Simple Old Physics Demonstration Revisited

Thread Starter

MrAl

Joined Jun 17, 2014
11,268
Hello there,

In the image attached, the blue ball on a string is being swung around in a circular clockwise path as shown.
It is released after a few full rotations shown in that position in the image. (EDITED this line for clarity)
The question is:
Which direction will the ball take when the string is released?
Is it:
A. The orange line path, straight out from the center.
B. The red line path, tangent to the circular path.
C. The curved light blue line path, curved along the original circular path.

Note that the dimensions are not to scale, in that the three possible path lines should be shorter to show the initial direction, although the ball may fly farther than that anyway.
Also note the plane of the circle is horizontal not vertical as the drawing suggests, so this is a view from the top down.

Good luck :)
 

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WBahn

Joined Mar 31, 2012
29,865
Hello there,

In the image attached, the blue ball on a string is being swung around in a circular clockwise path as shown.
It is released after a few full rotations when the string becomes horizontal, shown in that position in the image.
The question is:
Which direction will the ball take when the string is released?
Is it:
A. The orange line path, straight out from the center.
B. The red line path, tangent to the circular path.
C. The curved light blue line path, curved along the original circular path.

Note that the dimensions are not to scale, in that the three possible path lines should be shorter to show the initial direction, although the ball may fly farther than that anyway.
Also note the plane of the circle is horizontal not vertical as the drawing suggests, so this is a view from the top down.

Good luck :)
What is being "revisited" about it? As you say, it is a very old demo. What about it has you scratching your head?

Your description has some contradictions. At the end you say that we are looking down at the plane of the circle, which is horizontal.

But in the beginning you say that the ball is released when the string becomes horizontal.

Well, isn't the string always horizontal (ignoring gravity) or never horizontal (always pointed down at the same angle due to gravity)?

I'm pretty sure I know what you mean, but questions like this should be carefully constructed to be internally consistent and unambiguous.

To find your answer, just draw a free-body diagram of the ball after the string is released.

Since the only force acting on it is gravity, which acts normal to the drawing (specifically, into the page), it won't affect the motion in the plane of the page. You are probably discounting air resistance, but if not, that will act in the opposite direction than the velocity, and so won't affect the direction of motion, just the magnitude (unless you are taking into account the rotation of the ball about it's axis, in which case there are some aerodynamic forces that would produce a slight force perpendicular to the velocity (which would be directed toward the center of the circle, if I'm visualizing it correctly). If the ball is light enough (like a ping pong ball), this force is can have a very pronounced effect, but if it's a moderately heavy ball, it will have very little impact.

So now apply Newton's Laws, and you will have your answer. Provided you can correctly determine the instantaneous velocity (or at least its direction) at the moment of release.
 

WBahn

Joined Mar 31, 2012
29,865
I don't see how this would work, in my mind the string would simply wind around the center point.
The mechanics are given in detail, but imagine twirling the ball over head holding the string in your hand.

If you connect the string to a shaft, then as long as the shaft has a large enough diameter (it doesn't take much, depending on the mass of the ball and the length of the string) then it will work fine. If you put a heavy nut on the end of a string that's a foot or so long, and get it spinning and then try to hold you hand as motionless as possible, you'll see that the point of contact with your fingers is moving in a pretty small circle, perhaps a half inch to an inch in diameter. Getting it started might need a little help (the same way that swinging it in a circle overhead requires a different motion of your hand than once it's moving and stabilized.
 

boostbuck

Joined Oct 5, 2017
492
The answer is C, it seems. Even allowing for ideally non-elastic string, relativistic effects mean it is still C, for a limited amount of time.

 

WBahn

Joined Mar 31, 2012
29,865
The problem statement forces us to make reasonable assumptions, which to my mind, for a problem presented like this (i.e., presented at a level that you would expect to see about a month into a Physics I class), would include an ideal, non-elastic and massless string. I don't believe it is reasonable (i.e., "fair") to ask a question that strongly implies a level of detail that is drastically different than the level of detail required to be used in the analysis. That forces the person given the problem to use a crystal ball to divine the writer's intent. It's one thing if there is some context to fall back on, such as what topics have been recently discussed in class, but here we have ZERO context to relay on.

If effects like that need to be taken into account in order to get the intended answer, then the problem statement needs to make it clear that those things need to be considered. Imagine if now someone asks the same question but the answer they deem is correct requires taking the gyroscopic precession of the ball and the rotation of the Earth into account? Or an answer that required taking time dilation and length contraction into account? Why would anyone take those into account unless the problem statement gave some clue that it was expected.

Furthermore, notice that it doesn't say how the string is released -- specifically, it doesn't place any requirement that the release occurs at the center end of the circle and not at the ball itself. Releasing it at the center (and thereby leaving the string attached to the ball) brings several complicating factors that are virtually always ignored UNLESS the problem statement makes it clear that they shouldn't be. These not only include the effect of finite Young's modulus, but also the effect of the inertia of the string on the motion of the ball since now the ball has to exert a largely outward force on the string to accelerate the string's center of mass away from where its center of mass would to go if there were no forces acting on it, which by Newton's Third Law, is going to exert a largely inward force in the opposite direction, which is going to be mostly toward the center of the circle.

In practice, using anything resembling a reasonable string, these effects are very difficult to observe (notice that, in the video, they were so hard to observe, even with a high-speed camera, that they weren't able to observe them), and so ignoring them is a very reasonable thing to do, especially for the problem as given. But even so, since the problem didn't preclude releasing the string at the ball end, one common way to remove the impact of the string's dynamics from the problem that has been used for well over a century is to simply use a ball that has a release mechanism in it. These are actually very easy to make since the tension in the string is very low. It used to be done with a tiny clockwork mechanism (often taken from something like a music box) that would release the string after about ten seconds. Today, of course, it would be rather trivial to make an electronic mechanism that would release it based on a wireless signal that is triggered by the ball getting to a reference point (perhaps by the string breaking a light beam that is just inside the ball so that the release is almost exactly when the center of the ball is at the reference point).

Having said all that, I found that, overall, the video was well done and informative (though it's stuff I've seen in other contexts). To a large degree, a video like this can get away with getting at an answer that requires taking things into account that are not consistent with the initial problem statement precisely because the video almost immediately sets out to provide the necessary context. The other thing that I thought interrupted the progression of the development was using the disk on the turntable and trying to claim that it is equivalent to the string. It's not. As soon as the disk starts sliding, it still has substantial frictional forces acting on it that are not equivalent to the tension wave in the string. Then switching to the reference frame of the rotating platform seemed to just muddy the waters even more since now we are viewing things in a non-inertial reference frame, especially without even mentioning what you would expect to observe in that frame in the event that case B were true or how what is observed supports the claim for case C being true. So what insight is the viewer supposed to glean from that side trip that is relevant to the problem being explored?

But, again, I thought it was a nice video that can definitely add a nice bit of depth to even a Physics I course at the right point, though I would remove the whole disk-on-platform part and move it to another video that is focused on non-inertial reference frames.
 

Thread Starter

MrAl

Joined Jun 17, 2014
11,268
The problem statement forces us to make reasonable assumptions, which to my mind, for a problem presented like this (i.e., presented at a level that you would expect to see about a month into a Physics I class), would include an ideal, non-elastic and massless string. I don't believe it is reasonable (i.e., "fair") to ask a question that strongly implies a level of detail that is drastically different than the level of detail required to be used in the analysis. That forces the person given the problem to use a crystal ball to divine the writer's intent. It's one thing if there is some context to fall back on, such as what topics have been recently discussed in class, but here we have ZERO context to relay on.

If effects like that need to be taken into account in order to get the intended answer, then the problem statement needs to make it clear that those things need to be considered. Imagine if now someone asks the same question but the answer they deem is correct requires taking the gyroscopic precession of the ball and the rotation of the Earth into account? Or an answer that required taking time dilation and length contraction into account? Why would anyone take those into account unless the problem statement gave some clue that it was expected.

Furthermore, notice that it doesn't say how the string is released -- specifically, it doesn't place any requirement that the release occurs at the center end of the circle and not at the ball itself. Releasing it at the center (and thereby leaving the string attached to the ball) brings several complicating factors that are virtually always ignored UNLESS the problem statement makes it clear that they shouldn't be. These not only include the effect of finite Young's modulus, but also the effect of the inertia of the string on the motion of the ball since now the ball has to exert a largely outward force on the string to accelerate the string's center of mass away from where its center of mass would to go if there were no forces acting on it, which by Newton's Third Law, is going to exert a largely inward force in the opposite direction, which is going to be mostly toward the center of the circle.

In practice, using anything resembling a reasonable string, these effects are very difficult to observe (notice that, in the video, they were so hard to observe, even with a high-speed camera, that they weren't able to observe them), and so ignoring them is a very reasonable thing to do, especially for the problem as given. But even so, since the problem didn't preclude releasing the string at the ball end, one common way to remove the impact of the string's dynamics from the problem that has been used for well over a century is to simply use a ball that has a release mechanism in it. These are actually very easy to make since the tension in the string is very low. It used to be done with a tiny clockwork mechanism (often taken from something like a music box) that would release the string after about ten seconds. Today, of course, it would be rather trivial to make an electronic mechanism that would release it based on a wireless signal that is triggered by the ball getting to a reference point (perhaps by the string breaking a light beam that is just inside the ball so that the release is almost exactly when the center of the ball is at the reference point).

Having said all that, I found that, overall, the video was well done and informative (though it's stuff I've seen in other contexts). To a large degree, a video like this can get away with getting at an answer that requires taking things into account that are not consistent with the initial problem statement precisely because the video almost immediately sets out to provide the necessary context. The other thing that I thought interrupted the progression of the development was using the disk on the turntable and trying to claim that it is equivalent to the string. It's not. As soon as the disk starts sliding, it still has substantial frictional forces acting on it that are not equivalent to the tension wave in the string. Then switching to the reference frame of the rotating platform seemed to just muddy the waters even more since now we are viewing things in a non-inertial reference frame, especially without even mentioning what you would expect to observe in that frame in the event that case B were true or how what is observed supports the claim for case C being true. So what insight is the viewer supposed to glean from that side trip that is relevant to the problem being explored?

But, again, I thought it was a nice video that can definitely add a nice bit of depth to even a Physics I course at the right point, though I would remove the whole disk-on-platform part and move it to another video that is focused on non-inertial reference frames.
Hi,

Yes, it's kind of hard to formulate a question like this within a reasonable amount of time without missing some details. What I did remember to do was mention that the scale of the lines vs the circle were not to scale, so the lines could be much shorter than the diagram would indicate. What that does is allows us to evaluate answer C as a very short section of the curve, although it still lies on the curve as the video shows. Even a small amount of stretch in the cord (and every real life cord would stretch just a little, including a stainless steel wire) causes an effect that is not too apparent.

Also, if we go to much into depth about what is to be considered, we might have to give the answer away in the process. The whole idea is that it is non-intuitive about what actually happens. That's really the main point. Most people would say A or B I think, but then again most people consider the cord to be rigid and not stretchable. The slight stretch and tension are the key.

Also as the video shows nicely, this effect can be very small with a strong cord which has very little stretch. However, we could always increase the angular velocity and maybe the mass of the ball to get more stretch with more tension. Thus, the most general solution is C.
 

wayneh

Joined Sep 9, 2010
17,493
The answer is C, it seems.
Only in the realm of religion and not science. I mean you cannot observe that alleged relativistic effect in any real experiment, only theoretical ones. So if you fully believe the theories, you predict something you can't measure. I'm not saying it's wrong.
 

WBahn

Joined Mar 31, 2012
29,865
Also, if we go to much into depth about what is to be considered, we might have to give the answer away in the process. The whole idea is that it is non-intuitive about what actually happens. That's really the main point. Most people would say A or B I think, but then again most people consider the cord to be rigid and not stretchable. The slight stretch and tension are the key.
Yes, most people would consider the cord to be rigid and not stretchable, because that is a perfectly reasonable thing to do unless given some indication in the problem that it is unreasonable to do so. Just like most people, if given a simple circuit to analyze, would not consider the non-intuitive affect of current flowing in the Earth's magnetic field. At what point does it become disingenuous to expect people to read your mind about exactly what should and should not be taking into account?

How hard would it have been for them to phrase the problem as simply using a spring instead of a string?

Now you're giving the reader a fair indication of what complicating factors should be considered, and the resulting explanation is pulling a bunch of obscure factors out of thin air, but is rather laser-focused on the impact of that being a spring instead of an ideal string.
 

Thread Starter

MrAl

Joined Jun 17, 2014
11,268
Yes, most people would consider the cord to be rigid and not stretchable, because that is a perfectly reasonable thing to do unless given some indication in the problem that it is unreasonable to do so. Just like most people, if given a simple circuit to analyze, would not consider the non-intuitive affect of current flowing in the Earth's magnetic field. At what point does it become disingenuous to expect people to read your mind about exactly what should and should not be taking into account?

How hard would it have been for them to phrase the problem as simply using a spring instead of a string?

Now you're giving the reader a fair indication of what complicating factors should be considered, and the resulting explanation is pulling a bunch of obscure factors out of thin air, but is rather laser-focused on the impact of that being a spring instead of an ideal string.
Hi again,

I think they mentioned that in the video, about starting with a Slinky which is just a big giant spring. The idea was to generalize from there to things that were not quite as springy, but still stay in the realm of being real life objects like strings and ropes. Strings can have quite a bit of stretch to them and some a lot of stretch.

The main idea I think was that most people will assume that the trajectory is straight, one way or the other, and when they find out that's not really the case, it's like an epiphany, and almost too hard to believe at first. A lot of videos take this approach, like the bowling ball on the end of a long rope tied to the ceiling, and when released right in front of the demonstrators face, it swings back but does not bang them in the face. At first it looks like it is going to come back and break their nose or something, but it doesn't, and then the discussion turns to details about why not. If we give away too many details it may not be as exciting to find the real answer, just a plain old physics problem.
So I guess we could say they are fishing for an epiphany.
 
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