# D'alembert force and what the body "really" feels

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1. Apr 4, 2015

### eliraz.n.

hello everybody,

I have a question regarding the fictitious force (d'alembert force) we usually add to an examined body in a noninertial reference system. As I understood from reading and leraning about this topic, this force is artificially added only to compensate for exploring this body in noninertial reference system and that this force doesn't really exist - so the body doesn't actually "feel" it.

If I take a cylindrical body and accelerate it abruptly to about 20g (even in a vaccum environment- no aerodynamic effects), this body might go through buckling.

When I make a free body diagram of this body in an inertial reference system, the only force that this body undergoes is the thrust force - a single force which accelerates it.
For buckling we need to have compression (2 equal and opposing forces on a body), while I mentioned above only a single force.

When I explore this body in a noninertial reference system I add d'alembert force, and now it seems to solve the problem - on one hand we have the thrust (+F) force and on the other one we have the d'alembert force (-ma), so the body undergoes compression and buckling is now possible.

But, as I was taught - d'alembert force isn't real and can't be treated as a force which physically affects the body. In addition, I would like to find a consistent solution in every reference system, and not only in this private case of exploring a body in a noninertial reference system.

By the way, a similar example is the extension of a turbine blade while it rotates.
While it rotates in a constant velocity it only has a centripetal force towards the center of rotation (when exploring this body in a noninertial reference system), and still undergoes an extension (as a result of tension)...

Thanks Everyone!

2. Apr 4, 2015

### OldEngr63

First, an inert body does not "feel" anything at all; it has no nerves.

It is correct to say that the "d'Alembert force is not a force at all," so hang onto that. It is never, ever, necessary. You can always apply simply F = m*a, provided you don't mess up on the acceleration.

I have never seen a problem that was actually any simpler with d'Alembert than by simply using Newton's Second Law. It is popular, I think, because there is a myth about it giving you something for nothing. You are told that you only need to apply statics, and everybody knows that statics is easier than dynamics. Well, ... the hardest part of most dynamics problems is the kinematics, and if you don't get the acceleration expressed correctly (a kinematics problem), Mr. d'Alembert is dead in the water!

Forget d'Alembert and get serious about doing dynamics via Newton's Second Law, or an energy approach (but both require that you get the kinematics correct!).

3. Apr 4, 2015

### Randy Beikmann

eliriaz.n, I have a couple of comments for you. One is that even if you add a D'Alembert's force at the CG, it doesn't represent your problem well. If you accelerate the cylinder by applying a force at one end, you'll find that the compressive force within the cylinder (which is what would buckle it) is highest where the force is applied, gradually decreasing to zero at the other end - not at all like what it would be by applying the D'Alembert's force (the compressive force would be equal to the applied force from the point of application up to the CG, and zero from there to the other end).
Second, if you "suddenly apply" a force to accelerate the cylinder, this becomes a vibration problem. The suddenly applied force produces longitudinal waves in the cylinder. You can't treat it like a rigid body, because rigid bodies don't buckle! ;-)
Third, as OldEngr63 says, you never really benefit from using D'Alembert's forces. I have seen a few places where using one could have simplified the math in a problem, but it's not worth introducing "forces" that aren't really there, ESPECIALLY if you are new to physics. It's like playing with fire.

4. Apr 5, 2015

### eliraz.n.

Thanks both of you for your detailed replies.

I would like to point out that I usually don't use d'alembert force but would rather use newton's 2nd law, but since I couldn't find an explanation to the buckling issue with this equation, I tried every optional way to explain it. In addition, unfortunately, many people I consulted with suggested applying d'alembert force.

So, thanks for clarifying again (I was already told it in the past by my lecturer) that using this fictitious force isn't necessary and actually (in my opinion) not "elegant" enough when you have the ability to describe the body's kinematics by means of newton's 2nd law.

Randy, now I am even more curious about understanding the actual mechanism making the body buckle.
I understood from what you said that using newton's 2 law won't really help when considering a body that isn't rigid.
But actually there isn't a pure "rigid" body like we claim in the formulation of the newton's 2 law ... so when using newton's 2 law is good enough?

I tried searching some data about it, but couldn't find something relevant.
I am really interested in understanding in which case I have to use each approach (newton's 2 law, vibration problem etc.)

Thank you!
Eli

5. Apr 5, 2015

### felmon38

Hello Eli: you must use Newton's 2 law to study vibrations with the help of the Elastic theory.

6. Apr 5, 2015

### Randy Beikmann

Eli, you said

Randy, now I am even more curious about understanding the actual mechanism making the body buckle.
I understood from what you said that using newton's 2 law won't really help when considering a body that isn't rigid.
But actually there isn't a pure "rigid" body like we claim in the formulation of the newton's 2 law ... so when using newton's 2 law is good enough?

I tried searching some data about it, but couldn't find something relevant.
I am really interested in understanding in which case I have to use each approach (newton's 2 law, vibration problem etc.)

I actually didn't say you couldn't use Newton's 2nd law, I just said you couldn't treat the bar as a rigid body. As felmon38 said above, you would need to combine Newton's laws with elasticity theory to study this problem. This means using the 2nd law on each infinitesimal mass along the beam.
There is an actual application for this buckling problem that is very important. Imagine the rocket force acting upward on the base of a missile. The bottom of the missile structure is subjected to the entire propulsion force, so there is a large compressive stress there. But as you look further up in the missile, the compressive force is lower, because the force at that point only has to accelerate the mass in the part of the missile that is ahead of it. At the extreme tip of the missile, there is no compressive force (or stress), assuming we ignore aerodynamic loading.
This buckling problem destroyed a few missiles early in most rocket programs. But notice that this is not the buckling problem you usually see in elementary textbooks, where equal and opposite forces are applied at both ends - there the compressive force is the same all along the beam.
There are references I'm sure on this topic, which might be called "buckling in continuous beams subjected to a single axial end force," or something like that. I would definitely consider it grad-level material.

7. Apr 10, 2015