Surprising Physics: Acceleration Faster Than Freefall

[Creator]

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?

Good one, Reality. he, he
Capacitance is not only dependent on the permittivity, but also changes with the area of the plates which will vary with temperature. So I suspect that is the reason. If the plates are metallic, for example, and expand with temperature rise, a greater capacitance should result (provided the distance between the plates doesn't increase also).

Creator

 

[brewnog]

I did the hot water/cold water/freezing experiment a few weeks ago; I'd seen it on TV and just couldn't believe it. Sure enough, it worked.

The Mpemba Effect

Some pretty keen explanations for it, although I don't think it's been conclusively explained yet (though evaporation, convection, dissolved gases and supercooling have all been proposed).

 

[addman]

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?

One possible explanation- you are not just heating up the vacuum, but the whole circuit- wires, capacity etc.
Doing this causes more resistance in the capacitor.
as V = IR, voltage across the capacitor increases
now capacitance can be describes as C = Q/V
so as voltage increases, capacitance decreases. Therefore the capacitance is dependant not on the temperature of the dielectric but the temperature of the actual capacitor

 

[pack_rat2]

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?

An easy way to understand this is as follows. The reason a He balloon rises in the air is that the net upward force on it, due to the air pressure acting on its underside, is greater than the net downward force, due to the sum of its weight and the air pressure acting on its upper surface. The air pressure becomes greater the closer you are to the ground, just as water pressure increases as one dives deeper into a pool. In a car that's accelerating, the rearward force acting on the mass of the air works in the same way that gravity does in the vertical direction. It causes an imbalance of force that pushes the balloon forward.

 

[Andrew Mason]

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!

How about a catapult: a heavy rock falling at an acceleration of less than g can produce an upward acceleration of the projectile that is much greater than g.

Some may find it surprising but it isn't really. Actually I am not sure that most would find the example you gave to be surprising. The acceleration of the centre of mass of the board is less than g after all,

Ok. So how about a boomerang? Torque on the boomerang about a horizontal axis causes the boomerang to move in a circle about a vertical axis!.

AM

 

[jdavel]

How about sailboats moving across the water faster than the speed of the wind?

 

[carlfogel]

I did the hot water/cold water/freezing experiment a few weeks ago; I'd seen it on TV and just couldn't believe it. Sure enough, it worked.

The Mpemba Effect

Some pretty keen explanations for it, although I don't think it's been conclusively explained yet (though evaporation, convection, dissolved gases and supercooling have all been proposed).

Here's a link to the data from a nice experiment from a data acquistion company that demonstrated the Mpemba effect:

http://www.picotech.com/experiments/mpemba_effect/results.html

The hot 42C water froze much faster than the colder 18C water sample.

 

[pallidin]

How about sailboats moving across the water faster than the speed of the wind?

How is that possible?

 

[yourdadonapogostick]

http://www.phys.unsw.edu.au/~jw/sailing.html
http://www.scienceforums.net/forums/showthread.php?t=12447

 

[Integral]

I have separated my breaking chalk disscussion and moved it to to here

 

[pallidin]

http://www.phys.unsw.edu.au/~jw/sailing.html
http://www.scienceforums.net/forums/showthread.php?t=12447

OK, I understand now. Thanks for the links.
Sure seems weird even though it makes sense.

 

[vinter]

Here is another one I came across that has a little 'I didn't expect that' effect. It doesn't give you a shock in the beginning, but once you think about it, it seems impossible.
Basically, you have a vertical square iron plate of large dimensions and a comparatively small magnetic rod. You now stick the rod to the vertical plate such that the rod stands horizontal. The rod is not cylindrical so that it doesn't roll down. Keeping it in this horizontal position, you slide it towards one of the vertical edges of the plate. You keep sliding it until half of it is out of the plate and half inside. In this position, it remains stable. If you slide it even more, it still remains stable although it's centre of mass is now out of the plate.(This is one thing that doesn't appeal to the rational senses.) If you slide it more, at some point it rotates and falls down and that point comes BEFORE the rod is completely out of the iron plate. Now consider this position just before when it falls. The forces acting on it are :-
1. the magnetic force by the plate which gets canceled by the normal force.
2. the frictional force by the plate
3. gravity.
Since here, it is both in translational as well as rotational equilibrium, the downward gravitational pull must be nullified by an upward friction. But since the friction and the gravitation should have opposite torques, friction should be downwards?
What's going on!

 

[yourdadonapogostick]

i heard that if you have a inclined plane of the right material and at the right angle, friction makes objects roll against gravity. i have heard of this, but not seen it directly.

also, there is a hill around where i live where you can supposedly park at the bottom and a ghost will take your car to the top. if there is any validity to this, it is the above phenomina.

 

[yourdadonapogostick]

i was surprised that it is true that water will stop bullets fast enough that diving into water while being shot at could save your life. i always doubted it, but Mythbusters says i was wrong.

 

[BobG]

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 ?

I've never seen this one before. I think there could be two possible explanations for this, but I'm not sure which one (if either) is right.

Angular momentum stays constant (or close to it). The rotational energy changes - in fact, you lose rotational energy.

$$H=I\omega$$
$$E=\frac{1}{2}I\omega^2$$
(I is moment of inertia. ω is angular velocity.)

You can lose rotational energy by decreasing the angular velocity. Since angular momentum stays constant, the moment of inertia has to increase. Since you can't change the mass of the object, it's radius relative to the spin axis has to increase. Increasing the moment of inertia will also drive a decrease in angular velocity since you're losing energy with no way to gain it back, but at some point you hit an equilibrium for any given energy level (not that you'll stay at a given energy level for more than an instant).

In essence, all objects transition to a stable spin about the axis with the largest moment of inertia as they lose energy.

The effect of spinning a book or caclulator about the axis with the intermediate moment of inertia vs. minor axis or major axis is:

a) An optical illusion. Spinning about the minor axis has the same effect, but it's not as noticable since you're spinning about the long axis and it takes longer to transition to a stable spin.

b) A spin about the minor axis can be stable if you spin it with enough energy. A spin about the major axis will be stable because it is the axis with the lowest energy level. A spin about the intermediate axis could be stable if you spun at just the right angular velocity. Too much energy, it will move towards its minor axis regardless of the angle of release (ever spin a class ring?) - too little and it will move towards its major axis. The odds of finding the exact angular velocity required for a stable spin about the intermediate axis is pretty small. (This is my first choice).

 

[toocool_sashi]

If you slide it more, at some point it rotates and falls down and that point comes BEFORE the rod is completely out of the iron plate. Now consider this position just before when it falls. The forces acting on it are :-
1. the magnetic force by the plate which gets canceled by the normal force.
2. the frictional force by the plate
3. gravity.

I did not quite understand ur expirement clearly but i think uve forgotten 1 force...the force which ur applying 2 slide it?? or is it in equilibrium after the CoM is out of the square plate and u have also removed any physical contact with it?

 

[vinter]

I did not quite understand ur expirement clearly but i think uve forgotten 1 force...the force which ur applying 2 slide it?? or is it in equilibrium after the CoM is out of the square plate and u have also removed any physical contact with it?

My mistake. i think I did not explain the question properly.
When I said that you are sliding the rod slowly, I meant that you are sliding it very little and then leavin it to see what happens to it. The forces that I have listed are the forces acting on it in this situation, i.e., when you have left it to see what happens. I hope this makes it clearer.

 

[GENIERE]

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.

Yep! Grandpa remembers them, delivered twice a week to the milkbox on the porch along with the bread.

I'm certain I saw the experiment before I reached 6th grade.

...

 

[StatusX]

The forces acting on it are :-
1. the magnetic force by the plate which gets canceled by the normal force.
2. the frictional force by the plate
3. gravity.
Since here, it is both in translational as well as rotational equilibrium, the downward gravitational pull must be nullified by an upward friction. But since the friction and the gravitation should have opposite torques, friction should be downwards?
What's going on!

I don't know what you mean by "upward friction", but if I understand correctly, this isn't nearly as strange as you think. An similar experiment would be to hold a board so that a small part of it is on resting on a table and the rest is hanging over the ledge. If you glue the end to the table, and if the glue is strong enough, the board will be stable, and common sense would agree with this.

In your experiment, the balance of forces is as follows: The overhaning end of the rod exerts a torque about the edge of the plate which results in an upward force on the other end of the rod. The downward force on this end is the combination of gravity and the magnetic force. If this is greater than the force from the torque, the board will be at rest, with the balance of the downward force being countered by the normal force.

 

[Creator]

Yep! Grandpa remembers them, delivered twice a week to the milkbox on the porch along with the bread.

I'm certain I saw the experiment before I reached 6th grade.

...

Yep, sometimes older folk can really fill in the blanks.
I'm glad to see that someone else remembers these bottles (and the demonstration).

I'm sure I was in grammar school at the time I first saw it also.
So what was the physics lesson from the egg getting sucked into the bottle?

Creator

 

[Norseman]

i was surprised that it is true that water will stop bullets fast enough that diving into water while being shot at could save your life. i always doubted it, but Mythbusters says i was wrong.

What I find the weirdest about that episode was that the high power guns were less effective than the low power ones. Too fast and the bullet just gets ripped apart.

Edit: Okay, so here's my contribution. The Leidenfrost effect. Take a clean (non-teflon) pan and set it on the stove. Let it heat up (it will need to be well past the boiling point of water). While it's heating, let a drop of water fall on the pan. Notice that it sizzles away. As it gets hotter, the water should vaporize faster and faster. But, when the pan gets hot enough, the water no longer sizzles immediately and now begins to float around on the pan (yes float, the water doesn't stick to the pan anymore and if it's round you can spin the pan around to make the water droplets do laps, sometimes dozens of them) lasting for quite a while.

What has happened is the water vaporized so fast that a cloud of steam formed. The steam insulates the water and makes it take considerably longer to vaporize.

Alright, now for just fun. Take a candle. With a small bit drill, or a needle, make a hole near the wick. Insert a toothpick (make sure the candle doesn't have any metal embedded in the bottom). Place the candle in the microwave. Notice the candle starts releasing small clouds of plasma. I'm actually not sure what happens here, but I know it doesn't work without a toothpick. A plain wick won't do it.

 

[yourdadonapogostick]

you can do that with liquid nitrogen and a surface that is hotter than the boiling point of liquid nitrogen. that is how you can put liquid nitrogen in your mouth without freezing(warning: if you try this, DO NOT SWALLOW!)

 

[CarlB]

Here's a link to the data from a nice experiment from a data acquistion company that demonstrated the Mpemba effect:

http://www.picotech.com/experiments/mpemba_effect/results.html

The hot 42C water froze much faster than the colder 18C water sample.

Just from the slope of the curves, I'm going to guess that it has something to do with the amont of air entrapped in the water. That is, you have to heat the hot water up enough to just below a boil so that the air goes out of it.

A way of verifying that this is the solution would be to examine the icecubes. The cubes made from hot water should be clear throughout, while the cubes made from cold water should have all those little air bubbles.

Either the air bubbles have the effect of insulating the center of the cube, or they increase the heat of solidification due to the increased surface tension involved with all those air bubble surfaces.

If it is entrapped air, then rerun the experiment with cold water that has had its air removed.

Carl

 

[DaTario]

The forces acting on it are :-
1. the magnetic force by the plate which gets canceled by the normal force.
2. the frictional force by the plate
3. gravity.
Since here, it is both in translational as well as rotational equilibrium, the downward gravitational pull must be nullified by an upward friction. But since the friction and the gravitation should have opposite torques, friction should be downwards?
What's going on!

If you have a seesaw with two pivots instead of one, you will be able to balance it with several different weights, lying in a range. In a similar manner, when the rod stuck by magnetic force on the plate, it creates some pivots (i.e. more than one), and so it is able to maintain itself static for a range of forces.

 

[DaTario]

there was a beautiful problem in Physics Teacher of May I guess in which a ball is lauched horizontally in between two vertical and parallel walls. The ball bounce in the walls while the gravity pull it down. After 1 second the ball will be 4,9 meter below. This is Ok. But now consider the walls are substituted by mirrors, with 100% reflectivity. Now, instead of a ball, we send a laser beam horizontally. Of course the beam will reflect back and forth, but the question is: what will happen with the light 1 second later? (Hint: GR)

 

[Creator]

there was a beautiful problem in Physics Teacher of May I guess in which a ball is lauched horizontally in between two vertical and parallel walls. The ball bounce in the walls while the gravity pull it down. After 1 second the ball will be 4,9 meter below. This is Ok. But now consider the walls are substituted by mirrors, with 100% reflectivity. Now, instead of a ball, we send a laser beam horizontally. Of course the beam will reflect back and forth, but the question is: what will happen with the light 1 second later? (Hint: GR)

The light beam will be 4.9 meters lower after 1 sec. :tongue: (provided the mirrors are perfectly parallel!) Not likely, however, that you'll be able to do a table top experiment since even the best mirrors would not have sufficiently perfect reflectivity to bounce back and forth the required 3 x 10^8 times required for a mirror separation of 1 meter! Good gedanken experiment though.

Another one I like to do ( for H.S. demo) is to use a plastic ruler (bent backwards) to strike two marbles simultaneously, launching them from off the top of a table. Since each marble is struck with a different force one goes much farther horizontally than the other. The question to the class is: "Which one will hit the ground first?" Pretty simple, but it gets the gravitational point across.

 

[DaTario]

That's is it!

I also found it very interesting in deed.

 

[pallidin]

The light beam will be 4.9 meters lower after 1 sec. :tongue: (provided the mirrors are perfectly parallel!) Not likely, however, that you'll be able to do a table top experiment since even the best mirrors would not have sufficiently perfect reflectivity to bounce back and forth the required 3 x 10^8 times required for a mirror separation of 1 meter! Good gedanken experiment though.

Another one I like to do ( for H.S. demo) is to use a plastic ruler (bent backwards) to strike two marbles simultaneously, launching them from off the top of a table. Since each marble is struck with a different force one goes much farther horizontally than the other. The question to the class is: "Which one will hit the ground first?" Pretty simple, but it gets the gravitational point across.

I would imagine that in far less than 1 second, the light will be completely absorbed by the less than perfect reflections.
Even if the mirrored walls were 1000 feet apart, in one second each photon would have "potentially" reflected about 1 MILLION times ! I don't think(could be wrong) that a photon can reflect that many times without total loss.

 

[DaTario]

I guess, the best superconducting cavities can have the photon bouncing inside for still less than 0.5 seconds. There are perspectives of arriving at 1 second.

The experimental group dealing with such cavities is the French, Ecole Normale Superieur at Paris, Mr. Serge Haroche may be the lead researcher.

 

[Lyuokdea]

Although everybody here has probably heard of this, I've always enjoyed the three polarizer experiment. Basically, you set up two polarizers at 90 degree angles to each other so that there is no transmitted light through both polarizers. Then you set up a third polarizer in between the first two polarizers and spin it around changing the transmittted light from 1/8 of the original intensity to zero intensity and everywhere in between.

Without the mathematical idea of projections, it doesn't make any sense whatsoever, but then with the idea of projections, it shows just how important mathematics is in the physical world.

~Lyuokdea