FORCES SOME PHYSICISTS FORGET

While reading a fairly recent physics textbook I found a detailed discussion of fictitious or inertial forces. The textbook is PHYSICS For Scientists & Engineers, Third Edition, by Raymond Serway, James Madison University, Copyrights 1990, 1986, and 1982, Saunders Golden Sunburst Series, Saunders College Publishing, Philadelphia, Library of Congress Catalog Card Number 89-043325.

This is not meant to be a criticism of a book that is excellent in many ways and must have been a great challenge to write. It is still being used in teaching undergraduate physics. I use it only as an example of some prevalent ideas on the subject of inertial forces and inconsistencies rising from those ideas.

Section 6.3, MOTION IN ACCELERATED FRAMES, begins on page 135. According to Serway, an observer in an accelerating frame of reference must invoke fictitious forces (aka inertial forces) if he would use Newton's second law in his accelerated reference frame. Serway then claims that the invented forces appear real in the accelerated frame but are not forces resulting from interaction between the body and its environment, and therefore are not real forces. Serway’s claim in a positive form gives us a DEFINITION: A real force is one that results from the interaction of a body and its environment.

On page 136 Serway presents EXAMPLE 6.5 Linear Accelerometer. In that example a ball is suspended by a cord as a non-oscillating pendulum in a railroad boxcar that is accelerating, as illustrated by Figure 6.11(a). In order that we can see what is going on inside the boxcar, the facing side of the car has been removed. An arrow over the boxcar points rightward, indicating the direction of motion and acceleration. An observer stands upright on the ground near the tracks. The illustration depicts the cord displaced from the vertical by an angle theta (the ball to the left of the vertical from the point of suspension), the tension in the cord (T), and the downward gravitational force on the ball (mg). The observer sees the acceleration of the ball and boxcar to be the same and deduces that the horizontal component of tension (T) produces the acceleration, and that the vertical component of T balances the ball's weight. I do not believe that the omission of the horizontal component of T in that figure was an accidental oversight.

Immediately beneath Figure 6.11 (a) is Figure 6.11 (b), which depicts the same boxcar and suspended ball. An observer is now inside in the front of the boxcar, facing the rear, standing upright with arms and hands at sides, and looking at the suspended ball. The angle theta is the same. The horizontal component of T is labeled -ma and directed leftward from the ball.

For that second illustration Serway states that for the noninertial passenger in the car the sphere is at rest and there is no acceleration. That is why, writes Serway, the observer invokes fictitious force -ma to counter T's horizontal component, and thinks there is zero net force on the ball (italics his). Serway states that the interpretation of the situation is different in each of the two reference frames.

I suspect that Serway has not had daily experience commuting to work by rail. If he did, he certainly would know that anyone standing vertically with feet together and not holding on to anything will fall down in an accelerating railroad car. I do not believe the depicted position of that observer to be an accidental oversight or mistake. Were the observer to assume a spread-legs (in line with the direction of acceleration) braced position leaning forward (at about the angle theta), the observer would not fall over and would feel, resist, and know that there is a force of acceleration to be taken into account. Because it is well known that acceleration forces will move anything not secured in a boxcar, crates of heavy loads are often nailed to the wooden floors of boxcars to avoid damage to boxcar or contents.

Since in both illustrations the boxcar and track are horizontal we must assume that the engine pulling the train is producing the acceleration. That acceleration results from horizontal force generated through contact of the engine's drive wheels with the track. Couplings between the engine and subsequent cars transmit that force. The magnitude of that force is the product of the total mass of the train (and its contained objects) multiplied by the acceleration. Components of the train and the objects transported by the train (including observers) experience the same acceleration and, hence, a force in proportion to their individual masses.

Now although we might correctly think that acceleration of the train produces forces on its contents and passengers, we would be wrong to think that the acceleration of the train produces the motivating force in its engine. Clearly, it must be the engine that produces the force to accelerate the train and its contents. Equally clearly, if a reference frame containing one or more bodies is accelerating, forces are being applied to those bodies. Acceleration without force violates Newton’s second law. The notion of an accelerating reference frame devoid of mass bodies is meaningless. Only mass bodies can accelerate.

As with the train, the force causing acceleration of a reference frame is simultaneously applied to all objects in the reference frame. Because the source of that force is external to the bodies in the reference frame, that force is a part of the environment of those bodies. Therefore, observed forces on bodies in an accelerating reference frame do result from interaction between such bodies and their environment and, by the definition of a real force given above, those observed forces are real. The force that accelerates a reference frame is often a forgotten force.

Once the force that accelerates a reference frame is taken into account the apparent difference between an inertial and noninertial reference frame disappears. Observers in either reference frame find the same forces affecting the accelerometer. By not 'forgetting' the force created by the engine there is no need for postulating a 'fictitious force.'

If the accelerometer consisted, instead, of a vertically immobile, horizontal, helical compression spring, fastened at one end to the rear wall of the boxcar, and with a weight on the free end, both observers would see that the spring was compressed from its rest position. Both would recognize that a real force compressed the spring. They would recognize that the compressive force on the spring originated with the force on the train and its contents. By attaching a pointer to the free end of the spring and a calibrated scale behind the pointer and by then substituting various known weights either observer could verify Newton's second law, f=ma, without invoking fictitious forces. Note that the same device could be used to measure static forces where there is no acceleration.

On page 136 Serway presents EXAMPLE 6.9 Fictitious Force in a Rotating System. Two side by side illustrations depict a rotating turntable with a mass connected to the center of the table by a cord in figure 6.12. Illustration (a) has an observer standing next to the turntable, while illustration (b) has the observer in a reclining position along a radius on the turntable. We are subliminally asked to believe that the observer in (b) cannot feel, and need not resist, any force acting on him. According to Serway, that observer therefore invents a fictitious outward force mv²/2 (and calls it centrifugal force) to balance the force of tension in the cord.

Let us now imagine that the spring-and-weight force indicator is taken from the boxcar and fastened to the edge of the turntable, with the free end and weight resting on the turntable. Two opposing forces, at either end of the spring, would again compress the spring. The forces at the two ends of the spring would be designated centripetal force and centrifugal force by both observers. The observer as depicted on the turntable, without much source of centripetal force, would have to exert some effort to resist being thrown off the turntable.

There are amusement park turntable “rides” like that. Once the very smooth wooden turntable starts turning, almost everyone slides off. Few can position their exact center of gravity over the exact center of the turntable. If someone were to apply a pair of suction cups with handles to the turntable and hold on to the handles until the turntable reaches its steady angular velocity, the person would feel as if hanging from the rings in a gym and fighting against gravity. In that case, however, it would be centrifugal force being fought by the person’s centripetal force.

As with the linearly accelerating reference frame, the notion of an empty rotating frame is meaningless. Only the bodies in a rotating reference frame do the rotating. In the case of the rotating reference frame the force that has been forgotten is the force that put everything in that frame into rotation, creating their angular momentum, kinetic energy of rotation, and capability to exert forces on objects introduced into that reference frame.

Regarding the observer in the accelerating boxcar Serway wrote, in a disparaging sense, that the observer thought there was zero net force on the ball. According to Newton’s third law, for every force there is always an equal and opposite force. That law followed to its logical conclusion means that no matter how many forces act on a body, for each one there is always an equal and opposite force; and, therefore, the net force acting on any body is always zero. Surely Serway did not intend to slight Newton’s third law; however, that is what can inadvertently happen if one forgets the inertial force exerted by a body against an external force causing it to accelerate.

On page 816, Serway prepares to derive the circular orbital radius of a charged particle in a magnetic field. He writes, “Since the resultant force F in the radial direction has the magnitude of qvB, we can equate this to the required centrifugal force, which is the mass m multiplied by the centripetal acceleration v²/r.” At last centrifugal force becomes required and real, has a formula, and is equal and in opposition to centripetal force.



<font size=-1>[ This Message was edited by: Richard J. Hanak on 2002-08-09 21:31 ]</font>

<a name="20020809.7:06"> page 20020809.7:06 aka Sum`e
On 2002-08-09 21:30, Richard J. Hanak wrote:
FORCES SOME PHYSICISTS FORGET :: 7:08 P.M. PST
1: 5 Clocks Rev 99-3-16 {!cty of power} {{d4 Angstrom}}
2:================================================ ==============
3:BELOW find basic theory(structure?), based mostly on just two
4:concepts "SPIN" & "orbit" from which 5 enviornments are sought.
5:EACH having its own words to describe what takes place within.
6:NOTE at this time there are NO words for D5 = clock1 = fastest.
7:for each CLOCK dimension there would exist a table ?...........
8:_____<pre>
9:__d5__ clock 1: no words would be know about these(orbit//spin)
10***[ PREPOSED TABLE of minisqualPHYSICAL UNITS ]*********
1:_____ {{ gravitons? }}
2:__d4__ clock 2: electrons orbit proton // electrons spin
3:***[ PREPOSED TABLE of quantmPHYSICAL UNITS ]********
4:
5: ns Angstrom
6:_____ {{photons}}
7:__d3__ clock 3: Planets orbits the Sun // Planets Spin on axis
8:***[ PREPOSED TABLE of metaPHYSICAL UNITS ]*********
9: ^1.? ^2 VELO |-------erg0---^3-----| ? ^4 ?
20 TIME LENGTH CITY FORCE {fudge}[e6] WORK POWER MASS
1: {--default--} &Acc {factor} energy {default}
2: us ?-16 _raff e-30 #construkt !plank fg(-15)
3: ms ?-9 _felt e-24 #gravolti !graft ag(-12)
4: ms ?-4 _rif e-18 #parton !part pg(-9)
5: cs mm _sta 1.6 e-12 eVolt !surge ug(-6)
6: ds mm mm/ds _lyte e -6 #bolt !merg mg(-3)
7: s cm cm/s dyne 1 e 0 erg ! gram(UNIT)
8: SEC METER M/S NEWTON 10 e 6 Joule WATT kg( 3)
9: ?hr M _warm 3.6 e 12 kWhr !cty Mg( 6)
30 ?11hr kM KM/Hr _blite 4.2 e 18 kTonn !boom Gg( 9)
1: ?day ?+4 _shake e 24 #Rh.ictar !rattle (12)
2: ?14 3/4d?+9 _wiew e 30 #Tp.actor !wtcht (15)
3: ?yr ?+16 _sheen e 36 #Sf.un !flue2 (18)
4: ??Myr ?+25 _puff e 42 #O___blartor !wowe (21)
5: { _ preposed words for units of force for each scale level}
6: { # preposed words for units of energy for each scale level}
7: { ! preposed words for units of power for each scale level}
8:_____
9: </pre>
Continued on link below
http://www.badastronomy.com/phpBB/vi...#20020811.5:30

<font size=-1>[ This Message was edited by: HUb' on 2002-08-11 09:56 ]</font>

if he gives the angle and the force of tension then spliting it up between the hor and ver components would be redundant. perhaps you misinterpriated the illustration, the vertical line is proibibly there to show that the angle is off from the vertical.

from the vantage point of the passenger, the ball is remaining still, that is why he states that there is a net zero force on the ball. and that is why there is needed an extra force, to account for the angle on the string.

you are right that this is not an accident, the point of the illustration is to depect the actions on the ball in different perspectives. How the person is standing is unimportant. Also, previously he stated that the passenger was non-inertial, which is just another way of saying that this object has noting to do with the example it is just here for reference.

I do not think that you have the concept of reference frame right. whatever is outside the reference frame is ignored because is is not in the reference frame, this includes the force accelerating the reference frame. the reference frame is assumed to be the environment.

the force accelerating the train is not forgotten it is ignored because it is outside the reference frame, and therefore not in the environment

replacing the string with a spring causes no change in the example, because they are both ways of showing the forces present on the ball.

that is an incorrect conclusion to Newton's third law, and is accually in direct conflict with Newton's second law. in Newton's second law he states that acceleration is caused be a non-zero net force. if the net force acting on any body was always zero, then there would be no acceleration of any body.

just because it has a formula, doesn't make it real. it just means that it can be measured.

__________________
The universe is not only queerer than we imagine, it is queerer than we can imagine.
J. B. S. Haldane

I think you may be falling into a linguistic trap.

Let's look at the "force" of friction.

It's real enough: just try to go ice skating on a concrete sidewalk...

But it isn't a "fundamental" force. It ultimately is a function of the electromagnetic and gravitational forces.

Silas

The concept of 'inertial forces' is regarded as a sort of trick in Newtonian mechanics. What is fascinating here is the recognition that the Newtonian centrifugal force due to inertia is "a sort of trick." One would have expected the geocentric model of eg the geosynchronous satellite to be the one filled with tricks and fictional forces, but such is not the case. In the geocentric model, the forces are considered real.

<a name="20020811.5:30"> page 20020811.5:30 aka 5 clocks Continued
On 2002-08-09 23:21, HUb' wrote: To HUb' 2-8-11 <pre>
30 ?11hr kM KM/Hr _blite 4.2 e 18 kTonn !boom Gg( 9)
1: ?day ?+4 _shake e 24 #Rh.ictar !rattle (12)
2: ?14 3/4d?+9 _wiew e 30 #Tp.actor !wtcht (15)
3: ?yr ?+16 _sheen e 36 #Sf.un !flue2 (18)
4: ??Myr ?+25 _puff e 42 #O___blartor !wowe (21)
5: { _ preposed words for units of force for each scale level}
6: { # preposed words for units of energy for each scale level}
7: { ! preposed words for units of power for each scale level}
8:_____
9:__d2__ clock 4: Sun orbits center of Galixy // equinox presesses?
40***[ PREPOSED TABLE of astoPHYSICAL UNITS ]*******(planets & Suns)
1:_____
2:__d1__ clock 5: Galixy R>esesses(orbits) Universe // colide
3:***[ PREPOSED TABLE of faroutPHYSICAL UNITS ]****(ortdust & Galixies)
4:_____
5:__d0__ clock ?: beyond comprehension
6:***[ PREPOSED TABLE of beyond comprehension PHYSICAL UNITS ]****
7: d0 NOTE: was included in this version although not Theorized.
8: IF exists then CLOCK 1, d5 would be assumed NOT TO exist.
9: Thereby keeping the total number of dimensional constructs=5
50.... dated matter AutoDelete 01/01/05
1: Line 51 5:36 A.M. Math hour
2: as i recall this debait
3: it concerned a weight
4: suspended {hanging down}
5: in an accelerating vehicle
6:
7:
8:
9:
60
1: I have read it said
2: that a lighter than air balloon
3: held by a string
4:
5: Will move forward
6: under the same cercumstance
7:
8: although i've not seen this 4myself
9: the logic of it appeared true 2me
70

anyway back to Spin : Orbit Ratios
and the five clocks discussions {well theres none}
but i guess the ratio s does increase as delta D increases ? do not ask Phisist's Pllleeeese </pre>

WRONG! WRONG!! WRONG!!!

As has been pointed out to you before (in another thread) the correct statement of Newton's third law is:

For every action, there is an equal and opposite reaction.

If every force was met with an equal and opposite force, nothing would ever move since:

a=F/m

and if F=0, a=0

Your credibility goes down every time you twist, misapply, misconstrue, or misquote basic laws of physics to try to support your off the wall ideas. [img]/phpBB/images/smiles/icon_evil.gif[/img]

__________________
Any day you wake up on "the right side of the dirt" is a good day.

T. Anderson

moving_target: Newton’s second law, as he wrote it in his Principia, is: “LAW II. The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
If any force generates a motion, …”
Nowhere in the principia did he invoke the ideas of ‘net force,’ ‘zero net force,’ or ‘non-zero net force.’ The key is the phrase ‘motive force.’ If a body is restrained from movement and a force acts on it there will be two equal and opposite stationary forces. If a body is not restrained from movement there will be two equal and opposite moving forces: the motion producing force and the inertial force opposing it. If an object capable of generating a force met no opposition it could not even generate a force. Furthermore, if a body did not produce an opposing inertial force, any applied infinitesimal force would give it infinite acceleration. The inertial force met by a motive force is why the acceleration is in proportion to the motive force.

As for Newton’s third law, he continued immediately after it with explanatory text that begins with “Whatever draws or presses another is as much drawn or pressed by that other.” In the law and its explanations he made no qualifications and put no restrictions on the sources or natures of the forces involved.

Regarding centrifugal force you wrote Anything that is not real is imaginary, hence beyond objective measurement, and therefore not a subject of science.

Seems to me that if the inertial force is equal and opposite to the motive force, the body ain't going anywhere. Therefore, it would be "restrained from movement." For a body to go somewhere, the motive force has to be greater than the inertial force.

__________________
I am a doctor, but I don't play one on TV.

and thats the exact point that Richard danced around. there may be an equal but opposite force, but it is never on the same object. If it were on the same object then the forces would cancel each other out and, by Newton's second law, there would be no acceleration.

__________________
The universe is not only queerer than we imagine, it is queerer than we can imagine.
J. B. S. Haldane

<a name="20020812.5:41"> page 20020812.5:41 aka Page 31
On 2002-08-11 23:57, moving_target wrote: To: page 31 PAGE 1
5:42 A.M. HUb' ?
Well? my point would be {at this time}
that earthlings
simply do not understand what takes place:
anyway: according to me: {could easily be wrong}
there comes a point {when energys converted}
[from one form to another] Kenetic to impact
Where the energy available for release "EXCEEDS"
the ability of the absorbers [heat light mass removal etc]
to ballance the Equation: and energy THEN transfers into another REALM {read clock} (believe what you like) TBC

Let the earth be a coordinate system rotating uniformly relative to the universe. Then centrifugal forces would be in effect for masses at rest in the universe's coordinate system, while no such forces would be present for objects at rest with respect to the earth. The geosynchronous satellite is precisely such an object, at rest with respect to the earth, but viewed as having a centrifugal force acting on it with respect to the universe. Already Newton viewed this as proof that the rotation of the earth had to be considered as 'absolute,' and that the earth could not then be treated as the 'resting' frame of the universe. Yet, as E. Mach has shown, this argument is not sound. One need not view the existence of such centrifugal forces as originating from the motion of the earth; one could just as well account for them as resulting from the average rotational effect of distant, detectable masses as evidenced in the vicinity of
the earth, where the earth is treated as being at rest.

In quite precise language, Einstein taught that the centrifugal force on an object in the earth's rest frame (the condition satisfied by the hovering geosynchronous satellite) is inadmissible as evidence of the rotation of the earth, for in the earth's frame that force arises from "the average rotational effect of distant, detectable masses."

<font size=-1>[ This Message was edited by: Prince on 2002-08-12 18:55 ]</font>

OK, I see no problem here. So again, what the point? Is there one? Or are you just having a Newtonian mechanics love affair?

Where is it going? I know this is going to bring you back a few years Richard, but remember when your high school English teacher taught you that every essay must have a title, a theme, and yes, a conclusion? Maybe you were out that day.

Do I perceive that you are going to use Newtonian mechanics now to promote.... er ,...choke .. cough.....ugh...geocentrism??? [img]/phpBB/images/smiles/icon_biggrin.gif[/img]

G^2

<font size=-1>[ This Message was edited by: Gsquare on 2002-08-12 22:05 ]</font>

In quite precise language, Einstein taught that the centrifugal force on an object in the earth's rest frame (the condition satisfied by the hovering geosynchronous satellite) is inadmissible as evidence of the rotation of the earth, for in the earth's frame that force arises from "the average rotational effect of distant, detectable masses."

Equally in GR this force is inadmissable as evidence that the universe is rotating and the earth is static. Both frames are as valid as each other. So this advances neither the heliocentric nor the geocentric argument.

Nitpicky, I know, but there is no heliocentric argument. Nobody thinks the Sun is the center of everything. I assume you are referring to the Sun containing the CM of the solar system, and Earth, etc. going around that.

Yup what i meant was the sun containing the CM etc. Not really nitpicky since it has reminded me to define what i`m on about better. Basically i`m saying (again and again) that you can`t use GR to argue for a frame that is more correct than any other.

What an interesting discussion this has been. It's unfortunate that words like inertia and centrifugal still have a mysterious feel to some.

__________________
Marcus Asaro

"I'm not normally a praying man, but if you're up there, save me Superman!" - Homer Simpson.

KaptainK wrote:Let us begin with a translation of what Newton actually wrote in his third law and the first two explanatory sentences immediately following that law.

“LAW III. To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone.”

Those two explanatory sentences involve forces and do not necessarily imply motion. Subsequent sentences separately deal with opposite and equal motions. If KaptainK still equates action only with motion and not with force, then I must take it as a failure on my part to have adequately explained to KaptainK why Newton’s third law also applies to forces. I will therefore follow the maxim “When all else fails, consult the manual.” In this case the manual is Webster’s New Twentieth Century Dictionary Unabridged, Second Edition. The word action derives from the Latin noun actio, that derives from the Latin verb agere, to do, drive. The first definition given for action is:
“1. the doing of something; hence, the state of acting or moving; exertion of power or force, as when one body acts on another.”

Newton wrote his Philosophiae Naturalis Principia Mathematica in Latin. He would certainly have known the exact meaning of actio as ‘the doing of something.’ Whether a body moves or not, if it exerts a force it is doing something.

In the Principia, prior to presenting his Laws of Motion, Newton defined his terms. His third definition is:

“DEFINITION III. The vis insita, or innate force of matter, is the power of resisting, by which every body, as much as in it lies, continues in its present state, whether it be of rest, or of moving uniformly forwards in a right line.”

In the third sentence of explanatory text following that definition Newton wrote:
“Upon which account, this vis insita may, by a most significant name, be called inertia or force of inactivity. But a body only exerts this force when another force, impressed upon it endeavors to change its condition;…”

By his own words Newton’s inertial force, his ‘force of inactivity,’ was indeed meant to oppose any motivating force, and was meant to be subject to his third law of motion. However, it is important to remember that inertial force does not prevent a body from moving and arises only if the body is being accelerated; and if a body is being accelerated it must be moving.

Newton also wrote:
“DEFINITION IV. An impressed force is an action exerted upon a body, in order to change its state, either of rest, or of uniform motion in a right line.”
When he subsequently presents
“LAW II. The change of motion is proportional to the motive force impressed; …”
there can be no question that “the motive force impressed” includes only actions exerted upon a body and not actions exerted by a body such as its inertial force.

Motive force impressed is not the same as the net force KaptainK mistakenly applied in that equation. A zero net force does not preclude acceleration if one of its components is inertial force. Only if the sum of all impressed forces is zero will the acceleration be zero.


<font size=-1>[ This Message was edited by: Richard J. Hanak on 2002-08-13 20:05 ]</font>