What is the jerk of a falling object?

[TVP45]

>Huh?

I was replying to the poster who surmised the object was accelerating without moving.

>Say what? Where did you get this from? A finite change of velocity in "zero time" would of course be an infinite acceleration--but where do you think that happens? Certainly not when you drop a ball!

I was making an analogy to the derivative. Saying that an instant change in acceleration results in no jerk is like saying an instant change in velocity results in no acceleration.

>In elementary problems we usually neglect the time taken to remove the support force--the time to go from zero acceleration to 9.8 m/s^2. But that's just a simplification. In any case, the acceleration increases sharply (not infinitely sharply!), not the speed.

I'm not sure Newton would agree with you here. However, consider an object in free space subjected to a force.

>So?

The problem is with infinite jerk, there would be infinite yank, which is not observed. I agree with mech_engineer that the jerk is undefined, but I think it's a logical leap to equate "undefined" with "zero." However, it works pretty well in practice.

I like Mr. Niehoff's delta function construction, but in order for kinematics to hold together I think it must be a different way of saying the same thing. Then again I'm not sure how he derives the delta function from the equations of motion.


>Come on now. Where is this "immediate acceleration"?

F=ma. Another way of saying it is that an object's inertia resists a change in displacement, but not a change in velocity. Which makes sense, I think. It's the initial point that seems a bit dodgy.

So, here's an experiment you can do to see the non-instantaneous release when there is tension in a real object. Take two weights (maybe 2-3 lbs each) and tie them together with a long (maybe 12 inch) gumband. Hold the top weight about 5 feet above the ground, letting the other hang down from the gumband. Release it and watch what happens just before it hits the ground.

 

[Doc Al]

>Huh?

I was replying to the poster who surmised the object was accelerating without moving.

>Say what? Where did you get this from? A finite change of velocity in "zero time" would of course be an infinite acceleration--but where do you think that happens? Certainly not when you drop a ball!

I was making an analogy to the derivative. Saying that an instant change in acceleration results in no jerk is like saying an instant change in velocity results in no acceleration.

If the acceleration changed a finite amount in zero time, then of course the jerk would be infinite. But what makes you think this corresponds to anything real?

>In elementary problems we usually neglect the time taken to remove the support force--the time to go from zero acceleration to 9.8 m/s^2. But that's just a simplification. In any case, the acceleration increases sharply (not infinitely sharply!), not the speed.

I'm not sure Newton would agree with you here. However, consider an object in free space subjected to a force.

What makes you think that Newton wouldn't agree? OK, I'm considering an object in free space subjected to a force. So?

>So?

The problem is with infinite jerk, there would be infinite yank, which is not observed. I agree with mech_engineer that the jerk is undefined, but I think it's a logical leap to equate "undefined" with "zero." However, it works pretty well in practice.

Where are you observing this infinite jerk?

>Come on now. Where is this "immediate acceleration"?

F=ma.

Huh? Are you thinking: If a force is applied "immediately", then the object will begin accelerating "immediately"? Well...the point is that you can't apply a force "immediately".

Another way of saying it is that an object's inertia resists a change in displacement, but not a change in velocity.

Double huh?

An object's inertia "resists" a change in velocity. If the object's moving (with respect to some frame of reference) its displacement will quite happily change without the need for any applied force.

 

[Hernik]

You asked for an experiment where you could test whether there is a jerk when you release something hanging above the earth. I presume you're only interested in a possible jerk from the forces of gravity and not electromagnetic forces as have been proposed? If so I think the following experiment might give you the answer (But please correct me if I'm wrong - I'm not a physicist.):

Take a spaceship with a vibration free engine and a pebble.. (It's an expensive experiment, I agree).

Place the pebble on board ship. Let the spaceship accelerate with 1 G. When the ship is far away from any strong field of gravity turn off the engine. If the pebble moves you have your jerk. My guess is the pebble stays perfectly still.

 

[jdavel]

the pebble will move.

remember, while the engine is on, the pebble isn't floating weightlessly in the middle of the spaceship. it's jammed up against the back wall. so when the engine cuts off, the wall will act like a compressed spring and push the pebble forward. only if both the pebble and the back wall are infinitely rigid (which is impossible) will the pebble stay where it is.

 

[Hernik]

I see. I didn't get away from the elctromagnetic force!

 

[TVP45]

You asked for an experiment where you could test whether there is a jerk when you release something hanging above the earth. I presume you're only interested in a possible jerk from the forces of gravity and not electromagnetic forces as have been proposed? If so I think the following experiment might give you the answer (But please correct me if I'm wrong - I'm not a physicist.):

Take a spaceship with a vibration free engine and a pebble.. (It's an expensive experiment, I agree).

Place the pebble on board ship. Let the spaceship accelerate with 1 G. When the ship is far away from any strong field of gravity turn off the engine. If the pebble moves you have your jerk. My guess is the pebble stays perfectly still.

A pebble? Don't you like chocolate milk?

 

[adastra]

I am a student of phys, with my senses i think this.

A jerk appears when a body of a system of bodies is subject pseudo force.

Consider this : There is a system of bodies. Those bodies are connected to each other by some kind of force, say friction, or may be by some means, say string. According to the classical mechanics, what i know is, when one or more body(s), but not all are subject to acceleration, there is a change of inertia. Since this involves application of a force, those acted upon bodies feels a force.

Then friction (or other forces that are holding the other bodies) comes into stage. The acted upon bodies WILL be moving with respect to the other bodies or vice-versa. As soon as this starts, a second jerk appears on the bodies NOT acted upon. This involves pseudo force, which originates from inertia (i don't where from inertia originates). Friction will slow them, and make there relative velocity a minimum. If this minimum a zero, that means the bodies, which are NOT acted upon, will start moving TOGETHER WITH the bodies acted upon. A third jerk will appear here.

Similarly, when the strings are finally taut, and given momentum, they will give motion to bodies attached to them. Another jerk appears here.

For the stone.

All particles in it will suffer from 9.8067m/s^2 in equator. This will make a first jerk. If you have a tachometer or air speed indicator, with a armature added to the moving needle, and a stationary magnet, a sudden voltage diff. across the armature will appear, you might downlink it with small radio transmitter. A second jerk will appear to the air molecules near the stone. if you can manage a tiny (really tiny) magnet attached float with the stone, you can say the float sticks to air molecules, which rest on atmosphere, and the acceleration is balanced with the normal reaction from ground. As soon as the stone starts moving, the air viscosity will be more than the magnets attraction, so it will separate. some electronic arrangement might pick up this signal, and downlink with another frequency.

IF you do this experiment, please let me know, i will be happy.

 

[Littlepig]

Well, I think you are confusing this point of the motion: Classical Motion.

When we are talking in classical motion, we simplify (as Doc Al said and very Well) the release moment, in degree of our approximation, it would be an indetermination; that's why in classical motion, we simplify!?

Now, it's only a simplification (telling that t=0 is in t=t+h where h is the time the moving body need to reach the acceleration g.). That is why there is no jerk.

I guess that if you want to study the problem in that jerk precision, you must enter in Quantum Mechanics: You will need to take the account the repulsion/attraction environment, and telling that will be a da/dt!=0 due to magnetic fields..(correct me if I'm wrong Doc)

That is the same problem when the body hits the ground?! Can you make a derivational equation of motion of a ball bouncing up and down? No! You just put an |absolute| somewhere in order to the ball flip up.

Why all this simplifications? Because the nature and objectivity of mechanical Motion: It works mainly in areas of motion of rigid body's with approximations that make you know the right velocity and the right position at the same time, and where Gravitational forces are given by Newton's Law.

Littlepig

 

[TVP45]

Okay, I should have been more precise. When you remove your hand, the sum of forces goes from zero to non-zero. The acceleration does go from zero to g, but the velocity and momentum are integrals of the change in acceleration, so they change smoothly. The integral of a step function is a ramp...

Yes, you're correct and I wasn't, proving positively there was a jerk in my answer

 

[pterid]

Here is a patent application describing a practical "jerkmeter":

http://www.freshpatents.com/Sensor-...for-use-thereof-dt20060202ptan20060021435.php

 

[ejungkurth]

Here's I guess what I'm trying to say:

The way we currently look at things, the acceleration due to gravity is quadratic, because the force increases as the inverse square of the distance and the masses remain constant if we disregard relativistic effects.

But say we don't make any assumptions and we are equipped only to know the height of a falling body and the ability to measure its displacement at successive fixed time intervals. Say we raise the body high enough to get five measurements. We then have enough data points to fit a quartic equation.

But we get a seeming anomaly as the equation for acceleration has an offset from the origin. So we raise the body high enough to get six data points and fit the displacement to a quintic equation.

For the sake of argument, and I'll discuss more below, say that now the equation for acceleration passes through the origin but now the jerk has an offset. So we raise the body high enough to get seven data points, etc, etc. With an infinite number of measurements there would be no anomaly at all.

Now, if F=ma is right, the equation for acceleration should pass through the same offset regardless of its order. There would probably be small differences due the inexactness of the fits. Also, the coefficients of any term with a power higher than four should work out to zero.

If F=ma is wrong, then we would we either see the the offsets of the successive derivatives move monotonically away from the original value or drop to zero. If they drop to zero, that would be really neat. If they become monotonically less, then it would seem the anomalies will still resolve at some point. If they become monotonically greater, well, heck if I know.

 

[ejungkurth]

Whoops, I meant the coefficients of any term with a power greater than two, not four.

 

[Hernik]

A pebble? Don't you like chocolate milk?

I don't think it'll work with a liquid.. I didn't want to spill anything.

 

[jdavel]

Here's I guess what I'm trying to say:

The way we currently look at things, the acceleration due to gravity is quadratic...

Say what? The acceleration due to gravity near the Earth's surface is g. How is that quadratic?

 

[ejungkurth]

Because the gravitational force increases as the inverse square of the distance and the masses remain constant. Therefore the acceleration must increase as the inverse square of the distance.

We are able to treat the acceleration as constant because the difference between the true value and the approximate value is less than the tolerances necessary for most purposes.

 

[Doc Al]

Because the gravitational force increases as the inverse square of the distance and the masses remain constant. Therefore the acceleration must increase as the inverse square of the distance.

Realize that the inverse square law applies to point masses or to special symmetric mass distributions. Taken to great precision, you'd have to worry about the non-symmetric mass distribution near mountains, valleys, etc.

We are able to treat the acceleration as constant because the difference between the true value and the approximate value is less than the tolerances necessary for most purposes.

True. But any deviation from constant acceleration over small distances near the Earth is hardly cause to question Newtonian mechanics!

 

[ejungkurth]

Realize that the inverse square law applies to point masses or to special symmetric mass distributions. Taken to great precision, you'd have to worry about the non-symmetric mass distribution near mountains, valleys, etc.


True. But any deviation from constant acceleration over small distances near the Earth is hardly cause to question Newtonian mechanics!

Here's the thing: I happen to be a great believer in Newtonian mechanics. I think its awesome in its explanatory power. It is certainly the greatest achievement in physics, as not even Newton could calculate the positive effect it has had on the human condition.

However, I've been reading a lot lately about relativity, so I know that if I call Newton's equations into question, I am far from the first to do so. I also know that I would certainly not be the first to call Einstein in question. When I learned that the inventor of the atomic clock was one of these, it got me to thinking.

It occurred to me that the maybe the whole of motion due to gravitation is smooth and proceeds from zero, not just the velocity. So that got me to wondering what successively higher order approximations of displacement would show us.

On the other hand, we are so conditioned to thinking about motion in terms of polynomials that I think we get trapped into accepting that polynomials define motion rather than describe it. What if displacement due to gravity is not polynomial but has a extremely good 4th order polynomial approximation?

We laugh when we see Wile E. Coyote momentarily suspended, then suddenly yanked to his fate. I posit that neither is he suddenly forced to his fate, but proceeds according to uniform motion.

 

[adastra]

I do not quite understand where this thread is pointing to. Jerk appears together with acceleration, and, it's rather the change of inertia... I am a bit confused at why jerk is treated as the d/dt of acceleration.

the acceleration of a vertically fired rocket does changes, and d(acceleration)/dt is quite large. I have practical experience with this. But there's essentially no jerk.If fird in a calm day, and body smooth, low aerodynamic drag,and speed not crosses critical velocity value, the gyro stabilizers do not pick any signal at all.

 

[ejungkurth]

Well, hopefully, your experience has not been having had rockets fired at you. However, jerk is defined as a change in acceleration over time.

Even in the falling body example there is jerk because the acceleration is increasing.

 

[adastra]

o i c . thanks a million for clearing

 

[Doc Al]

Here's the thing: I happen to be a great believer in Newtonian mechanics. I think its awesome in its explanatory power. It is certainly the greatest achievement in physics, as not even Newton could calculate the positive effect it has had on the human condition.

However, I've been reading a lot lately about relativity, so I know that if I call Newton's equations into question, I am far from the first to do so. I also know that I would certainly not be the first to call Einstein in question. When I learned that the inventor of the atomic clock was one of these, it got me to thinking.

The only thing you seem to be calling into question is your understanding. Nothing at all you've stated in this thread (which is just about run out of steam) has questioned classical mechanics or relativity.

It occurred to me that the maybe the whole of motion due to gravitation is smooth and proceeds from zero, not just the velocity. So that got me to wondering what successively higher order approximations of displacement would show us.

And where did you ever get the idea that gravitation isn't smooth?

On the other hand, we are so conditioned to thinking about motion in terms of polynomials that I think we get trapped into accepting that polynomials define motion rather than describe it. What if displacement due to gravity is not polynomial but has a extremely good 4th order polynomial approximation?

We laugh when we see Wile E. Coyote momentarily suspended, then suddenly yanked to his fate. I posit that neither is he suddenly forced to his fate, but proceeds according to uniform motion.

Seems to me that you are at war with a figment of your imagination.

Well, hopefully, your experience has not been having had rockets fired at you. However, jerk is defined as a change in acceleration over time.

Even in the falling body example there is jerk because the acceleration is increasing.

Again: So?

 

[ejungkurth]

I'm not at war with my imagination, I'm using it. To tell you the truth, I didn't think this thread would go beyond the first couple of posts.

I'm not trying to mislead anybody, I'm just trying to exercise my capability to think abstractly. If I lost that capability, then I'd be stuck calling everybody I disagreed with wrong.

 

[Mathnphysics]

I agree that, if I tossed the same object straight up, it would go through zero velocity and would have no jerk. That object would always be accelerating at g.

But, if the object is held in place, it seems there should be a jerk as it begins to accelerate.

I'm trying to think of an experiment to test this. My jerkometer only works horizontally.

The object is always under the acceleration of gravity. That is, it always has a force exerted on it due to the acceleration. It only moves once you let go of the object because otherwise your hand is canceling this force. Therefore, the change in acceleration is zero because the gravitational force causing the acceleration is constant throughout.

 

[TVP45]

So, graph it: a vs t. Start at t= - 2 s. Remember that v is the area under the curve so you got to have a graph that has v=o, then v increasing.

 

[pghislain]

I have another view:

A masse suspended is a two opposed and equal forces system:

f = G - F

Where f = 0 if it is imobile.

So F = m * a and G = m * g; a = -g;

Its a bit basic, I know! A force and an acceleration do'nt have to be associated to a movement. A force to exist must be associated to a masse and an acceleration.
When you suspend a masse in order to avoid it to fall, you must produce a force and its acceleration is not null, even if it do'nt move. If you where in space, this force would project the mass Up but in this example, it just opposes the gravitation acceleration. Acceleration doesnot implies movement.

But in this case ... speed is not null. Yes as well as the accelerations, it is the resulting speed of the system that is null, as well as the resulting force is null.

When you stop suspending the mass, the system of force resumes itself to the gravity multiply by mass, which is a constant force. No jerk at all.

In all the case, for what I understand, jerk is only an analitical tool as well as jounce (4th derivation) regarding acceleration that is in fact, multiply by mass, a physical parameter of the world. Jerk only document acceleration caracteristics, it is not independent of acceleration in some physical effect to be presented, I supose.

I don't know any physical experience or fact or properties that jerk or jounce produce. Acceleration of a mass produce Force. Jerk of a mass produce ... nothing special : information regarding acceleration ! :) Jerk allow to define boundaries for the variation of the acceleration in order to produce Force that shall not indispose human being or destroy equipments. Jounce allow to get the min and max of jerk.

Do you know something of the real world that jerk or jounce manage, produce, ..., some new physical effect ?

 

[TVP45]

I don't know any physical experience or fact or properties that jerk or jounce produce. Acceleration of a mass produce Force. Jerk of a mass produce ... nothing special : information regarding acceleration ! :) Jerk allow to define boundaries for the variation of the acceleration in order to produce Force that shall not indispose human being or destroy equipments. Jounce allow to get the min and max of jerk.

Do you know something of the real world that jerk or jounce manage, produce, ..., some new physical effect ?

Well, yes. Jerk can damage cam followers. Jerk can derail trains. Jerk can (and in fact often does) cause cars to skid on turns. Jerk will cause your hot coffee to spill in your lap. And, so on. Generally, rotational jerk is a more common problem than linear jerk.