the train problem

[billy rubin]

okay this has been bothering me.

bernoullis principle states that the faster a fluid moves, tbe lesz pressure it exertz. this explains why aeroplanes fly and zailboatz can tack against the wind. but iz it limited to fluids? what is the mechanism?

imagine a train loaded with 40 container carz, a half mile long, that weighs ten million pounds. itz about to cross a trestle exactly one mile long, equipped with instantaneous tranzducers that can weigh the train az it crosses the bridge.
if the train stopz in the middle of the bridge, the transducers weigh it at 10 million pounds.

now have the train crozz tbe bridge at 60 miles per hour, so that it takes the locomotive one minute to cross the bridge. take a reading of the train's weight in the middle. im guessing it will be 10 million pounds.

or will it?

asking for a friend.

[No one]

42

[hermes2015]

Relativistic mass effects will be too small to measure at such a low velocity, so the train's weight will be essentially unaffected. This will not be the case as its velocity approaches the speed of light, when its mass will increase dramatically, meaning that it will never be able to reach the speed of light.

[billy rubin]

i was actually wondering whether a bridge that would collapse at 10 million pounds could be crossed by hitting it fast.

i believe the answer is yes, because bridges dont fail instantaneously, and the train will be across before the bridge falls. driving vehicles that routinely weigh 40,000 kiloz, this iz of personal interest.

but relativity brings up another question. suppose the trestle is one light year long, and can support something over 10,000 million pounds.. the train speeds up to near light-speed ( it has limitlezs energy). az it speeds up its masz eventually exceeds the bridge capacity. so the bridge will ultimately fail, not because the original mass was too great, but because the velocity was too high.

[Dark Lightning]

The relativistic mass will only increase in the direction of the motion, not down. There is only the same up/down speed as before, which is essentially zero vertically with respect to the tracks.

[billy rubin]

mass is a vector?

that's bizarre.

i'm still trying to wrap my head around bernoulli and pressure. i used to use faucet vacuum aspirators



and i always wondered why the aspirator section produced vacuum as the water rushed by, rather than leaking water out like a hole in a pipe.

i beiieve the water outlet was somewhat restrictive, even if only from friction along the walls of the tube, so it seemed more reasonable to me that the hole in the side should have been under pressure, rather than vacuum.

but it didn't work that way.

i'm afraid the text that accomanied ^^^thjis illustration wasn't helpful:

Faucet Aspirator Vacuum Pump
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[Icarus]

Tell your friend that Bernoulli principal does not apply to that train and the bridge.   There are basic equations in the structural engineering fields that describe rolling, or transient, loads across a beam.  Consider the bridge as a simple beam.  The long train will cover the entire bridge so the load can be conditionally assigned as an evenly distributed load.   That equation is different but still in general agreement with the rolling load one. 

If the train stops while there are parts of the train on the bridge it will present almost the the same, but not quite the same kind of down force as when the train is stopped.   It is safe to say that the bridge will either hold the train up or fail, regardless of the speed or lack of speed of the train.

Bernouli equation is pretty simple. ( Hey, your carburetors utilize the principal.)   Lets talk about an airplane wing.  The camber, or curvature, is usually larger on the top of the wing than on the bottom.  Air that travels over the top of the wing must go faster than the air on the bottom of the wing if the molecules of air are to meet at the exit point. The wing exhibits more lift at the top of the wing than on the bottom   

The Bernouli equation involves the Greek letter rho which is the density (weight pr unit volume) of the medium in which the flow is subjected.   Air is considered as a fluid in these cases. The principal works as well for air, other gasses, and fluids such as water or other viscous fluids.   The equation is pretty simple. It says that the  local pressure or lack of it is as follows.  Rho times velocity squared all divided by two.  That is oversimplifying the physics but that is the general idea.   The air or water density is pretty much constant, so the determining factor is velocity. A given amount of air passing through a pipe or over a reduced area must move faster than it did as the larger opening or surface. 

The train is not much subject to the Bernouli principal because it blasts the air out of the way in the top, bottom, and sides of the vehicle components.  There is little measuraable difference in the air streams around the body of the train.  If little or no difference in the velocities of the air are present then there is no appreciable difference in the pressures on the four sided objects.


In your carburetors....oh dear I hope that you are not still using Amals.....there is a section in the bore where the bore diameter  is reduced.  The Venturi as it is called, has a Venturi pipe that  will be situated at about the middle of that reduced area.  The air is flowing through the entrance of the carb at somewhere near atmospheric pressure. At the Venturi the air velocity is increased and so there is a drop in pressure...a  suction. That suction delivers some fuel to the outlet pipe. and ultimately down the air stream toward the inlet valve.

The bridge will collapse no matter how fast the train is going unless it was designed to hold the whole train in the first place. A beam will fail instantaneously whether the load is going fast or not.  If a two by four will rupture when you hit it with a sledge, does it wait to shatter?

[Recusant]

The relativistic mass will only increase in the direction of the motion, not down. There is only the same up/down speed as before, which is essentially zero vertically with respect to the tracks.

Can you cite a source for this? I admit I'm not a master of special relativity, but as I understand it, the mass of an object in acceleration at relativistic velocities increases because the energy involved can be thought of as adding mass to the object (mass/energy equivalence principle). I was unaware of any directional element to this. The below is from Wikipedia, but it seems to conveys the idea accurately.

A macroscopic body that is stationary (i.e. a reference frame has been chosen to correspond to the body's center of momentum) may have various kinds of internal energy at the molecular or atomic level, which may be regarded as kinetic energy, due to molecular translation, rotation, and vibration, electron translation and spin, and nuclear spin. These all contribute to the body's mass, as provided by the special theory of relativity. When discussing movements of a macroscopic body, the kinetic energy referred to is usually that of the macroscopic movement only. However all internal energies of all types contribute to body's mass, inertia, and total energy.

Perhaps what you're talking about is the way that "relativistic mass" varies according to the frame of reference of the observer, but I'm interested in hearing a more detailed explanation of the idea you're presenting here. You may be able to dispel a misconception on my part.

[hermes2015]

The relativistic mass will only increase in the direction of the motion, not down. There is only the same up/down speed as before, which is essentially zero vertically with respect to the tracks.

Can you cite a source for this? I admit I'm not a master of special relativity, but as I understand it, the mass of an object in acceleration at relativistic velocities increases because the energy involved can be thought of as adding mass to the object (mass/energy equivalence principle). I was unaware of any directional element to this. The below is from Wikipedia, but it seems to conveys the idea accurately.

A macroscopic body that is stationary (i.e. a reference frame has been chosen to correspond to the body's center of momentum) may have various kinds of internal energy at the molecular or atomic level, which may be regarded as kinetic energy, due to molecular translation, rotation, and vibration, electron translation and spin, and nuclear spin. These all contribute to the body's mass, as provided by the special theory of relativity. When discussing movements of a macroscopic body, the kinetic energy referred to is usually that of the macroscopic movement only. However all internal energies of all types contribute to body's mass, inertia, and total energy.

Perhaps what you're talking about is the way that "relativistic mass" varies according to the frame of reference of the observer, but I'm interested in hearing a more detailed explanation of the idea you're presenting here. You may be able to dispel a misconception on my part.

I majored in physics and chemistry for my first degree, but I am also by no means a master of special relativity, so would like to be enlightened as well.

[billy rubin]

In your carburetors....oh dear I hope that you are not still using Amals.....there is a section in the bore where the bore diameter  is reduced.  The Venturi as it is called, has a Venturi pipe that  will be situated at about the middle of that reduced area.  The air is flowing through the entrance of the carb at somewhere near atmospheric pressure. At the Venturi the air velocity is increased and so there is a drop in pressure...a  suction. That suction delivers some fuel to the outlet pipe. and ultimately down the air stream toward the inlet valve.

heavenz yez, i still have amals in two or three BSAs and a norton. if their tune happenz to be correct for the machine they work well enough. on seriouz machinez i have round zlide mikuniz. on tbe race bike i uze flat slide keihin FCRs:



i tune tbe jetting with an AF meter hooked to an oxygen zensor in the tailpipes to get close, then uze a stopwatch on timed runz at a local airztrip.

ive never dynoed the serious machine. i tune the old way looking at speed and plug color. currently im fazter than tbe high tech people.

on aspiration, i understand the resultz well enough. im just not internalizing the reazon why an interface between a moving fluid and a surface rezults in a relative  preszure drop. i have a bleeder valve on the inlet plumbing in my truck that displays the problem.





when a hose is attched to this 4-inch fitting and i apply 20 inches of mercury to the line, brine is drawn into the truck and tbe bleeder line (with the rubber hoze) dizplays vacuum.when i apply prezsure to the 4-inch line, the bleeder shows prezsure. in both cazes a fluid is moving past the internal orifice of the bleeder, but the prezsure at tbe bleeder reflectz tbe vacuum or pressure in the tank.

when the tank merely drains under the prsssure of the head of water, the bleeder is under the same pressure and water runz out. when tbe tank is being emptied under vacuum the bleeder also drains water.

at the other end is a similar bleeder valve attached to the production tanks. if iopen the bleeder just as i open the line to vacuum from thevtruck, it leakz water because the column isnt moving. chanin noting else,the same bleeder will show vacuum once the brine nthe line is moving rapidly.

as you zay, whether vacuum or prezzure is prezent at an orifice exposed to a moving fluid zeemz a function of velocity less so than pressure. ill have to think zome more.

and clean up some typos

[Dark Lightning]

The relativistic mass will only increase in the direction of the motion, not down. There is only the same up/down speed as before, which is essentially zero vertically with respect to the tracks.

Can you cite a source for this? I admit I'm not a master of special relativity, but as I understand it, the mass of an object in acceleration at relativistic velocities increases because the energy involved can be thought of as adding mass to the object (mass/energy equivalence principle). I was unaware of any directional element to this. The below is from Wikipedia, but it seems to conveys the idea accurately.

A macroscopic body that is stationary (i.e. a reference frame has been chosen to correspond to the body's center of momentum) may have various kinds of internal energy at the molecular or atomic level, which may be regarded as kinetic energy, due to molecular translation, rotation, and vibration, electron translation and spin, and nuclear spin. These all contribute to the body's mass, as provided by the special theory of relativity. When discussing movements of a macroscopic body, the kinetic energy referred to is usually that of the macroscopic movement only. However all internal energies of all types contribute to body's mass, inertia, and total energy.

Perhaps what you're talking about is the way that "relativistic mass" varies according to the frame of reference of the observer, but I'm interested in hearing a more detailed explanation of the idea you're presenting here. You may be able to dispel a misconception on my part.

I majored in physics and chemistry for my first degree, but I am also by no means a master of special relativity, so would like to be enlightened as well.

I'm going to have to go crack open my text book and get back to you guys.

[Dark Lightning]

It would appear that my books containing special relativity are in storage. I went to Wikipedia and yes, I was correct about the transverse mass not changing. See the third paragraph, here-

https://en.wikipedia.org/wiki/Mass_in_special_relativity#The_relativistic_mass_concept

It's pretty straightforward- the transverse forces rely on velocity in those directions, and if the train is on a straight track, those velocity terms will be zero, yielding simply the mass.

[Recusant]

Cool. I'll gnaw on that in my mathematically toothless way for a bit. Would you be willing to help me attempt to understand this concept?

[Dark Lightning]

It's pretty straightforward. No velocity means no force, means no change of mass, per the equations. Do your own homework, you! 

[hermes2015]

It's pretty straightforward. No velocity means no force, means no change of mass, per the equations. Do your own homework, you! 

Thanks, that is enlightening. I'm never too old to learn something new.