> wrote:
On Jun 4, 1:55 pm, wrote:
No, the point is the weight of the balloon equals the weight of the
contained gas plus the weight of the balloon.
The density of the balloon equals the total weight divided by the
volume.
If the density of the balloon is less than the surrounding air, it
goes up.
If the density of the balloon is greater than the surrounding air, it
goes down.
That's it. Pressures around the balloon have nothing to do with the
balloon going up or down.
This is just plain wrong, Jim. If you immerse a cinderblock in water
by a rope, it will still go down, but its apparent weight (the tension
you feel in the rope) will decrease. This decrease is not because
gravity has changed (it hasn't). It is because there is a NEW force
acting on the block, and that is the buoyancy force upwards. Now,
where the hell did the buoyancy force come from? What could be acting
on the cinderblock to produce the buoyancy force? There is only one
thing available, and that's the surrounding water. But the only way
that water can exert a force on the brick is through its pressure
acting on the block, and the fact that this pressure results in a
buoyancy force UPWARDS tells you that there MUST be a gradient in the
pressure of the water on the cinderblock.
If you have a can of Campbell's Cream of Buckshot Soup, and a can of
Campbell's Cream of Styrofoam Soup, there is NO difference whatsoever
in the buoyancy force between the two cases. (How could it be
different? The water can't see the contents of the can.) However, the
downward gravitational force on the Cream of Buckshot Soup is greater
than this buoyancy force (and so it goes down), and the gravitational
force on the Cream of Styrofoam Soup is less than this same buoyancy
force (and so that can goes up).
So, by that logic, if take a 10 foot round balloon, fill it with
hydrogen, tie it off, then attach a short hose to the static port
of an altimeter and stick the hose next to the bottom, then the
top of the balloon, I will see something other than a 10 foot
difference in altitude because the buoyancy force increases the
air pressure on the bottom of the balloon?
Now I take a 10 lead sphere and hang it from a support and do the same
thing with the altimeter. Does the altimeter now the top of the lead
sphere much lower than the bottom of the sphere because of the
negative buoyancy force increasing the air pressure at the top?
--
Jim Pennino
Remove .spam.sux to reply.
No, you still didn't get it quite right. A 10 ft radius balloon has a
volume of 4200 cubic feet or 119 cubic meters.
The density of air is 1.3 kg/cubic meter. From the top to the bottom
of either the hydrogen balloon or the lead balloon, the pressure
difference is
(1.3 kg/m^3)(9.8 m/s^2)(6.1 m) = 78 N/m^2, about 7.7E-4 atm.
If you integrate the pressure difference over the surface of the
balloon, you find that the buoyant force upwards is 1500 N. This
buoyant force is the *same* for the lead balloon and for the hydrogen
balloon and points upwards in both cases. [This integral is left as an
exercise for the reader.]
Now, the graviational weight of the hydrogen in a 10 ft radius balloon
is 105 N. The weight of the lead balloon is 13E6 N. It is pretty easy
to see that 1500 N > 105 N, which is why the hydrogen balloon rises.
It is also pretty easy to see that 1500 N < 13E6 N, which is why the
lead balloon falls.
As I said, the gravitational forces acting on the 10 ft hydrogen and
lead balloons are dramatically different. The buoyant force, due to
the small atmospheric pressure gradient from top to bottom of both
balloons, is the same.
So, you spent 5 paragraphs to say that air pressure changes by
about 1" Hg per 1000 feet?
I believe I said that about 3 or 4 posts ago.
I agreed with you that the pressure difference (and hence the buoyancy
force) is too small to affect the flight of a tennis ball in any
significant way.
You also said that the gradient in pressure had nothing whatsoever to
do with why a balloon rises, and I've just spent 5 paragraphs
explaining to you why what you said is a load of hooey.
And you spent several posts to say there are no "magic" pressure
differentials due to the force of buoyancy and the only pressure
change is that due to altitude?
No, I didn't say anything of the kind. I said that the force of
buoyancy is due *precisely* to pressure differentials, though no magic
of any kind is required.
I believe I also said that about 3 or 4 posts ago.
--
Jim Pennino
Remove .spam.sux to reply.- Hide quoted text -
- Show quoted text -
I think we are arguing symantics.
It is my feeling that some are arguing for magic pressure
differentials that are caused by the force of buoyancy rather than
the reality that the pressure differential due to altitude is
always there and is what causes buoyancy in the first place.
--
Jim Pennino
Remove .spam.sux to reply.
.
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| User: "PD" |
|
| Title: Re: How high will a tennis ball go? |
05 Jun 2007 11:49:15 AM |
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|
On Jun 5, 10:25 am, wrote:
In sci.physics PD <TheDraperFam...@gmail.com> wrote:
On Jun 4, 9:15 pm, wrote:
In sci.physics PD <TheDraperFam...@gmail.com> wrote:
On Jun 4, 5:35 pm, wrote:
In sci.physics PD <TheDraperFam...@gmail.com> wrote:
On Jun 4, 1:55 pm, wrote:
No, the point is the weight of the balloon equals the weight of the
contained gas plus the weight of the balloon.
The density of the balloon equals the total weight divided by the
volume.
If the density of the balloon is less than the surrounding air, it
goes up.
If the density of the balloon is greater than the surrounding air, it
goes down.
That's it. Pressures around the balloon have nothing to do with the
balloon going up or down.
This is just plain wrong, Jim. If you immerse a cinderblock in water
by a rope, it will still go down, but its apparent weight (the tension
you feel in the rope) will decrease. This decrease is not because
gravity has changed (it hasn't). It is because there is a NEW force
acting on the block, and that is the buoyancy force upwards. Now,
where the hell did the buoyancy force come from? What could be acting
on the cinderblock to produce the buoyancy force? There is only one
thing available, and that's the surrounding water. But the only way
that water can exert a force on the brick is through its pressure
acting on the block, and the fact that this pressure results in a
buoyancy force UPWARDS tells you that there MUST be a gradient in the
pressure of the water on the cinderblock.
If you have a can of Campbell's Cream of Buckshot Soup, and a can of
Campbell's Cream of Styrofoam Soup, there is NO difference whatsoever
in the buoyancy force between the two cases. (How could it be
different? The water can't see the contents of the can.) However, the
downward gravitational force on the Cream of Buckshot Soup is greater
than this buoyancy force (and so it goes down), and the gravitational
force on the Cream of Styrofoam Soup is less than this same buoyancy
force (and so that can goes up).
So, by that logic, if take a 10 foot round balloon, fill it with
hydrogen, tie it off, then attach a short hose to the static port
of an altimeter and stick the hose next to the bottom, then the
top of the balloon, I will see something other than a 10 foot
difference in altitude because the buoyancy force increases the
air pressure on the bottom of the balloon?
Now I take a 10 lead sphere and hang it from a support and do the same
thing with the altimeter. Does the altimeter now the top of the lead
sphere much lower than the bottom of the sphere because of the
negative buoyancy force increasing the air pressure at the top?
--
Jim Pennino
Remove .spam.sux to reply.
No, you still didn't get it quite right. A 10 ft radius balloon has a
volume of 4200 cubic feet or 119 cubic meters.
The density of air is 1.3 kg/cubic meter. From the top to the bottom
of either the hydrogen balloon or the lead balloon, the pressure
difference is
(1.3 kg/m^3)(9.8 m/s^2)(6.1 m) = 78 N/m^2, about 7.7E-4 atm.
If you integrate the pressure difference over the surface of the
balloon, you find that the buoyant force upwards is 1500 N. This
buoyant force is the *same* for the lead balloon and for the hydrogen
balloon and points upwards in both cases. [This integral is left as an
exercise for the reader.]
Now, the graviational weight of the hydrogen in a 10 ft radius balloon
is 105 N. The weight of the lead balloon is 13E6 N. It is pretty easy
to see that 1500 N > 105 N, which is why the hydrogen balloon rises.
It is also pretty easy to see that 1500 N < 13E6 N, which is why the
lead balloon falls.
As I said, the gravitational forces acting on the 10 ft hydrogen and
lead balloons are dramatically different. The buoyant force, due to
the small atmospheric pressure gradient from top to bottom of both
balloons, is the same.
So, you spent 5 paragraphs to say that air pressure changes by
about 1" Hg per 1000 feet?
I believe I said that about 3 or 4 posts ago.
I agreed with you that the pressure difference (and hence the buoyancy
force) is too small to affect the flight of a tennis ball in any
significant way.
You also said that the gradient in pressure had nothing whatsoever to
do with why a balloon rises, and I've just spent 5 paragraphs
explaining to you why what you said is a load of hooey.
And you spent several posts to say there are no "magic" pressure
differentials due to the force of buoyancy and the only pressure
change is that due to altitude?
No, I didn't say anything of the kind. I said that the force of
buoyancy is due *precisely* to pressure differentials, though no magic
of any kind is required.
I believe I also said that about 3 or 4 posts ago.
--
Jim Pennino
Remove .spam.sux to reply.- Hide quoted text -
- Show quoted text -
I think we are arguing symantics.
It is my feeling that some are arguing for magic pressure
differentials that are caused by the force of buoyancy rather than
the reality that the pressure differential due to altitude is
always there and is what causes buoyancy in the first place.
Then you and I are in agreement about the physics. I have my doubts
about the validity of what you thought others were arguing for. 'Nuff
said.
PD
.
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| User: "Gib Bogle" |
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| Title: Re: How high will a tennis ball go? |
07 Jun 2007 06:07:19 PM |
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It is quite surprising that this acrimonious disagreement should take
place on a maths newsgroup, when a very trivial amount of mathematics
would remove the argument.
Consider (for ease of exposition) a balloon shaped like a vertical
cylinder, with cross-section area A. Let the upper surface be at
elevation h2, and the lower surface at elevation h1 (i.e. cylinder
length = h2-h1).
The atmospheric pressure at elevation h (where h is small) can be
approximated by
P(h) = P0 - Ra.g.h
where Ra = density of air (at this elevation).
The buoyancy force (upwards) on the balloon is therefore (approximately)
FB = A.(P(h1)-P(h2)) = A.(h2-h1).g.Ra
The gravitational force (downwards) is
FG = A.(h2-h1).g.Rb
where Rb = average density of the balloon (total mass/volume)
So FB > FG when Ra > Rb, and FB is a result of the gradient in
atmospheric pressure. How can there be an argument about this?
.
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| User: "" |
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| Title: Re: How high will a tennis ball go? |
06 Jun 2007 12:06:39 PM |
|
|
On Jun 5, 4:06 am, PD <TheDraperFam...@gmail.com> wrote:
On Jun 4, 9:15 pm, wrote:
In sci.physics PD <TheDraperFam...@gmail.com> wrote:
On Jun 4, 5:35 pm, wrote:
In sci.physics PD <TheDraperFam...@gmail.com> wrote:
On Jun 4, 1:55 pm, wrote:
No, the point is the weight of the balloon equals the weight of the
contained gas plus the weight of the balloon.
The density of the balloon equals the total weight divided by the
volume.
If the density of the balloon is less than the surrounding air, it
goes up.
If the density of the balloon is greater than the surrounding air, it
goes down.
That's it. Pressures around the balloon have nothing to do with the
balloon going up or down.
This is just plain wrong, Jim. If you immerse a cinderblock in water
by a rope, it will still go down, but its apparent weight (the tension
you feel in the rope) will decrease. This decrease is not because
gravity has changed (it hasn't). It is because there is a NEW force
acting on the block, and that is the buoyancy force upwards. Now,
where the hell did the buoyancy force come from? What could be acting
on the cinderblock to produce the buoyancy force? There is only one
thing available, and that's the surrounding water. But the only way
that water can exert a force on the brick is through its pressure
acting on the block, and the fact that this pressure results in a
buoyancy force UPWARDS tells you that there MUST be a gradient in the
pressure of the water on the cinderblock.
If you have a can of Campbell's Cream of Buckshot Soup, and a can of
Campbell's Cream of Styrofoam Soup, there is NO difference whatsoever
in the buoyancy force between the two cases. (How could it be
different? The water can't see the contents of the can.) However, the
downward gravitational force on the Cream of Buckshot Soup is greater
than this buoyancy force (and so it goes down), and the gravitational
force on the Cream of Styrofoam Soup is less than this same buoyancy
force (and so that can goes up).
So, by that logic, if take a 10 foot round balloon, fill it with
hydrogen, tie it off, then attach a short hose to the static port
of an altimeter and stick the hose next to the bottom, then the
top of the balloon, I will see something other than a 10 foot
difference in altitude because the buoyancy force increases the
air pressure on the bottom of the balloon?
Now I take a 10 lead sphere and hang it from a support and do the same
thing with the altimeter. Does the altimeter now the top of the lead
sphere much lower than the bottom of the sphere because of the
negative buoyancy force increasing the air pressure at the top?
--
Jim Pennino
Remove .spam.sux to reply.
No, you still didn't get it quite right. A 10 ft radius balloon has a
volume of 4200 cubic feet or 119 cubic meters.
The density of air is 1.3 kg/cubic meter. From the top to the bottom
of either the hydrogen balloon or the lead balloon, the pressure
difference is
(1.3 kg/m^3)(9.8 m/s^2)(6.1 m) = 78 N/m^2, about 7.7E-4 atm.
If you integrate the pressure difference over the surface of the
balloon, you find that the buoyant force upwards is 1500 N. This
buoyant force is the *same* for the lead balloon and for the hydrogen
balloon and points upwards in both cases. [This integral is left as an
exercise for the reader.]
Now, the graviational weight of the hydrogen in a 10 ft radius balloon
is 105 N. The weight of the lead balloon is 13E6 N. It is pretty easy
to see that 1500 N > 105 N, which is why the hydrogen balloon rises.
It is also pretty easy to see that 1500 N < 13E6 N, which is why the
lead balloon falls.
As I said, the gravitational forces acting on the 10 ft hydrogen and
lead balloons are dramatically different. The buoyant force, due to
the small atmospheric pressure gradient from top to bottom of both
balloons, is the same.
So, you spent 5 paragraphs to say that air pressure changes by
about 1" Hg per 1000 feet?
I believe I said that about 3 or 4 posts ago.
I agreed with you that the pressure difference (and hence the buoyancy
force) is too small to affect the flight of a tennis ball in any
significant way.
I guess my remarks in the original thread started off all this stuff
about bouyancy forces and pressure differences. The point was (poorly
worded, I will admit) not that buoyancy force on the tennis ball could
be important, but that pressure differences in the atmosphere are non-
trivial. I was just suggesting (again, not well worded) that the drag
effects could vary with altitude, to the extent they are affected by
pressure. (That was in response to a previous message stating that
such pressure differences could be ignored.) Of course, the effects
could only matter if the ball goes hundreds of meters up.
R.G. Vickson
You also said that the gradient in pressure had nothing whatsoever to
do with why a balloon rises, and I've just spent 5 paragraphs
explaining to you why what you said is a load of hooey.
And you spent several posts to say there are no "magic" pressure
differentials due to the force of buoyancy and the only pressure
change is that due to altitude?
No, I didn't say anything of the kind. I said that the force of
buoyancy is due *precisely* to pressure differentials, though no magic
of any kind is required.
I believe I also said that about 3 or 4 posts ago.
--
Jim Pennino
Remove .spam.sux to reply.- Hide quoted text -
- Show quoted text -
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| User: "Eric Gisse" |
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| Title: Re: How high will a tennis ball go? |
06 Jun 2007 05:36:20 PM |
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On Jun 6, 10:06 am, "C...@shaw.ca" <C...@shaw.ca> wrote:
[...]
I guess my remarks in the original thread started off all this stuff
about bouyancy forces and pressure differences. The point was (poorly
worded, I will admit) not that buoyancy force on the tennis ball could
be important, but that pressure differences in the atmosphere are non-
trivial. I was just suggesting (again, not well worded) that the drag
effects could vary with altitude, to the extent they are affected by
pressure. (That was in response to a previous message stating that
such pressure differences could be ignored.) Of course, the effects
could only matter if the ball goes hundreds of meters up.
If it really bothers you, just toss in a constant term corresponding
to the force from buoyancy.
Did you know that g isn't really constant and that the Earth isn't
really spherical? For something like this, /it does not matter/. I'd
be surprised if you could reliably keep the initial velocity within
10% of your expected value.
[...]
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| User: "Bob Cain" |
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| Title: Re: How high will a tennis ball go? |
04 Jun 2007 04:39:10 PM |
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Puppet_Sock wrote:
On Jun 3, 10:02 pm, "C...@shaw.ca" <C...@shaw.ca> wrote:
[snip]
Are you sure? Even a small child's helium-filled balloon floats up
because of the pressure difference in air at the bottom and top of the
balloon---and that is for an object a few tens of cm in size.
Absolutely not. A balloon floats because of the difference in
density between the inside and outside, not top and bottom.
Socks
Why then does a helium balloon in a closed car move forward when
accelerating and rearward when braking?
Bob
--
"Things should be described as simply as possible, but no simpler."
A. Einstein
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| User: "PD" |
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| Title: Re: How high will a tennis ball go? |
04 Jun 2007 12:44:20 PM |
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On Jun 3, 9:02 pm, "C...@shaw.ca" <C...@shaw.ca> wrote:
On Jun 3, 5:38 pm, Chris W <1qaz...@cox.net> wrote:
I have a problem that I need a little help with. If I could remember
much from my calculus classes in college I could probably figure it out
but I need help now.
I want to know how high an object will go when launched vertically at a
known speed. If we ignored wind resistance that would be easy but in
the case I am looking at, it would also make it far to inaccurate.
However to make it a reasonable problem we will assume the height isn't
going to be enough to significantly change the air pressure.
Are you sure? Even a small child's helium-filled balloon floats up
because of the pressure difference in air at the bottom and top of the
balloon---and that is for an object a few tens of cm in size. Perhaps
the safest approach is to first solve the problem neglecting pressure
differences, then estimate the pressure differences a posteriori. If
they are "significant" you should try again, now putting in the
effects of decreasing pressure with altitude, or perhaps perform a
"perturbation" computation about the original solution.
The thing that makes a difference for the child's balloon is that
difference in pressure between bottom and top of the balloon is
significantly higher than the gravitional pull downward on the
balloon. You are correct that the pressure difference is not zero, but
it is likely to be much, much smaller than either the drag force or
the gravitational force downwards on the balloon and so will not
dramatically change the answer. Even if it's not, the point the OP
makes (correctly) is that the pressure difference doesn't change
significantly over the trajectory of the ball, and so one can just
change the pure weight of the ball to be the effective weight of the
ball (the weight minus the buoyant force) without loss of generality.
PD
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| User: "Eric Gisse" |
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| Title: Re: How high will a tennis ball go? |
03 Jun 2007 08:30:01 PM |
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On Jun 3, 5:38 pm, Chris W <1qaz...@cox.net> wrote:
I have a problem that I need a little help with. If I could remember
much from my calculus classes in college I could probably figure it out
but I need help now.
[..]
1) F_newton = m*a
2) F_drag = b*v
3) F_gravity = m*g
Sum the forces, make sure the directions are right, and solve the ODE.
Realistically, drag won't affect the tennis ball that much. Just apply
the work-energy theorem and call it a day.
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| User: "Chris W" |
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| Title: Re: How high will a tennis ball go? |
03 Jun 2007 09:27:49 PM |
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Eric Gisse wrote:
On Jun 3, 5:38 pm, Chris W <1qaz...@cox.net> wrote:
Realistically, drag won't affect the tennis ball that much. Just apply
the work-energy theorem and call it a day.
If you ignore any drag or other loss, the tennis ball will leave the air
cannon at well over 1000 ft/sec. How could drag not be a huge part of
the equation at speeds like that?
--
Chris W
KE5GIX
"Protect your digital freedom and privacy, eliminate DRM,
learn more at http://www.defectivebydesign.org/what_is_drm"
Gift Giving Made Easy
Get the gifts you want &
give the gifts they want
One stop wish list for any gift,
from anywhere, for any occasion!
http://thewishzone.com
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| User: "Phil Holman piholmanc@yourservice" |
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| Title: Re: How high will a tennis ball go? |
06 Jun 2007 09:29:39 PM |
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"Chris W" <1qazse4@cox.net> wrote in message
news:GMK8i.32772$7T.6457@newsfe18.lga...
Eric Gisse wrote:
On Jun 3, 5:38 pm, Chris W <1qaz...@cox.net> wrote:
Realistically, drag won't affect the tennis ball that much. Just
apply
the work-energy theorem and call it a day.
If you ignore any drag or other loss, the tennis ball will leave the
air cannon at well over 1000 ft/sec. How could drag not be a huge
part of the equation at speeds like that?
This from a discussion a while back on firing a bullet straight up. We
did calculate the deceleration due to both gravity and drag.
Indeed, interesting thread. But let's derive equations that describe the
vertical motion of a bullet after it leaves rifle barrel.
1) The equation of the motion at rising: dV/dt= - g - kV^2
Let V(t) be the speed of the bullet at moment t (Initial moment t=0)
Then integration of the motion equation gives:
V={v[sqrt(k/g)]-tan[sqrt(gk)t]}/{sqrt(k/g)+v(k/g)tan[sqrt(gk)t]}
v is initial velocity. At the maximum height V(t)=0. Solving for t gives
the time T1 required for the bullet to reach its highest point:
T1=sqrt[1/(gk)]arctan{v[sqrt(k/g)]}
Let h(t) be the height of the bullet at moment t (Initial moment t=0,
initial height h=0) Integration of V(t) gives:
h=(1/k)Ln{cos[sqrt(gk)t]+v[sqrt(k/g)]sin[sqrt(gk)t]}
To determine the maximum height H we calculate the position of the
bullet at T1. H=h(T1): H=[1/(2k)]Ln[1+(k/g)v^2]
2) The equation of the motion at falling: dV/dt = g - kV^2
Let V(t) be the speed of the bullet at moment t (Initial moment t=0)
Initial velocity is 0 now. Then integration of the motion equation
gives: V=sqrt(g/k)th[sqrt(gk)t] Here th(x) is the hyperbolic tangent.
Let h(t) be the height of the bullet at moment t (Initial moment t=0,
initial height h=H) Integration of V(t) gives: h(t)=H -
(1/k)Ln{ch[sqrt(gk)t]} ch(x) is the hyperbolic cosine. To determine the
time T2 it takes for the bullet to fall back down
from the highest point we must solve for t the last equation:
h(t)=0 I hope there in no bug in the calculations
dV/dt= - g - kV^2
k = ½*Cd*rho*A/m = (½*.1*.076/32.2*.001104)/(.02563/32.2) = .0001631
g = 32.2
dV/dt = -32.2 -.0001631V^2
V(t)={v[sqrt(k/g)]-tan[sqrt(gk)t]}/{sqrt(k/g)+v(k/g)tan[sqrt(gk)t]}
T1=sqrt[1/(gk)]arctan{v[sqrt(k/g)]} =
sqrt[1/(-32.2*-.0001631)]arctan{1000[sqrt(-.0001631/-32.2)]} =
13.7989*arctan(2.2506) = 15.9056 seconds
h=(1/k)Ln{cos[sqrt(gk)t]+v[sqrt(k/g)]sin[sqrt(gk)t]}= -6131.2*ln{cos[sqr
t(-32.2*-.0001631)15.9056]+1000[sqrt(-.0001631/-32.2)]sin[sqrt(-32.2*-.0
001631)15.9056]} = -6131.2*ln{cos1.15267+2.2506*sin1.15267}= 5526 ft
Terminal velocity Vt (Cd backwards = .2)
½*Cd*rho*Vt^2*A = W
½*.2*.076/32.2*Vt^2*.001104 = .02563
Vt = Sqrt(.02563*32.2/(½*.2*.076*.001104))
Vt = 313.6 ft/sec
Phil H
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| User: "Eric Gisse" |
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| Title: Re: How high will a tennis ball go? |
03 Jun 2007 09:37:01 PM |
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On Jun 3, 7:27 pm, Chris W <1qaz...@cox.net> wrote:
Eric Gisse wrote:
On Jun 3, 5:38 pm, Chris W <1qaz...@cox.net> wrote:
Realistically, drag won't affect the tennis ball that much. Just apply
the work-energy theorem and call it a day.
If you ignore any drag or other loss, the tennis ball will leave the air
cannon at well over 1000 ft/sec. How could drag not be a huge part of
the equation at speeds like that?
At velocities larger than ~15m/s, drag goes from being proportional to
velocity to proportional to the square of velocity. Do you know how to
solve a nonlinear ODE?
--
Chris W
KE5GIX
"Protect your digital freedom and privacy, eliminate DRM,
learn more athttp://www.defectivebydesign.org/what_is_drm"
Gift Giving Made Easy
Get the gifts you want &
give the gifts they want
One stop wish list for any gift,
from anywhere, for any occasion!http://thewishzone.com
.
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