Surprising Physics: Acceleration Faster Than Freefall

[Galileo]

Take a flat board of uniform density. Mass M and Length L.
Now hold the board horizontally at the edge of a table. So you hold one end of the board at distance L from the edge of the table, while the other end is resting on the table.

Now release the board. Gravity will exert a torque about the axis where the board touches the table. The gravitational force will act on the center of gravity of the board, so:
$$\tau = \frac{L}{2} Mg$$
The moment of inertia of this board about an axis at the edge is
$$I=\frac{1}{3}ML^2$$
So the board will rotate with an angular acceleration of:
$$\alpha = \frac{\tau}{I}=\frac{3}{2}\frac{g}{L}$$
That means for the part of the board at the loose end at the moment of release an acceleration of:
$$a=\frac{3}{2}\frac{g}{L}L=\frac{3}{2}g$$

Faster than freefall!

Some of you may not be surprised by it, but I was.
I realize that the normal force at the end is responsible, but still. It's kinda counterintuitive. I didn't expect it.

Does anyone else got funny and surpising physics about which you say "I didn't expect that?".

EDIT: Fixed a typo. Thanks Brad.

 

[ZapperZ]

I do, and this is an old one.

Take a helium-filled balloon with you next time you get on a train. The balloon should be the typical ones you get at a fair, with a string tied to it at one end, and you hold the other end.

Now while holding on to one end of the string, let the balloon just be suspended without hitting the ceiling or sides of the train. As soon as the train starts to accelerate, look at it. If there are no considerable air movement in the train (i.e. windows are not open, etc), while the train is accelerating, you will see the balloon tilts FORWARD, along the direction the train is travelling.

This is counter-intuitive, because we all feel that we're being pushed BACKWARDS when the vehicle we're in is accelerating forward. Yet, the balloon appears to have a forward push!

You'll see something strange too if the train makes a sharp turn (works better in a car or bus). If it is turning to the right, while all of you in the vehicle feel a "centrifugal force" pulling you to the left, the balloon will shift to the right!

There is, of course, a simple explanation for this, but why spoil the fun? :)

This is one example where one's "intuition" can be easily wrong. Only after one realizes the explanation for it does one find this observation "intuitively clear". This is why I say that intuition is nothing more than an accumulated knowledge of what we understand.

Zz.

 

[Brad Barker]

in the equation for angular acceleration, it should be "tau" over "I," not "m." ...at first it that got me to say, "what the hell?"

 

[Brad Barker]

I do, and this is an old one.

Take a helium-filled balloon with you next time you get on a train. The balloon should be the typical ones you get at a fair, with a string tied to it at one end, and you hold the other end.

Now while holding on to one end of the string, let the balloon just be suspended without hitting the ceiling or sides of the train. As soon as the train starts to accelerate, look at it. If there are no considerable air movement in the train (i.e. windows are not open, etc), while the train is accelerating, you will see the balloon tilts FORWARD, along the direction the train is travelling.

This is counter-intuitive, because we all feel that we're being pushed BACKWARDS when the vehicle we're in is accelerating forward. Yet, the balloon appears to have a forward push!

You'll see something strange too if the train makes a sharp turn (works better in a car or bus). If it is turning to the right, while all of you in the vehicle feel a "centrifugal force" pulling you to the left, the balloon will shift to the right!

There is, of course, a simple explanation for this, but why spoil the fun? :)

This is one example where one's "intuition" can be easily wrong. Only after one realizes the explanation for it does one find this observation "intuitively clear". This is why I say that intuition is nothing more than an accumulated knowledge of what we understand.

Zz.

does it have to do with the extremely low density --> mass --> inertia so that it will not resist being accelerated nearly as much as bodies will?

 

[Nenad]

I do, and this is an old one.

Take a helium-filled balloon with you next time you get on a train. The balloon should be the typical ones you get at a fair, with a string tied to it at one end, and you hold the other end.

Now while holding on to one end of the string, let the balloon just be suspended without hitting the ceiling or sides of the train. As soon as the train starts to accelerate, look at it. If there are no considerable air movement in the train (i.e. windows are not open, etc), while the train is accelerating, you will see the balloon tilts FORWARD, along the direction the train is travelling.

This is counter-intuitive, because we all feel that we're being pushed BACKWARDS when the vehicle we're in is accelerating forward. Yet, the balloon appears to have a forward push!

You'll see something strange too if the train makes a sharp turn (works better in a car or bus). If it is turning to the right, while all of you in the vehicle feel a "centrifugal force" pulling you to the left, the balloon will shift to the right!

There is, of course, a simple explanation for this, but why spoil the fun? :)

This is one example where one's "intuition" can be easily wrong. Only after one realizes the explanation for it does one find this observation "intuitively clear". This is why I say that intuition is nothing more than an accumulated knowledge of what we understand.

Zz.

Its a nice experiment, but its very easy to understand why. I got it in grade 10 while my teacher was doing the same principle with a piece of corq in a water container. The reason this happens is because the air in the train is more dense and heavier than the helium in the baloon. Therefore, when the train accelerates, the air heavier air is pushed to the back of the train, and the lighter helium is pushed foreward. Its kind of like boyancy.

 

[ZapperZ]

Its a nice experiment, but its very easy to understand why. I got it in grade 10 while my teacher was doing the same principle with a piece of corq in a water container. The reason this happens is because the air in the train is more dense and heavier than the helium in the baloon. Therefore, when the train accelerates, the air heavier air is pushed to the back of the train, and the lighter helium is pushed foreward. Its kind of like boyancy.

Well, I DID say that there is a simple explanation for this! :)

I've described this scenario without indicating what happened to the balloon to a class of 1st year intro physics students, and the overwhelming number of them (almost 75%) answered what I expected - the balloon gets pushed back like everything else in the train. Then I gave them a bunch of mylar balloons and asked them to investigate this for themselves over the weekend. [I was later told by a colleague that there were reports of a bunch of students boarding onto Chicago's CTA trains heading into the city with mylar balloons] Of course, most of them came back surprised at what they saw. We had a very lively discussion on what was involved, and most importantly, why they were fooled.

The students thought that this was the most enjoyable and memorable part of the whole course, as I later found out in their course evaluations.

It is why I've always had a fondness for this exercise.

Zz.

 

[krab]

There's actually a simpler demonstration of the same effect. Take a bubble level; one of those used by carpenters -- I think also called a "spirit level". Put on a level table and accelerate it forward. Notice that instead of the bubble hanging back from inertia, it hangs forward.

 

[ZapperZ]

There's actually a simpler demonstration of the same effect. Take a bubble level; one of those used by carpenters -- I think also called a "spirit level". Put on a level table and accelerate it forward. Notice that instead of the bubble hanging back from inertia, it hangs forward.

Yup. This is certainly an identical effect. However, imagining a bunch of college kids boarding a train with mylar balloons, and then looking at them curiously as soon as the train moves, now that is worth the money I spent on those balloons! :)

Zz.

 

[krab]

I agree. For more fun, ask them in part 2 of the experiment to design and calibrate an accelerometer from the mylar balloon system. :-)

 

[krab]

Back to Galileo's original question. There are many effects that are surprising and counter-intuitive. You can get lots more of them in Flying Circus of Physics by Jearl Walker. I checked, and it's available from Amazon.

 

[ZapperZ]

Back to Galileo's original question. There are many effects that are surprising and counter-intuitive. You can get lots more of them in Flying Circus of Physics by Jearl Walker. I checked, and it's available from Amazon.

I agree, especially the section that says that hot water freezes faster than cold water! :)

Zz.

 

[Cyrus]

I thought that was up to much debate. I thought that they both freeze at the same temperature, however the heat content in making teh hot water is greater, not the time it takes

 

[geometer]

I agree, especially the section that says that hot water freezes faster than cold water! :)

Zz.

This old chestnut rears its head every once in a while. Common sense should tell you that hot water can't freeze faster than cold water. Assuming the same heat transfer rate, the hotter water has more heat to transfer so should take longer to reach freezing than the cold water. Some claim that this is circumvented by the the fact that convection currents are established in the hot water which improves mixing and therefore heat transfer.

However:

To test this a few years ago, I prepared a bath of water and ice which was at a constant 33 degrees Fahrenheit (about .6 degrees C) or so, and then put equal amounts of hot water (200 degrees Fahrenheit, 93 degrees C), and cold water (60 degrees Fahrenheit, 15.6 degrees C) in identical containers, immersed them in the cold bath, one at a time, and timed how long it took for each container to reach equilibrium with the cold bath. In all trials, the hot water took significantly longer than the cold water. I also added some dye to the samples to check for the establishment of convection currents and didn't see any evidence of these in either the cold or hot water.

 

[Nenad]

Yup. This is certainly an identical effect. However, imagining a bunch of college kids boarding a train with mylar balloons, and then looking at them curiously as soon as the train moves, now that is worth the money I spent on those balloons! :)

Zz.

Ive heard of this, but I never understood why it would happen.

 

[ZapperZ]

This old chestnut rears its head every once in a while. Common sense should tell you that hot water can't freeze faster than cold water. Assuming the same heat transfer rate, the hotter water has more heat to transfer so should take longer to reach freezing than the cold water. Some claim that this is circumvented by the the fact that convection currents are established in the hot water which improves mixing and therefore heat transfer.

However:

To test this a few years ago, I prepared a bath of water and ice which was at a constant 33 degrees Fahrenheit (about .6 degrees C) or so, and then put equal amounts of hot water (200 degrees Fahrenheit, 93 degrees C), and cold water (60 degrees Fahrenheit, 15.6 degrees C) in identical containers, immersed them in the cold bath, one at a time, and timed how long it took for each container to reach equilibrium with the cold bath. In all trials, the hot water took significantly longer than the cold water. I also added some dye to the samples to check for the establishment of convection currents and didn't see any evidence of these in either the cold or hot water.

In the EXACT scenario in which this claim was made, there are two important aspects that you should pay attention to: (i) both the hot and cold water are in an insulated container (in the "old" days in which this tale was told, they were in wooden buckets); and (ii) they are also in open containers (i.e. no lids). So "convection" isn't the only or primary explanation for this.

The book that krab mentioned includes several published references on this effect, so you can investigate this to your heart's content.

Zz.

 

[geometer]

In the EXACT scenario in which this claim was made, there are two important aspects that you should pay attention to: (i) both the hot and cold water are in an insulated container (in the "old" days in which this tale was told, they were in wooden buckets); and (ii) they are also in open containers (i.e. no lids). So "convection" isn't the only or primary explanation for this.

The book that krab mentioned includes several published references on this effect, so you can investigate this to your heart's content.

Zz.

Interesting. My samples weren't in "insulated" containers except for the insulation provided by a pyrex beaker, but they were in open containers. Oh, and I made sure the samples were the same mass too since the mass of a material appears in the heat transfer equations.

 

[Cyrus]

Take a flat board of uniform density. Mass M and Length L.
Now hold the board horizontally at the edge of a table. So you hold one end of the board at distance L from the edge of the table, while the other end is resting on the table.

Now release the board. Gravity will exert a torque about the axis where the board touches the table. The gravitational force will act on the center of gravity of the board, so:
$$\tau = \frac{L}{2} Mg$$
The moment of inertia of this board about an axis at the edge is
$$I=\frac{1}{3}ML^2$$
So the board will rotate with an angular acceleration of:
$$\alpha = \frac{\tau}{I}=\frac{3}{2}\frac{g}{L}$$
That means for the part of the board at the loose end at the moment of release an acceleration of:
$$a=\frac{3}{2}\frac{g}{L}L=\frac{3}{2}g$$

Faster than freefall!

Some of you may not be surprised by it, but I was.
I realize that the normal force at the end is responsible, but still. It's kinda counterintuitive. I didn't expect it.

Does anyone else got funny and surpising physics about which you say "I didn't expect that?".

EDIT: Fixed a typo. Thanks Brad.

I decided to reply in quote since his post will be on the last page. One question for you guys. I followed his proof and it seems to make sense to me. But in the end, dident he solve for the tangential component of acceleration? He finds this to be greater than g, but isint that a part of its rotational acceleration? The acceleration he is trying to think of as faster than g, would that be the acceleration with respect to the center of mass of the board, which does not move until the board losses complete contact with the table? And after that does occur, wouldent it then simply be acceleration due to gravity?

 

[krab]

I don't understand what you mean by "tangential". He correctly calculated the acceleration of a point at the end of the board. It is not acceleration with respect to the centre of mass. The centre of mass is not stationary but is itself accelerating and so is not an inertial frame. It also can be seen as a rotational acceleration of the board, but so what?

If the problem confuses you, think of the following limitting case: A point mass attached to the midpoint of a massless rod. One edge of the rod is on the table. Since the rod is massless, it does not play a role in the dynamics: the point mass initially falls with acceleration g. But this means the other end of the rod must be accelerating at a rate of 2g.

 

[Cyrus]

Hmm, I think I might have misread part of his post the first time. Does he mean that the board is held over a table so that only the very edge of the board is in contact with the table? I think I missed that part when I read it. I thought that he ment part of the board was hanging over the table and part of the board was not, now I see that he means ALL of the board is hanging off the edge except for the exact edge of the board. Thanks for your help krab

"I realize that the normal force at the end is responsible, but still. It's kinda counterintuitive. I didn't expect it."

Did the normal force play any role in this situation? I thought it is the torque caused by gravity that is responsible, along with the moment of inertia.

 

[Larry717]

Egg into a Coke bottle

I am surprised every time I see this. Can ZapperZ (or anyone else) explain the physics involved here?

Larry

 

[Gokul43201]

Here's another one, but what makes it not as nice as the helium balloons or the spirit level, it that the explanation is not so simple.

Take any cuboidal object, with the three sides of fairly differing lengths (no two sides within 20% of each other). There are several common objects that satisfy this : ruler, calculator, book (preferably hard-cover), multimeter, flat wooden board (1 X 4 at most...nothing too big), audio/video tape, etc.

Okay, so this object has three lines joining opposite face centers, which I call its 3 axes. Now try and spin the object in the air about each of these 3 axes, one at a time. Can you get the object to spin stably about the longest axis ? And the shortest one ? But how about the third axis ?

 

[ZapperZ]

I am surprised every time I see this. Can ZapperZ (or anyone else) explain the physics involved here?

Larry

I'm not sure that I know or have heard of this one. So someone else will have to respond to this.

Zz.

 

[Larry717]

Egg into a Coke bottle-2

ZapperZ,

I don't know if this is right, but does it sound plausible?

You take something combustible and light it (maybe a match will do), then drop it into the coke bottle. A peeled egg is placed on the mouth of the bottle
and falls into the bottle.

Does the match burn away most of the air in the bottle, leaving a partial vacuum, causing the egg to squeeze into it?

Are there any books you could recommend that might have this mentioned?

Thanks!

Larry

 

[Integral]

In reference to post #1.

If you can find a video of a falling chimney you will see that it breaks up before it hits the ground. Your calculations are the exact reason that it breaks up in the air.

An interesting Corollary:
Such a falling column will usually break into 3 big sections and a certain amount of debris, sort of like 3.14 pieces. It can be said that a falling column will break into Pi pieces. You can see this by dropping a new, full length piece of chalk on the floor.

 

[Integral]

ZapperZ,

I don't know if this is right, but does it sound plausible?

You take something combustible and light it (maybe a match will do), then drop it into the coke bottle. A peeled egg is placed on the mouth of the bottle
and falls into the bottle.

Does the match burn away most of the air in the bottle, leaving a partial vacuum, causing the egg to squeeze into it?

Are there any books you could recommend that might have this mentioned?

Thanks!

Larry

You are essentially correct.
I do not think it would work very well with a normal coke bottle, the neck is simply to small, you need a bottle with a neck slightly smaller then the egg. I have done this by placing the bottle (a wine carafe) with the egg in the neck in a freezer. Now the lower pressure inside is due to the Ideal gas law, we have fixed volume of gas, by reducing the temperature we must also reduce the pressure,

 

[Loren Booda]

Soak egg in vinegar for a couple of days, making shell pliable?

 

[Integral]

Soak egg in vinegar for a couple of days, making shell pliable?

I did it with a peeled, hard boiled egg.

 

[Loren Booda]

Integral, how does one generate the quote label "Originally posted by..."? After all these years I should know.

 

[Integral]

Integral, how does one generate the quote label "Originally posted by..."? After all these years I should know.

Use the quote button, lower right corner of each message.

 

[Integral]

Many years ago I was working at the local University Physics dept. as a Lab tech. Part of my job was to investigate and develope new experiments, I was playing with a Kundts tube variation, where instead of the traditional metal rod I had a pretty powerful speaker feeding directly into the glass tube. This thing could really make the dust dance. One time when a very nice resonant frequency, in addition to the cork dust being piled into the usual pattern at one motion node there was a very thin curtin of dust creating a perfect cross section of the tube. I could observe the individual dust particles gently milling around in a very near mono layer of dust. Only once in the time I spent with that apparatus did I observe such a phenomena.

 

[DaveC426913]

Therefore, when the train accelerates, the air heavier air is pushed to the back of the train, and the lighter helium is pushed foreward. Its kind of like boyancy.

Ive heard of this, but I never understood why it would happen.

Because we can see the balloon, we assume it has a certain weight. Because we cannot see air, we intuitively (yet wrongly) presume it has no mass.

When the train accelerates, we assume the balloon, even filled with helium will have some inertia, and appear to go backward. It never occurs to us that the air in the room has weight and thus density and, in fact, more density than the balloon! Everything gets pushed back, balloon and air, but the air gets pushed back more.

 

[DaveC426913]

... when the train accelerates, the air heavier air is pushed to the back of the train, and the lighter helium is pushed foreward. Its kind of like boyancy.

In fact (as Einstein pointed out with his Principle of Equivalency where acceleration by force and gravity are equivalent) it is not merely *like* bouyancy - it is identical.

 

[Reality_Patrol]

Here's one I don't have an answer for:

Make a parallel plate capacitor with a vacuum dielectric at room temperature. Seal and evacuate the gap to create a good vacuum if desired. Run 2 small leads to each plate to be used to measure the capacitance via a small-signal AC-impedance technique. Take 2 additional capacitance measurements at temperatures above and below room temperature. All (3) measurements should show a different capacitance. So what?

Well the standard textbook formula for capacitors show that the only thing that can vary in this experiment, to explain the change in capacitance, is the permittivity. Yet, it's a vacuum dielectric.

So, does the permittivity of free-space vary with temperature? If so, does the velocity of light depend on the temperature of free-space?

 

[Creator]

I do, and this is an old one.

Take a helium-filled balloon with you next time you get on a train. The balloon should be the typical ones you get at a fair, with a string tied to it at one end, and you hold the other end...
.
Zz.

I always thought that was one of the most interesting. Except I had my students do it in a car and tie the string of the balloon to the right seat next to them. That way they could make a more 'controlled?' experiment as they alternately floored the gas and slammed on the brakes. (Unexpected experimental results include loud horns , scretching of tires, and other cars swerving off the road. )

Also I asked them to test a left turn; (We in America have driver seat on the 'correct' side of the auto ). Everything shifted to the right, but the balloon would slap you in the head. So then I would say, open the windows and see what happens; which of course, eliminated the effect since there was no compression of air against the window. --which should have given a clue to the clueless.

Creator

 

[Creator]

ZapperZ,

I don't know if this is right, but does it sound plausible?

You take something combustible and light it (maybe a match will do), then drop it into the coke bottle. A peeled egg is placed on the mouth of the bottle
and falls into the bottle.

Does the match burn away most of the air in the bottle, leaving a partial vacuum, causing the egg to squeeze into it?

Are there any books you could recommend that might have this mentioned?

Thanks!

Larry

I think that's an old one that was originally done with the old type milk bottles (which had much larger necks than coke bottles). Anybody remember those things? ask grandpa about them.

Anyway, another related 'trick' (and equally old) is heating up with a bunsen burner an open one gallon metal gasoline container (preferably without gasoline in it,he, he ). Then put the cap back on tight and shove it into a pan of ice. Watching the can schrivel up into a mass of metal is always a hit.

Creator