# What is the jerk of a falling object?

1. Jan 29, 2008

### ejungkurth

Suppose an object is suspended above the Earth, then released. It immediately accelerates to 32.2 f/s^2. There should be a jerk as the acceleration changes. Is there an experimental method to measure that jerk? Experimental as opposed to just doing the math. Thanks.

2. Jan 29, 2008

### Staff: Mentor

3. Jan 29, 2008

### ejungkurth

Jerk is a change in acceleration

4. Jan 29, 2008

### TVP45

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.

5. Jan 29, 2008

### Staff: Mentor

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...

6. Jan 29, 2008

### Mech_Engineer

A jerk would be a change in acceleration with respect to time.

When you are holding the object, the acceleration and velocity is presumed to be zero, so assuming letting go of the object takes 0 seconds your acceleration instantaneously goes to -g, -32.2 ft/s^2. Therefore, the derivative (slope, a.k.a. jerk) of the step acceleration function is infinite, so the jerk is really defined as indeterminite at the point you release the object. However before and after you release the object, the jerk is 0.

I guess it should also be pointed out, that this would assume falling a small distance or neglecting air resistance. The jerk could in theory be non-zero if the object fell for a long time and you were taking into account the wind resistance on the object.

Last edited: Jan 29, 2008
7. Jan 29, 2008

### TVP45

I don't want to beat a dead horse, but...

A finite object can't be released instantaneously, so da/dt will not be infinite. Big, but not infinite. There will be a jerk.

And, because you have to start looking at it before the release, velocity and momentum will not change smoothly but abruptly at the foot of the ramp.

This is much easier to see in circular motion than in linear motion. And, it is a very small effect generally, but it's there.

8. Jan 29, 2008

### ejungkurth

I'm just curious about how the effect, or lack thereof, might be measured empirically.

9. Jan 29, 2008

### Ulysees

If you account for relativity's very subtle effects at low speeds, the acceleration is not constant because the inertial mass increases as the object speeds up.

So there a very small negative jerk, that only exists in the frame of the outside stationary observer, but in the frame of the object you feel no jerk if you're an observer there.

Also, the gravitational field gets stronger as the object gets a little closer to the centre of the earth. This is a positive jerk.

Which jerk is bigger? I'd go for the positive one due to the gravity gradient. Anyone care to guess the relativistic jerk, what it works out to?

Last edited: Jan 29, 2008
10. Jan 29, 2008

### Ulysees

How about getting in a lift, and someone cuts the wire holding it. You'd get a sudden jerk like in a theme park ride, and then experience what people call "zero gravity", and then experience a lot of pain as you hit the bottom.

11. Jan 29, 2008

### Ulysees

I'm not saying this to you, by the way, just wanted to describe the "experience" of jerk.

12. Jan 29, 2008

### TVP45

I am absolutely convinced you can feel it. Here's the experiment I propose. Put a passenger in your car. Have the person wear their most expensive white clothes. Give them a glass of chocolate milk filled within 5 mm of the top. Find a straight steep hill. Here in Pittsburgh, we have one that goes 24 degrees. Drive carefully and smoothly onto the hill. Carefully speed up to 20 mph. Take your foot off the gas. At the instant the car reaches zero velocity, SLAM on the brakes. Look at your passenger. Run.

13. Jan 29, 2008

### Ulysees

Wait a second, I take it back, what I said about the experience of jerk in a lift as the wire is cut is wrong. You don't feel any jerk at all, because you were standing on the floor, not hanging from the ceiling.

14. Jan 29, 2008

### Ulysees

15. Jan 29, 2008

### ejungkurth

mech_engineer and berkeman

You guys are on track. Just so you know, I aced mechanics and vector calculus (and diffeq), but that was twenty years ago, and I'm indulging in a little speculation.

True that jerk in this situation is -g/t. But the limit as t approaches zero is negative infinity. Yes, it is indeterminate, but it is indeterminably large. So where does the yank go? Ditto for the successive derivatives of motion.

Could it be that acceleration (and the successive derivatives of motion) is (are) equally distributed over the path of the falling object, but not necessarily constant?

As I said, I have had classical mechanics drilled into me pretty well. Far be it from me to argue with Newton. So, I wonder if there has been a definitive experiment to show that there is immediate (instantaneous is not the correct term) acceleration due to gravity.

There is a seeming contradiction. But what is a seeming contradiction to me has often been explained.

Can there be a more coincidental name than Heaviside? I'm not sure that a step function explains the dilemma any better than the conjecture that a function that should approach infinity just goes to zero.

16. Jan 29, 2008

### ejungkurth

PS

berkeman, you mentioned smooth acceleration. But what I am thinking is smooth motion. Smooth w.r.t. acceleration, jerk, snap, crackle, pop, ad infinitum. They said I was mad. I was able to refute them and then some. The straightjacket is actually a fashion statement.

17. Jan 29, 2008

### Ben Niehoff

In the ideal limit (where an object can be "instantaneously" released), then the jerk is a delta function. A delta function (not strictly a "function", per se) is defined such that it is zero everywhere except the origin, and its definite integral over any interval containing the origin is 1.

The derivative of a delta function is an even stranger beast.

18. Jan 29, 2008

### Ben Niehoff

One way you could possibly measure jerk is with an electronic device. There exist (rather simple) circuits called "differentiating amplifiers"; using an op-amp, capacitors and resistors, you can make a circuit such that the output is the derivative of the input. Then, merely tie the input voltage to something you can more easily measure, such as acceleration. Voila! A jerkometer.

Differentiating amplifiers are not used nearly as much as their cousins, the integrating amplifiers. The reason is that integrators tend to smooth out a signal, while differentiators tend to introduce noise and make the voltage blow up.

19. Jan 29, 2008

### ejungkurth

Dear Mr. Niehoff,

I am intrigued by your offerings, however, I am unaware of a conjecture that relates electromagnetic forces to the forces of gravity. Can you expound?

20. Jan 30, 2008

### TVP45

No, the jerk is only right at the beginning. You can easily see it if you graph v vs t and notice the little "bump" at the beginning of the ramp. This is a fairly well-known phenom in cam design and civil engineering; as I posted earlier it is pretty easy to see (and measure) in circular motion - tough in linear.

If you start with a point mass, then you can get immediate acceleration and that is, of course, a very different animal. But, finite objects do not have instantaneous movement. If you want, I'll figure out an experiment for you to see that.