Unanswered Questions about Tossed Coins

[Beanyboy]

I am sincerely convinced you are not stupid. It's just that you have difficulty distinguishing position $x$, velocity $v = {dx\over dt}$ and acceleration $a = {dv\over dt} = {d^2 x\over dt^2}$

Awesome! Listen to that voice. That is the one that will drive your understanding if you are willing to put in the work too.

 

[Beanyboy]

Awesome! Listen to that voice. That is the one that will drive your understanding if you are willing to put in the work too.

My stupidity never ceases to amaze me. I try to compensate with stubbornness. Thanks for your support.

 

[Stephen Tashi]

"Of all the intellectual hurdles which the human mind has confronted and has overcome in the past fifteen hundred years, the one which seems to me to have been the most amazing in character and the most stupendous in the scope of its consequences is the one relating to the problem of motion... " (Butterfield)

Learning the scientific approach to motion requires ignoring everyday experience! Teachers of physics have less sympathy with students' intuitions about motion that historians of science, like Butterfield. Physicists are used to "saving the phenomena" (a phrase with long history in philosophy and science). After one knows a scientific theory, it becomes natural to interpret experience in a way that it conforms to the theory. Students are expected to "save the phenomena" rather than save the scientific theory when it appears to be contradicted by everyday experience.

It is our everyday experience that to cause motion and keep an object in motion, we must continue to exert a force on the object. (e.g. pushing a wheelbarrow). The scientific (Newtonian) view is that it requires zero force to keep an object moving at a constant velocity. Newton's approach to motion was an extraordinary achievement. People accustomed to saving the phenomena of ordinary experience by interpreting it in terms of Newton's approach may think that Newton's approach is intuitively obvious. The history of science shows otherwise.

As a student, your main job is to understand the theory completely (e.g. F = MA, so when velocity is constant F = 0. F is the net force, not the force exerted only by yourself, etc.) If the theory is an outstanding intellectual achievement in the history of science, don't expect it to be an obvious consequence of everyday experience.

 

[vela]

I do have the 12th edition, but Fig. 3.8 is on p.74 in mine. Is it the one with the stone being launched from the cliff-top?

Yes, that's the figure. I was looking at the electronic version, which might be formatted differently than the print version.

 

[Mark44]

Thanks for the help. I'm beginning to see where my problem lies - conflating velocity with acceleration. I assumed, wrongly, that since v = 0, then a must be 0 too.

I hope you understand now that they are very different concepts.

Another of your misunderstandings is thinking there are two forces on the coin. At the very beginning of the experiment, when the person tosses the coin into the air, there are two forces: an upward push and the force due to gravity acting downward. However, as soon as the coin leaves the person's hand, the only force on the coin is that due to gravity. All we're interested in for this problem is the trajectory of the coin once it has left the person's hand.

 

[Beanyboy]

I've learned so much from so many of you, I want to thank you all sincerely. I need to cogitate on this some more - a lot more. I have good company in "Five Easy Lessons", by Randall Knight, a book that's for Physics Teachers, but one I find very useful. I'm not first, nor won't be the last to fall foul of the "medieval impetus theory of motion". I'm very glad to have Hewitt's "Conceptual Physics" on board, and Reif's "Understanding Basic Mechanics" too. Reif's work on cognition in "Applying Cognitive Science to Education" is invaluable too.

Hewitt warns of disappearing down the pedagogical black hole of Kinematics, but I feel that the motion/force relationship is so fundamental to a proper understanding of, well, every damned thing that has to do with Physics, I'm going to dig in and sort it out as best I can.

I feel sorry for those of you out there that have to teach this, especially if you're constrained by time, which is usually the case within education. I have the luxury of having the time to obsess about this and not having to worry about exams.

Yours in gratitude for now,
Beany

 

[FactChecker]

Your initial question is a good one. Apparantly, the book is talking only about after the coin has been tossed and it already has upward velocity with no more force tossing it up. If you include the tossing of the coin, then there are forces other than gravity -- the force that tosses the coin.

 

[Beanyboy]

Learning the scientific approach to motion requires ignoring everyday experience! Teachers of physics have less sympathy with students' intuitions about motion that historians of science, like Butterfield. Physicists are used to "saving the phenomena" (a phrase with long history in philosophy and science). After one knows a scientific theory, it becomes natural to interpret experience in a way that it conforms to the theory. Students are expected to "save the phenomena" rather than save the scientific theory when it appears to be contradicted by everyday experience.

It is our everyday experience that to cause motion and keep an object in motion, we must continue to exert a force on the object. (e.g. pushing a wheelbarrow). The scientific (Newtonian) view is that it requires zero force to keep an object moving at a constant velocity. Newton's approach to motion was an extraordinary achievement. People accustomed to saving the phenomena of ordinary experience by interpreting it in terms of Newton's approach may think that Newton's approach is intuitively obvious. The history of science shows otherwise.

As a student, your main job is to understand the theory completely (e.g. F = MA, so when velocity is constant F = 0. F is the net force, not the force exerted only by yourself, etc.) If the theory is an outstanding intellectual achievement in the history of science, don't expect it to be an obvious consequence of everyday experience.

There is so much to take in here! You've opened new doors for me, particularly: the aims of Science, Scientific Realism and Anti-Realism. Your last line is particularly illuminating. I'm reminded of the remark, "the tyranny of common-sense". Thanks ever so much.

 

[Beanyboy]

Your initial question is a good one. Apparantly, the book is talking only about after the coin has been tossed and it already has upward velocity with no more force tossing it up. If you include the tossing of the coin, then there are forces other than gravity -- the force that tosses the coin.

Thanks. On the whole, I'm happy with Hewitt's book. His emphasis on the qualitative understanding appeals to me. I did buy his other book "Problem Solving In Conceptual Physics", to beef-up the Math aspects.

 

[Beanyboy]

dear Bb,

Seems you have some elementary background missing, let's try to fill that up:

http://pi.math.cornell.edu/~numb3rs/jrajchgot/508f.html

In this link, the first graph shows (only qualitatively) something similar to your coin flight: Initially it goes upward with an upward velocity. The acceleration is constant and in an opposite direction, so the upward velocity decreases linearly with time. It reaches zero at some point, meaning the extreme position (max height) is reached. Velocity changes sign and from now on is downward, in the same direction as the acceleration. Meaning its magnitude increases: falling faster and faster.

The acceleration (blue line) has been constant and negative (= downward) all the way from time zero

Studying the graphs sorted my head out! As a result of the link I went ahead and ordered Giancoli's Physics book. Many, many thanks.

 

[Beanyboy]

Learning the scientific approach to motion requires ignoring everyday experience! Teachers of physics have less sympathy with students' intuitions about motion that historians of science, like Butterfield. Physicists are used to "saving the phenomena" (a phrase with long history in philosophy and science). After one knows a scientific theory, it becomes natural to interpret experience in a way that it conforms to the theory. Students are expected to "save the phenomena" rather than save the scientific theory when it appears to be contradicted by everyday experience.

Came across some free video lectures from the University of Edinburgh, Prof. Michela Massimi on "Saving The Phenomena". Wasn't aware of this at all until you brought it to my attention. Thanks again.

 

[sophiecentaur]

Learning the scientific approach to motion requires ignoring everyday experience!

I would say that it rather requires you to unthink the sort of indoctrination you have been subjected to by non-Scientists who have not 'thought' but just re-stated the ancient ideas that have been passed from previous generation to generation. In my view, the Intuition that people carry with them is usually Learned from outside and not figured out internally. Every experience we have is interpreted by our brains on its way from eyes and ears to conscious models. We are all really poor witnesses and all our experiences are edited with the rules that we have already learned.
I would say that, at this stage in my Physics career, my reaction to mechanical events is intuitive, coloured by the 'obvious' message of Newton etc..

 

[FactChecker]

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It is our everyday experience that to cause motion and keep an object in motion, we must continue to exert a force on the object. (e.g. pushing a wheelbarrow). The scientific (Newtonian) view is that it requires zero force to keep an object moving at a constant velocity.

Although the everyday experiences of pushing a car on a smooth road, ice skating, riding a bicycle, etc. give good clues that initiating motion requires much more force than maintaining motion; it tells us that initiating motion is very dependent on mass and maintaining is dependent on friction.
Before Newton, everyday experience and common sense told people that the moon and sun floated in the air and were not attracted by gravity.
So our intuition derived from everyday experiences must always be modified to include learned mathematics and physics.

 

[CWatters]

I think it would be constructive for the OP to sketch graphs of height (position), velocity and acceleration all vs time for the coin toss. It's quite enlightening.

 

[sophiecentaur]

I'm left wondering how does that become zero?,

The only time that the net force is zero is when its motion is not changing at all - i.e. once it has landed and it is not accelerating and it's going nowhere. In that case, its weight force (downwards) is exactly balanced by the (upwards) force from the ground.

Have you yet accepted that you may actually have to throw away some of your preconceptions before you will ever come to terms with this? This process is called Learning.

 

[PeterO]

I'm confused. According to my textbook (Hewitt), if we discount air-resistance, the ONLY force acting on a tossed coin at all points of its trajectory, is mg. For me, this begs the question: what then is causing the coin to move upward during the first half of its trajectory?

Many situations like this become simpler if you ask the question the other way round. Don't ask "why does it keep going?", ask "why doesn't it stop?".
The answer is often -"it eventually does". eg the coin, which is traveling up, eventually stops moving up - just not instantly. (note: the upward motion was caused by the flick of the thumb which started it moving in the first place)

 

[PeterO]

Describing the "initial upward velocity" as a force seems to contradict Hewitt's assertion that the ONLY force acting on the object throughout its trajectory, is mg. We now seem to be implying there are in fact TWO forces acting on the object: "upward initial velocity" and "mg".

Thanks for the help, but still confused here.

Imagine you were blind-folded and led out onto a pedestrian bridge over a freeway then had the blindfold removed. You would see cars traveling at quite high speed. They did NOT start moving just because you started looking at them.
Similarly, if you were blind folded and facing someone doing a coin toss, you might remove the blindfold when you hear the "ting" of the coin being flicked into the air. The first thing you would see is the coin rising into the air. It did NOT rise because you started looking at it, it started moving because of what someone did to the coin just before you started looking at it. Under the influence of "mg", that upward motion will gradually reduce (losing speed) and then, still under "mg", the coin would begin moving down, gaining speed until it hits something and possible stops (or bounces).
Even at the instant of time when it was not moving up it is still under the influence of "mg" - why would gravity turn off just because a coin stopped moving up.
Indeed, if you flicked a coin up, then slightly later flicked another coin up beside the first, the first coin would stop but the second coin would be slowing down, showing the gravity was still working (just incase you wanted proof).