Month: December 2014

094 Fascinating Magnetic Toy 1: Magnetic Seal

The manufacturer provided the diagram below, which shows the magnets in the seal and ball to be misaligned by 45°.

You may want to refer to the manufacturer’s write-up on how this results in the rotational motion of the ball (because I have not figured it out yet).

http://www.arborsci.com/Data_Sheets/P8-1181_DS.pdf

The magnetic spinning ballerina works by the exact same principle.

093 Levitron

Apparently, Levitrons come with a ring magnet in the base. The copycat Levitron I found in the lab actually placed 4 bar magnets at the 4 corners of the base (all with N-pole facing up).

Nevertheless, I think the magnetic field formed should be similar to the one shown below. I didn’t occur to me that the magnetic field of a ring magnet is so interesting: as in our situation, because of the “switch” in magnetic field lines, the magnetic top is repelled when it is above a certain height, but attracted when it is nearer to the ring magnet.

This explains the trouble I had in getting the Levitron to work. The region of space where equilibrium is possible is very tiny. And it is an unstable equilibrium that can be destroyed by the slightest disturbance. Hence the spinning is crucial in keeping the spinning top in the upright orientation.

092 Eleven Dollars

As far as I can tell, folding the dollar note has the following benefits:

1. It stiffens the note. Without the fold, the dollar note is spineless and cannot hold up any weight.

2. Without unfolding the note completely, the coin now has a bigger region for its C.G. to be positioned to achieve equilibrium.

3. I suspect that unfolding the dollar note has similar benefit as demonstrated in the “seeking C.G.” demo. Specifically I mean the underlying Physics helped to automatically position dollar note below the C.G. of the coin.

🙂

Standing Wave on Free String — xmdemo 091

The string is fixed at one end but free on the other end. Standing waves formed on such a string must have a node at the fixed end, and an antinode at the free end.

As such, the fundamental (1st harmonic) that can be formed corresponds to one quarter-segment. The next standing wave that can be formed corresponds to three quarter-segments (3rd harmonic), followed by five quarter-segments (5th harmonic) and so on.

Even harmonics are not possible because half-segments will require nodes to be formed at both ends, which is not possible for such a string with one free end. This is very similar to the situation in open pipes, where only odd harmonics can be formed.

090 Accuracy and Precision: Dart Throws

Precision is about the deviation of data among themselves (caused by random errors).

Accuracy is about the deviation of data from the true value (caused by systematic errors).

Of the three, Set B has the poorest precision. However, the average of the three data is almost right on the bull’s eye, making it the most accurate.

Basically, large random errors may cause a large spread in the data. However, since random errors are random, they can be effectively dealt with by taking repeated measurements and averaging the data.

Fountain Boy — xmdemo 089

– The diagram below shows what is most likely in the fountain boy: trapped air above a body of water.

Initially, surface tension helped to hold in the water. However, when hot water is poured onto the boy, the higher temperature leads to higher pressure of the trapped air, which pushes the water out of the boy.

Seeking Centre of Gravity — xmdemo 088

Consider the forces acting ON THE RULER.

By considering rotational equilibrium, taking moments about the C.G. of the ruler, we come to the conclusion that the normal contact force is always larger on the finger that is NEARER to the C.G. of the ruler (N2 in the figure). (In other words, the ruler rests more heavily on the finger that is nearer to its C.G.)

This implies that the friction f2 generated at N2 is also larger. (This is because the maximum friction between two surface is increased if two surfaces press against each other harder) Since f2 is stronger than f1, the ruler gets pushed towards f1 . In other words, the ruler sticks with the finger nearer the C.G., and skids above and towards the finger further from the C.G. The underlying physics guarantees that the two fingers will eventually meet at the C.G. of the ruler.

This “auto zoom-in” mechanism fails if the two fingers are not equally rough. This is what happened in the video when the ruler is wrapped with a layer of rubber at one finger but not the other, the higher coefficient of static friction at the “rubbered” finger can exert a larger friction despite a smaller normal contact force.

P.S. The alert student will realize that this explanation is incomplete. Because it cannot explain why the two fingers do not close in towards the C.G. together once they are equidistant from the C.G.. Instead the fingers take turns to skid towards the C.G.. For a complete explanation, we need to involve static and kinetic coefficient of friction.

Dropper Popper — xmdemo 087

The energy of the jump comes from the energy stored in the deformation of the popper. The gravitational potential energy merely serves as the activation energy required to unleash the stored energy. In fact, the height of the jump does not change with the height from which the popper was dropped.

Apparently, chemistry students are familiar with the concept of activation energy. As a physics tutor, this toy reminds me of the energy required to trigger nuclear fusion or fission.

Celtic Stone — xmdemo 086

I have absolutely no idea whatsoever how this thing works. Apparently it has to do with something called “product of inertia”. I don’t understand it at all. But next time if my boat starts spinning when I step into it, I can tell myself it is due to “product of inertia”. Haha.

The following article seems useful: http://www.arborsci.com/Data_Sheets/P2-2140_DS_Teacher.pdf

Rubber Band Shooting — xmdemo 085

This phenomenon deserves a more scientific study.

But at present, it does look to me that the “twister” shot achieves a longer range because it managed to minimize the air resistance it encounters during its flight. The “twister” shot imparts to it an initial angular momentum. By keeping to this orientation, the rubber band minimizes the cross sectional area it presents to the air. The “vanilla” shot does not have any initial angular momentum and simply tumbles its way through the air, incurring more air resistance when it presents a larger cross sectional area to the air.

The advantage of the “twister” shot looks similar to that of tossing a horizontally oriented cardboard sideway as compared to simply shoving it into the air.

Why does the “twister” shot spin? Clearly it has something to do with one side of the rubber band being more stretched than the other. So the tension in one side of the rubber band is higher than the other. But tensions are internal forces to the rubber band. So it is not so clear to me how that translates into a net torque during release.