# Surprising physics

1. Sep 3, 2004

### 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!!!
:surprised
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.

Last edited: Sep 3, 2004
2. Sep 3, 2004

### ZapperZ

Staff Emeritus
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.

3. Sep 3, 2004

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?"

4. Sep 3, 2004

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?

5. Sep 3, 2004

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.

6. Sep 3, 2004

### ZapperZ

Staff Emeritus
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.

7. Sep 3, 2004

### 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.

8. Sep 3, 2004

### ZapperZ

Staff Emeritus
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.

9. Sep 3, 2004

### 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. :-)

10. Sep 3, 2004

### 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.

11. Sep 3, 2004

### ZapperZ

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

Zz.

12. Sep 3, 2004

### 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

13. Sep 3, 2004

### geometer

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.

14. Sep 3, 2004

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

15. Sep 4, 2004

### ZapperZ

Staff Emeritus
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.

Last edited: Sep 4, 2004
16. Sep 4, 2004

### geometer

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.

17. Sep 29, 2004

### Cyrus

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?

18. Sep 30, 2004

### 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.

19. Sep 30, 2004

### 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.

Last edited: Sep 30, 2004
20. Oct 5, 2004

### 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