How Things Move: Exploring Forces and Motion

[david smith]

OK, I can appreciate that.

So, aside from the trivial algebraic manipulation of the equation, the only actual conceptual change of the D'Alembert approach is to consider inertia (-ma) to be a force. This is equivalent to working in the non-inertial rest frame of the object under consideration. In this frame there exists a ficticious force equal to -ma that must be introduced in order to have Newton's first and second laws hold.

Are you familiar with the concepts of non-inertial reference frames (e.g. rotating reference frame) and ficticious forces (e.g. centrifugal force)? If not, then I would recommend you begin studying those topics in order to understand the concepts in the D'Alembert approach.

The inertial force is like any other ficticious force. In particular it violates Newton's 3rd law and it is always proportional to the mass of the object. Ficticious forces can do work in the non-inertial coordinate system and accelerometers cannot detect acceleration due to ficticious forces.

Dale

I had learned about centrifugal / centripedal and coriolis force/effect but I did some reading to refresh and very useful it was too.

However at the end of the day centrifugal and coriolis forces are effects of perception due to the observers viewpoint being within the inertial rest frame or the rotating frame.
They are not forces at all as can be acertained by the observer outside the rotating frame who see that it is the rotating frame that chages direction and experiences acceleration, whereas the particle within it continues unhindered in the same direction.IE Newtons first law.
The centrifugal force feel as if it is at 90dgs to the centre of rotation beacuse the inside viewers perception of the acceleration changes at the same angular velocity as the objects.
Centripedal is a real force reaction to centrifugal force and it appears to me that Inertial force is a real reative force to acceleration.

So I read this paper, On the Origin of Inertial Force, C. Johan Masreliez Redmond, WA
jmasreliez@estfound.org. Which gives a very thorough explanation of the origin of inertial force, much of which was beyond me but essentially he is saying inertial force is a reation to acceleration within the inertial reference frame. IE unlike gravity and almost opposite to gravity it cannot be felt at rest whereas gravity cannot be felt in freefall.

So as such if a body requires a force to accelerate it then there are two questions.

You can't apply a force without an opposing force. So if a body with momentum collides with another body at rest, the body at rest has to accelerate and invoke a reactive inertial force. However the first body cannot apply any force to accelerate the second body until the second body has accelerated so then how can the applied force accelerate it. This appears to be a chicken and egg situation.

And

If two bodies act on each other in the way explained above then there are two inertial forces. One with a negative acceleration and one with a positive acceleration repectively related to their mass. With the other ficticious forces there was no acceleration and no change of direction IE no force.However with this configuration there are two ficticious forces that do cause acceleration and change of direction. Therefore they cannot be ficticious. Can they?

Obviously I still can't see inertial force from your perspective even tho I understand what you are saying. F=ma but ma is not an opossing force like a = f/m gives an equivalent sum but is not equal to a. Is this because you always view from the perspective of acceleration and I from the perspective of force. Therefore I always see balanced forces and you see unbalanced forces.


Ayway I've done many hours of reading and you have helped me to understand more, so its all good.


Cheers Dave

 

[rcgldr]

Cetrifugal force is just as real as any reaction force. It's the centripital force that accelerates an object "inwards", and centrifugal force is the reaction force, equal to mass times acceleration as it always is.

 

[david smith]

Cetrifugal force is just as real as any reaction force. It's the centripital force that accelerates an object "inwards", and centrifugal force is the reaction force, equal to mass times acceleration as it always is.

Jeff

True, but isn't the centrifugal force an inertial force also. EG A car travel in a straight lime at 10m/s and object on the dash board is also traveling in the same direction at 10m/s. The car suddenly turns thru 90dgs but the object that has negligible friction on the dashboard interface continues on its original course at 10m/s at that point it appears to the passenger that something / someforce has accelerated it sideways toward the sidewindow. This is the apparent centrifugal force but it is actually the car, not the object, that experiences accelleration as it changes direction to go thru a turn.
The same principle applies even when the car goes around a long bend.

At the point that the object hits the window there is a 'real' centripedal force that accelerates it in the opposite direction and the object also accelerates the car thru its action on the window but as the car is relatively massive it does not change direction. Therefore the centrifugal force also becomes real in terms of the inertial reference frame.

I think this is how Dale concludes that inertial force is fictitious by the fact that it can only exist as a reaction to acceleration. However to my way of thinking both forces are the result of reactive accelerations and so both are either ficticious or real depending how you think about them.

In the case of a continuous rotation at a constant angular velocity such as a roundabout.
If the roundabout was enclosed so there was no reference to the resting frame then the observer, who is also the object within the rotational frame, would have no way of knowing about their angular velocity. At the same time they would feel the force that pushes them against the walls of the roundabout. This is the centipetal force holding them into the roundabout and their reactive inertial force, which again is the tendency to carry on in a straight line but because the tangent vector of the linear acceleration infinitely changes directly proportionaly to the angular deflection of the rotation it always appear to be pushing straight in and have a reaction straight in IE at 90dgs to the centre of rotation.

If the side wall suddenly disappeared then the person would fly out at a tangent to the arc but to another observer inside the roundabout it would appear that the first person had flown out at a right angle to the centre of rotation. The tangental vector can be thought of as having two vectors of origin in the x, y, directions. Again the second observers perspective does not allow them to see the true tangental motion since they both have a similar velocity in onedirection (eg x vector) and so the second observer only sees the velocity in the direction that has a vector at 90dgs to the centre (eg y vector).

That's my understanding at least

Cheers Dave

 

[Andy Resnick]

Yes longer strides induce higher GRF which then overcome the frictional forces of the shoe - ice interface and you slip and slide into a heap. Andy, When doing gait analysis in a lab we usually measure the ground reaction forces and combine this with kinematic data about the limbs of interest, usually using 3D video camera systems that log relative positions of markers on the body thru time and space.
We use inverse dynamics to characterise the joint, limb and muscle actions. The model is a linked segment rigid body from which we can derive forces moments and powers.
This is a link to a good summary of the technique.http://www.sportsci.com/adi2001/adi/services/support/tutorials/gait/chapter2/2.3.asp

<snip>

Can you now see how I (wrongly it seems) relate momentum of the CoM to kinetic energy requirements of the human mechanical system.
Since higher forces do not necessarilly indicate faster walking, can you also see how I queried, is it the forces applied or the energy transfer that cause motion?

Now I've written that I can see that higher forces or higher energy use does not indicate faster gait. Both are being wasted trying to accelerate the Earth in various directions.Cheers Dave

This was a highly informative post- thank you!

Edit: How is this model modified for walking up or down steep inclines?

 

[david smith]

Andy

In answer to your question:

Edit: How is this model modified for walking up or down steep inclines?

It is unusual to study the gait on an incline, I have not done so formaly. Most studies / gait analysis are done on a flat surface of a lab or clinic. There obviously is a limitation here but the flat ground gives us a universal reference frame for 'normal gait' or as I prefer a 'gold standard' gait. Most of us are normal in that we can ambulate perfectly well for our daily lives and do so without pathology. Most of us are do not attain the gold standard which is just an arbritary bench mark for reference. These bench marks contain parameters such as, Joint angular range of Motion, Joint compliance to a force, Joint neutral position, 3D GRF, muscle firing timing, moments, powers step length, cadence, etc.

The main differences for stair climbing V's normal ammbulation would be the greater range of motion required by the joints to progress upwards and forwards, this requires greater physiologial energy and forces and ultimately more metabolic energy requirements.
In this case gravity is a greater consideration in the equation where there is likely to be large sinusodial amplitude and an overall raising of the mass to a higher potential energy level.

Gait analysis for the purposes of rehabilitation might be done on an incline or on stairs where the individual requires this. However it is often quite plainly obvious why someone might have difficulty or pain when engaging in these activitie. EG they have restriction, for whatever reason of hip knee or ankle flexion / dorsiflexion. If these Ranges of motion are restricted in terms of angular deflection or stiffeness then clearly it inhibits the progression of the centre of mass to the optimum position for continued efficient forward progress.

Sometimes there is a need to study certain activities when considering optimum designs for prosthetics or orthotics.

The fact is that ambulation looses forward momentum thru a gait cycle. In any activity where forward motion is required, and in terms of this thread and the CoM, the CoM must be in the optimum position at the optimum time to be accelerated forward by the muscular action. If it is not it will tend to be accelerated sub optimally and forward progression will be inhibited.


I have attached some PDF's of papers that may interest you.


As a point of interest, I live I Folkestone Kent and have seen many Nepalese soldiers from the Gurka regiment. They live / come from the mountains of Nepal and I was suprised to discover that they have a huge range of dorsiflexion (flexion of the top of the foot toward the front of the leg) of the ankle. Norm = 10dgs (on a good day) they had 40dgs+
which means their ability to get the CoM ahead of their feet are not restricted by the stiffness of the ankle joint when walking up steep hills. In theory this means they should be able to walk uphill easier. If you watch films of Nepalese sherpas climing mountains they appear to walk with ease uphil even with large loads, they walk as if on flat ground (almost).


Cheers Dave Smith

 

[david smith]

Russ wrote

As was already stated, that's just word salad. It doesn't actually mean anything. Kinetic energy and momentum are two different things. There is no such thing as "kinetic energy of momentum".

Russ, I have been doing some reading on energy, work and momentum.
How does your statement above correlate with the following

I realize that Ke cannot be mv since Ke is a scalar and mv is a vector and is like saying 'what direction is the weight of this book'.
However Ke is scalar because velocity is squared. And velocity is squared because of the premise that energy = work and work = F * d => 1/2mv^2.

Can I ask why is energy determined a F*d and not F*time. Usually F*t is the impulse that momentum can be passed from one body to another. Therefore Ft=mv, and by determining the change in momentum of one body in relation to another we can find the total energy used or lost.
If EnergyK = F*t it might make the problem of the link between physiological work and mechanical work of the human body easier to resolve. I guess that's a mute point since we are stuck with Work = F*d = 1/2mv^2 = Ek

Wouldn't that (Ek=F*t) leave us with conservation of momentum and energy in all cases?
IE momentum is energy.

E.G. A 10-gram bullet is fired from a rifle at a speed of 700 m/sec into a 1.50-kg wooden block suspended by a string that is two meters long.


After the collision, through what vertical distance (h) does the block rise?
0.91 meters
During the collision we can only use conservation of momentum.

mbullet(vo bullet) + Mblock(vo block) = (m + M)vc
(0.01)(700) + (1.5)(0) = (0.01 + 1.5) vc
7 = (1.51) vc
vc = 4.64 m/sec

After the collision, the block and bullet are now behaving as one object. We can use conservation of energy to determine how high the pendulum swings.

KEbottom + PEbottom = KEtop + PEtop
KEbottom = PEtop
½mvc2 = mgh
½(1.51)(vc)2 = (1.51)(9.8)h
½(4.64)2 = 9.8h
h = 0.91 m


How much KE is lost during the collision?
2434 J
To determine how much KE is lost, compare the total KE before the collision to the total KE afterwards.

KEbefore = ½(mbullet)(vo bullet)2 + ½(Mblock)(vo block)2
= ½(0.01)(700)2 + ½(1.5)(0)2
= 2450 J

KEafter = ½(mbullet + Mblock)(vc)2
= ½(1.51)(4.64)2
= 16.3 J

This collision lost 2434 J of energy, or 99.3% of the bullet's original energy! http://dev.physicslab.org/Document.aspx?doctype=3&filename=Momentum_MomentumEnergy.xml

Where did it go?

Both momentum and kinetic energy are in some sense measures of the amount of motion of a body. http://galileoandeinstein.physics.virginia.edu/lectures/momentum.html

The difference comes from the fact that most collisions are not perfectly elastic and so while momentum is always conserved energy is not. http://en.wikipedia.org/wiki/Momentum

What if you take this premise

Part 1: Kinetic energy is not ½mv².


A 4kg object dropped 1m (meter) has the same amount of ½mv² as a 1kg object dropped 4m, because force times distance equals ½mv² for an accelerating mass. But a rocket accelerating the masses to those velocities requires twice as much energy as fuel for the large mass as for the small one.

Therefore, both masses do not have the same energy; the rocket does not transform energy in proportion to ½mv²; ½mv² is not kinetic energy; and a gallon of fuel does not produce a consistent amount of ½mv².

Part 2: Kinetic energy is mv.


A 4kg object dropped for 1s (second) has the same amount of mv (momentum) as a 1kg object dropped for 4s, because force times time equals mv for an accelerating mass. A rocket accelerating the masses to those velocities uses the same amount of energy as fuel for both masses.

Therefore, both masses have the same amount of energy; the rocket transforms energy in proportion to mv; mv is kinetic energy; and a gallon of fuel produces a consistent amount of mv.



This proof shows that momentum is all there is to energy. ½mv² is just an equation. How could they both be conserved at the same time when they have different dynamics, which was the original question? The decision to conserve them both was rationalism for convenience, not a law of nature. ref Gary Novak http://nov55.com/ener.html

Also

E=mc^2 Therefore m = E/c^2 energy increases as speed increases and as mass is energy mass increases as speed increases http://galileo.phys.virginia.edu/classes/252/energy_p_reln.html

Velocity is speed with a vector so as mass or velocity increases so does energy

Kinetic energy of a body can be related to the momentum by the equation.

Ek = p^2/2m http://en.wikipedia.org/wiki/Kinetic_energy



I know that energy is like fuel (storage, amount, scalar) and momentum is motion (velocity, mass, time, distance, vector) but the catch is that as velocity increases so does energy and mass. So they are bound together unlike petrol and a car where the faster a car goes the less fuel it will have.

I know I have worn you to a frazzle on this one but one more answer would be appreciated.
Please

Cheers Dave

 

[Dale]

However at the end of the day centrifugal and coriolis forces are effects of perception due to the observers viewpoint being within the inertial rest frame or the rotating frame.
They are not forces at all as can be acertained by the observer outside the rotating frame who see that it is the rotating frame that chages direction and experiences acceleration, whereas the particle within it continues unhindered in the same direction.IE Newtons first law.

Yes, exactly the same as with the inertial force.

Centripedal is a real force reaction to centrifugal force and it appears to me that Inertial force is a real reative force to acceleration.

A reaction force is part of an action-reaction pair satisfying Newton's 3rd law. The key point about an action-reaction pair is that they act on two different bodies. So the centripetal force cannot be a reaction force to the centrifugal force since they both act on the same body.

So as such if a body requires a force to accelerate it then there are two questions.

You can't apply a force without an opposing force. So if a body with momentum collides with another body at rest, the body at rest has to accelerate and invoke a reactive inertial force. However the first body cannot apply any force to accelerate the second body until the second body has accelerated so then how can the applied force accelerate it. This appears to be a chicken and egg situation.

Even when considering more than one body the inertial force is not a reaction force. For example, consider three electrons (initially at rest) located at the points of an equilateral triangle. In the D'Alembert approach each electron experiences 3 forces, two electrostatic, and one inertial. Each electrostatic force on one electron is matched by an equal and opposite electrostatic reaction force on another electron, thus satisfying Newton's 3rd law as all real forces do. In contrast, the inertial forces are not matched by any equal and opposite force on any other electron, thus violating Newton's 3rd law as all ficticious forces do.

However with this configuration there are two ficticious forces that do cause acceleration and change of direction. Therefore they cannot be ficticious. Can they?

Ficticious forces certainly can cause (or prevent) acceleration in their non-inertial frame. Ficticious forces can also do work. Sometimes they are even conservative so they can be associated with a potential field.

Please do not think that the word "ficticious force" is a derogatory statement that I am using to belittle the D'Alembert approach. On the contrary, the term "ficticious force" is simply the technical term, and I find ficticious forces can be quite useful when properly understood and applied in an appropriate problem. My dislike of the D'Alembert approach is not that the inertial force is a ficticious force, but rather that the approach is very confusing and adds little value.

 

[Dale]

Can I ask why is energy determined a F*d and not F*time. Usually F*t is the impulse that momentum can be passed from one body to another.

Why would we need another name for the same thing? As you say F*t is already (change in) momentum, so why would use the word energy to also refer to the same thing? If we didn't call F*d energy then what would you prefer we call it?

 

[david smith]

Why would we need another name for the same thing? As you say F*t is already (change in) momentum, so why would use the word energy to also refer to the same thing? If we didn't call F*d energy then what would you prefer we call it?

Work --- Energy and work are defined by the same units, why not energy and momentum instead?

Although I'm not really arguing it should be changed, like some do. However they appear to be paranoid conspiracy theorists, we are right and everybody else is wrong type, when you read their work. Then again this was said about Galileo and Socrates etc and they were right, mostly. Intuitively momentum is very much like energy and you know what they say, if it smells like cr--, looks like cr-- and tastes like cr--, chances are it is cr--, Which some might say is what I'm talking anyway

LoL Dave

 

[david smith]

Dale

Originally Posted by david smith
So as such if a body requires a force to accelerate it then there are two questions.

You can't apply a force without an opposing force. So if a body with momentum collides with another body at rest, the body at rest has to accelerate and invoke a reactive inertial force. However the first body cannot apply any force to accelerate the second body until the second body has accelerated so then how can the applied force accelerate it. This appears to be a chicken and egg situation.

Even when considering more than one body the inertial force is not a reaction force. For example, consider three electrons (initially at rest) located at the points of an equilateral triangle. In the D'Alembert approach each electron experiences 3 forces, two electrostatic, and one inertial. Each electrostatic force on one electron is matched by an equal and opposite electrostatic reaction force on another electron, thus satisfying Newton's 3rd law as all real forces do. In contrast, the inertial forces are not matched by any equal and opposite force on any other electron, thus violating Newton's 3rd law as all ficticious forces do.

Originally Posted by david smith
However with this configuration there are two ficticious forces that do cause acceleration and change of direction. Therefore they cannot be ficticious. Can they?

Ficticious forces certainly can cause (or prevent) acceleration in their non-inertial frame. Ficticious forces can also do work. Sometimes they are even conservative so they can be associated with a potential field.

Please do not think that the word "ficticious force" is a derogatory statement that I am using to belittle the D'Alembert approach. On the contrary, the term "ficticious force" is simply the technical term, and I find ficticious forces can be quite useful when properly understood and applied in an appropriate problem. My dislike of the D'Alembert approach is not that the inertial force is a ficticious force, but rather that the approach is very confusing and adds little value.

I see what you are saying here, even tho I don't know much about electrostatic force other than its a type of gravity between electrons and reading up about it it is difficult to get a definition of the Electromagnetic force (EMF) only definitions of its action, EG Coulombs law.

It seems to me that the two EMF vectors equal one resultant force vector, which is resisted by an inertail force in the opposite direction to the resultant force vector. Obviuosly the electron can only accelerate in one linear direction so there can only be one linear reaction vector.

My interpretation of your explanation:

One body A acts on another the second body B accelerates and a particle within the inertial frame apparently accelerates in the opposite direction until it hits the wall of the second body B. As it apparently moves within the inertial frame there is an apparent force actin on it which is ficticious. OK.

The same as centrifugal force, as you say, which would mean we should have a name for the force that acts on the particle when it hits tha second B bodies wall and accelerates in the same direction (same direction as body A and B). Like centripedal force, but there isn't. Can you explain why?


If I accept what you say then I still have to ask, since there is some time lag between acceleration of body B and the particle hitting the second bodies wall, how is the acceleration of the second body B started and I would have to conclude that it is the transfer of momentum which would equal a transfer of a certain amount of energy.

The transfer of energy however, requires a force, F*t, so I would conclude that there is no time lag and therefore the ficticious force acts like a real force and resists the applied force instantaneously, simultaneously and oppositely IE F(A)=ma(particle B) and in fact the same happens in reverse to body A. Just as Newton said equal and opposite reactions.

Therefore while an inertial force can be considered ficticious in the term you speak of it can be also considered real since it always acts as a real force.

I think that probably settles my mind on the subject Dale, thanks very much but I would be interested in your response tho.

Also it occurs to me that some of these arguments in this thread appear tautalogical.

IE you can argue that Ek is not momentum as long as you stick to the rule that Ek = F*d and not F*t. To disprove this by making the counter argument that Ek is F*t and is equivalent to momentum is invalid and therefore nonesense.

Also
Inertial force is ficticious as long as you stick to the rule that there are equal and opposite accelerations and not forces. I see equal and opposite forces.

Which kind of goes back to this query from the same post that you did not answer before:

If two bodies act on each other in the way explained above then there are two inertial forces. One with a negative acceleration and one with a positive acceleration repectively related to their mass. With the other ficticious forces there was no acceleration and no change of direction IE no force.However with this configuration there are two ficticious forces that do cause acceleration and change of direction. Therefore they cannot be ficticious. Can they?


Cheers Dale, I am enjoying this voyage of discovery.

 

[Dale]

Regarding your energy and momentum comments, if you ever get interested in relativity you should investigate the four-momentum. It is a concept that unites energy and momentum in the same way that time and space are united into spacetime. Energy is not momentum any more than time is space, but they are intimately connected and that connection is very interesting. It is much more illuminating than simply trying to get rid of energy by redefining it to be the same as momentum.

they appear to be paranoid conspiracy theorists, we are right and everybody else is wrong type

It has nothing to do with paranoia. If someone were to suggest that we use the word "red" to refer to the taste of sugar you would say "we already have a perfectly good word for that, 'sweet', and what word would you use to describe the color of an apple?". Your suggestion is silly for all the same reasons. It is not about conspiracies or right or wrong, it is about clear communication.

Also it occurs to me that some of these arguments in this thread appear tautalogical. IE you can argue that Ek is not momentum as long as you stick to the rule that Ek = F*d and not F*t. To disprove this by making the counter argument that Ek is F*t and is equivalent to momentum is invalid and therefore nonesense.

The idea that everyone else in the world should drop all standard definitions at your every whim is patently absurd. Use the standard definitions of terms. If you have a truly new idea then use a new term for it, but don't change established terms. Anything else only leads to communication breakdown and serves no useful purpose.

To help you understand how silly your argument sounds perhaps this translation will help. To me this comment:

IE you can argue that Ek is not momentum as long as you stick to the rule that Ek = F*d and not F*t.

Sounds like this: "IE you can argue that red is not sweet as long as you stick to the rule that red = the color of an apple and not the taste of sugar."

 

[Dale]

As it apparently moves within the inertial frame there is an apparent force actin on it which is ficticious. OK.

Almost. "As it apparently stays stationary within the non-inertial frame there is an apparent force acting on it which is ficticious."

Therefore while an inertial force can be considered ficticious in the term you speak of it can be also considered real since it always acts as a real force.

There are several features that ficticious forces have that distinguish them from real forces:
1) they appear only in non-inertial reference frames
2) they are undetectable by accelerometers
3) they are proportional to the mass
4) they violate Newton's 3rd law

The inertial force satisfies all four of these. It is ficticious. Why don't you stop making pointless objections and start thinking about what it implies and how you can use it.

Inertial force is ficticious as long as you stick to the rule that there are equal and opposite accelerations and not forces. I see equal and opposite forces.

In the attached image I have drawn the 3-electron situation that I was describing earlier, and I have drawn it according to the D'Alembert approach with the inertial forces considered as actual forces. Consider electron A. The electrostatic force x acting on A is equal and opposite to the electrostatic force -x acting on B. They consititute an action-reaction pair satisfying Newton's 3rd law. Similarly with force y acting on A and -y acting on C. So, which force acting on B or C is equal and opposite to z? There is none, it does not satisfy Newton's 3rd law, it is a ficticious force.

 

[david smith]

Dale

From your electron diagram I would say that I am able to see more clearly what you mean.
Where there is more than one force acting on a body then each force has an equal and opposite reaction but the resultant acceleration also results in a fictitious force in the opposite direction IE INERTIAL FORCE. So therefore the same must be true even where there is one force acting on a body even though it is not so apparent.

So is this right?: Imagine if there were three planets A,B,C, and A and C each have 400 times the mass of B.

They come to be arranged in a triangular formation; whereupon they are each acted upon by each other’s gravity. A and C have equal and opposite forces, BC and AB also have equal and opposite forces. They all tend to accelerate toward each other. However B has a much greater acceleration in a direction toward the centre of AC and therefore has an inertial force in the opposite direction to the acceleration, which has no equal and opposite reaction force. Have I got it at last?

So what about the case where two bodies (A & B) act on each other with a non-elastic collision.

Ex1) They both have the same mass, A has momentum X and collides with B which has zero momentum. They stick together and the resultant velocity of A+B is the original momentum divided by the resultant mass. In the time it took for mass AB to achieve the final velocity, i.e. ½X, there was force applied = F*t (force impulse). Is it correct to say that during the force impulse there was equal and opposite reactions between A and B and that this action reaction was the inertial force of each. Furthermore that it is not possible to define whether one or the other is action or reaction.

Or is it? If one body has momentum and the other does not or there is a relative momentum differential then there must always be a resultant momentum in the direction of the greatest momentum. IE (mv1)100kg * 20m/s V’s (mv2)50kg * 30m/s = resultant velocity in direction of mv1, so perhaps the larger momentum = the applied force. Which intuitively makes sense. So could I say that F*t = the relative change in momentum in the direction of the largest momentum (with respect to theta)

If this is true then it is also true to say that A did work on B in terms of F*d.
The Kinetic energy of AB is 1/2mv^2 => (m(A+B)/2)* (½ X)^2 = ½ EkA
After A did the work on B, AB had half the original energy. Momentum conserved but energy isn’t in a non-elastic collision. How do we account for that lost energy? Especially when there is no energy lost in an elastic collision. The force time integral stays the same (I think, but I may have the maths wrong). IE with the same mass the force time integral (area under the curve) is no larger as the time reduces. So if a 100kg mass decelerates from 20m/s to 0m/s in 1 sec then this is a force of 2000N. If the same mass decelerates to 0m/s in 0.5s then this equals a force of 4000N. (2000*1) / (4000*2) = 1 = same integral. Lost energy doesn’t seem to be related to the F*t?

Does the Earth have momentum with respect to an object free falling by gravity towards it?
If two bodies have equal and opposite force in terms of gravity then the object, say 200kg mass, attracts the Earth with the same force as the Earth attracts the object. However the Earth has a infinitesimally smaller acceleration than the object but they both would have the same momentum at time of impact.?

One more question – If as mass accelerates the force increases (F=ma) then if a given mass decelerates to zero velocity in zero time, is this equal to infinite force or no force?

Dale wrote

It has nothing to do with paranoia. If someone were to suggest that we use the word "red" to refer to the taste of sugar you would say "we already have a perfectly good word for that, 'sweet', and what word would you use to describe the color of an apple?". Your suggestion is silly for all the same reasons. It is not about conspiracies or right or wrong, it is about clear communication

I think you might be getting the wrong end of the stick Dale. I was pointing out that there are some people, who appear to be highly qualified in physics, that argue that the energy equation Ek = 1/2mv^2 (F*d) is wrong. But then when you read other work by the same people they also think many things are wrong and that there is some kind of conspiracy going on and perpetuated by the establishment to suppress the truth. However when you read their arguments they sound quite logical. But then I'm not educated enough in physics to see the 'wood for the trees' as it where. (Example below) Also that the arguments are tautological in both ways until you can show why you use the original defining equation ie F*d or F*t.

Cheers Dave
Example

Simple and Unquestionable

Mathematical Proof

Kinetic Energy is not ½mv² but mv


Nitty Gritty Perspective

Physicists designed a definition of energy which erased some difficult questions which they could not answer. They cannot understand force amplification through a lever. But they know that force decreases as distance increases on a lever. So defining energy as the combination of force and distance assures that the total is always the same, and energy is conserved through a lever.

What if force is one of the forms of energy? Then physicists cannot explain how force amplification conserves energy. The truth is, force is one of the forms of energy regardless of definitions, because force and motion are interchangeable.

But physicists get around that problem by referring to force as potential energy, when it absorbs energy from motion. Potential energy is a self-contradictory word game. Potential energy supposedly is not energy, because the concepts are too mysterious to explain, while it supposedly is energy in conserving the energy which it absorbs. Like all word games, it is played in two contradictory ways.

When the definition of energy is corrected, the mysteries cannot be swept under a rug. When force times distance is not energy, then energy is not conserved through a lever. This means conservation laws must be modified to include amplification of energy where levers amplify force. And potential energy disappears, as force is one of the forms of energy.

A model for concepts is an elastic collision. As two objects move toward each other, they have energy of motion, and no force exists between them. As they collide, force between them develops and reduces the motion. At some point, all motion stops, and then the objects are pushed apart. When the motion stops, there is no kinetic energy, and all of the energy has been converted to force. Therefore, force is one of the forms of energy. Physicists call it potential energy, but that word game is dishonest.

So the driving force of the erroneous definition of energy is that physicists do not want a complex form of conservation laws which allows energy to be amplified through a lever. Not wanting correct concepts is not science. Trying to simplify away complexities destroys the ability of science to determine what the laws of nature really are.

Small minded persons will say no one sat down and conspired this. It took a few hundred years, but the decisions were arbitrated along the lines described above. For example, the Leibniz analysis which defined the existing concept of kinetic energy began with the force-distance combination for no explainable reason. Leibniz obviously liked the force-distance combination, because it does magical things for the analysis of levers.



The Test

A 4kg object dropped 1m (meter) has the same amount of ½mv² as a 1kg object dropped 4m, because force times distance equals ½mv² for an accelerating mass. But a rocket accelerating the masses to those velocities requires twice as much energy as fuel for the large mass as for the small one.

Therefore, both masses do not have the same energy; the rocket does not transform energy in proportion to ½mv²; ½mv² is not kinetic energy; and a gallon of fuel does not produce a consistent amount of ½mv².

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A 4kg object dropped for 1s (second) has the same amount of mv (momentum) as a 1kg object dropped for 4s, because force times time equals mv for an accelerating mass. A rocket accelerating the masses to those velocities uses the same amount of energy as fuel for both masses.

Therefore, both masses have the same amount of energy; the rocket transforms energy in proportion to mv; mv is kinetic energy; and a gallon of fuel produces a consistent amount of mv.

All logic and evidence of energy points to the same conclusion. The logic created the need to derive the mathematical proof.

About ninety percent of physics is corrupted by the error

Defining Energy

After showing mathematically that the energy equation is in error, there needs to be an explanation of what the error means. This page explains some of that.

What is the Definition of Energy.

Energy takes many forms. The first to be identified was kinetic energy. It is somewhat of a reference for defining energy, because it is tangible and easy to conceptualize.

Energy has been misdefined in that the formula for kinetic energy is incorrect as shown mathematically on other pages. On this page, the logic is described apart from the mathematics.

The formula is KE = ½mv². It indicates that the energy of motion is in proportion to mass times velocity squared. Squaring the velocity is the problem, because no mass can move at velocity squared. As a result, the formula is an abstraction apart from the motion of the mass. explanation

A similar contradiction in logic shows up in the force-distance form of the analysis. Supposedly, kinetic energy is proportional to force times distance for an accelerating mass. However, the force does not move through any distance relative to the mass it acts upon. Distance relates to the starting point, which the force does not act upon.

As indicated elsewhere (including collision analysis) transformations of kinetic energy need to be analyzed relative to the point where the energy acts (impact points), while force times distance creates a reference frame relative to the starting point. Errors result from the incorrect reference frame.

Kinetic energy should be represented as mv, which is called momentum. It is proportional to force times time for an accelerating mass.

This material is reduced to simple logic not to be pedantic but to show how the logic changes as the concepts are corrected. It also allows some original analyses to be derived from the logic.

Original Concepts.
The original basis for defining kinetic energy in terms of mv² was that momentum is supposedly not a conserved quantity. Later, momentum was considered to be conserved. So the historical basis for the definition of energy contradicts modern concepts.

It also contradicts the logic of Newton's laws which indicate that the force-time combination must be conserved through all interactions, because otherwise forces would not be equal and opposite. Force times time produces a defined amount of mv, not ½mv².


Shortly before Newton's time (1642-1727), Rene Descartes (1596-1650) drew the conclusion that there is a fixed amount of momentum in the universe, because it is conserved during interactions (momentum being mass times velocity, mv). From his studies of collisions, he concluded that changes in motion are produced by force, and force is quantitated in proportion to momentum divided by time (F = mv/t).

Newton then extended the concept stating three important laws. They are:



1. Force equals mass times acceleration.

2. For every force, there must be an equal and opposite force.

3. An object at rest stays at rest, or an object in motion maintains its motion unless a force acts upon it. (Which is inertia.)


At around that time, Leibniz (Gottfried Wilhelm von -) published a paper (in 1686) claiming to prove that momentum is not the conserved quantity of motion—mv² is. Eventually, Leibniz's view became the concept of kinetic energy in spite of contradictions with Newton's laws.

The issue was how to relate force to motion in order to get a quantity which is conserved. While force creates motion, one additional factor must be known to quantitate the results. One must know how long the force acts upon the mass. There are two alternatives for completing the quantitation. One alternative is to measure the time that the force acts; and the other is to measure the distance that the mass moves while the force is acting upon it. To multiply the force times time yields the resulting momentum (Ft = mv). To multiply the force times the distance yields the resulting ½mv² (Fs = ½mv²).

Eventually, the conclusion was drawn that both quantities are conserved, even though Leibniz directly stated that his analysis does not conserve momentum. During elastic collisions, both mv and ½mv² are conserved. But during inelastic collisions, both cannot be conserved simultaneously. The applications of energy function by the dynamics of inelastic collisions, because the force moves with the mass it is acting upon.

Some persons claimed that the disagreements were nothing but semantics. But in fact, the issue is not semantics, because energy is used in discrete quantities as fuel. Fuel will only produce a definable amount of mv, not ½mv².

For example, the rate at which energy is added to a system (energy divided by time) is called power. With mv divided by time, power becomes force only (mv/t = F). With ½mv² divided by time, power becomes force times velocity (½mv²/t = Fv).

 

[Dale]

From your electron diagram I would say that I am able to see more clearly what you mean.
Where there is more than one force acting on a body then each force has an equal and opposite reaction but the resultant acceleration also results in a fictitious force in the opposite direction IE INERTIAL FORCE. So therefore the same must be true even where there is one force acting on a body even though it is not so apparent.

So is this right?: Imagine if there were three planets A,B,C, and A and C each have 400 times the mass of B.

They come to be arranged in a triangular formation; whereupon they are each acted upon by each other’s gravity. A and C have equal and opposite forces, BC and AB also have equal and opposite forces. They all tend to accelerate toward each other. However B has a much greater acceleration in a direction toward the centre of AC and therefore has an inertial force in the opposite direction to the acceleration, which has no equal and opposite reaction force. Have I got it at last?

Yes, this is correct.

So what about the case where two bodies (A & B) act on each other with a non-elastic collision.

In this force the normal contact forces are real forces that are equal and opposite. Using the D'Alembert approach there are also (ficticious) inertial forces. Since the contact force is the only real force then the inertial forces are each equal and opposite to their respective contact forces, and therefore equal and opposite to each other, but this is just a coincidence by considering such a simple problem. That is why I started with the 3 electron example, it makes the distinction clear.

Ex1) They both have the same mass, A has momentum X and collides with B which has zero momentum. They stick together and the resultant velocity of A+B is the original momentum divided by the resultant mass. In the time it took for mass AB to achieve the final velocity, i.e. ½X, there was force applied = F*t (force impulse). Is it correct to say that during the force impulse there was equal and opposite reactions between A and B and that this action reaction was the inertial force of each.

No, the action reaction pair was the contact forces, as I mentioned above. In general the inertial forces are not equal and opposite.

Furthermore that it is not possible to define whether one or the other is action or reaction.

Yes, that is true in general for any action-reaction pair.

Or is it? If one body has momentum and the other does not or there is a relative momentum differential then there must always be a resultant momentum in the direction of the greatest momentum. IE (mv1)100kg * 20m/s V’s (mv2)50kg * 30m/s = resultant velocity in direction of mv1, so perhaps the larger momentum = the applied force. Which intuitively makes sense. So could I say that F*t = the relative change in momentum in the direction of the largest momentum (with respect to theta)

I don't know what you are saying here. Especially, what is theta?

If this is true then it is also true to say that A did work on B in terms of F*d.
The Kinetic energy of AB is 1/2mv^2 => (m(A+B)/2)* (½ X)^2 = ½ EkA
After A did the work on B, AB had half the original energy. Momentum conserved but energy isn’t in a non-elastic collision. How do we account for that lost energy? Especially when there is no energy lost in an elastic collision.

That is correct. Momentum is always conserved in any isolated collision, but kinetic energy is not conserved in a non-elastic collision. Instead, in a non-elastic collision some of the kinetic energy is used to do work deforming the colliding bodies, generating heat, etc.

The force time integral stays the same (I think, but I may have the maths wrong).

I'm not 100% sure, I have never worked that out explicitly, but my guess would be that the force time integral would be different. The total (vector) momentum of the system is conserved, but in the elastic collision each individual particle experiences a greater change in momentum than in the non-elastic collision. Since it experienced a greater change in momentum then it must have experienced a greater force time integral.

Does the Earth have momentum with respect to an object free falling by gravity towards it?

Sure, the Earth has momentum in any reference frame where it is moving.

If two bodies have equal and opposite force in terms of gravity then the object, say 200kg mass, attracts the Earth with the same force as the Earth attracts the object. However the Earth has a infinitesimally smaller acceleration than the object but they both would have the same momentum at time of impact.?

Only in their center of momentum frame. In any other frame they will have different momenta. However, their change in momentum will be the same magnitude in all reference frames.

One more question – If as mass accelerates the force increases (F=ma) then if a given mass decelerates to zero velocity in zero time, is this equal to infinite force or no force?

I will leave this one up to you to answer. What is the acceleration in this case? Remember acceleration is a change in velocity divided by a change in time.

I was pointing out that there are some people, who appear to be highly qualified in physics, that argue that the energy equation Ek = 1/2mv^2 (F*d) is wrong. But then when you read other work by the same people they also think many things are wrong and that there is some kind of conspiracy going on and perpetuated by the establishment to suppress the truth.

They are crackpots, as you should have been able to tell immediately from their conspiracy theories.

In any case, the energy equation cannot be wrong, it is a definition so it is correct by definition! I must say that your repeated failure to grasp this simple concept and your gullibility in accepting a conspiracy theorist as authoritative are much more worrisome than your understandable confusion by the D'Alembert approach. Use your own mind, how rational are the conspiracy theorists that you know personally, specifically when talking about the subject of their conspiracy theory?

 

[david smith]

Hey Dale

I suppose that concludes this thread. Just to say Isn't that the beauty of forums, one can ask or explore any question, whether profound, simple, stupid or silly but within the forum's theme and anyone can choose to answer, in any way they see fit. As you did very well, and I thank you for enlightening me.

All the best Dave


All the best Dave

 

[Dale]

I suppose that concludes this thread. Just to say Isn't that the beauty of forums, one can ask or explore any question, whether profound, simple, stupid or silly but within the forum's theme and anyone can choose to answer, in any way they see fit. As you did very well, and I thank you for enlightening me.

Hi Dave,

No problem, and good luck in your gait analysis research.