Paper tricks, soap bubbles and more
Partha Bandyopadhyay
You often need very simple things to demonstrate experiments that seem almost magical. Here are four simple experiments with paper.
Tear the paper into three pieces
Take a paper strip 2-3 cm wide and about 15 cm long. Fold it in the middle and use a pair of scissors to make a cut (about 1 cm in length) approximately in the middle of the folded strip and parallel to its width.
Unfold the strip. There will be two equal cuts situated at equal distances from its ends. Now holding the two ends of the strip between the thumbs and forefingers of your two hands, try to pull it apart into THREE pieces. Try to apply equal force.
Try with smaller and bigger cuts and different positions of the cut. You will always end up with two pieces and not three! Why?
At the microscopic level, the cuts are never equal – no matter how carefully one makes them. The paper is weaker at the bigger cut and starts coming off from there. The cut becomes bigger and the paper even more weak. The process continues till the two pieces come apart. (This vindicates the saying: a chain is only as strong as its weakest link). Perforation in a bank cheque ensures that it comes off just from there. A shallow dent in the middle of a tablet (medicine) serves the same purpose.
Paper falling under gravity
We have all read about Galileo’s famous experiment at the tower of Pisa. Recent findings suggest that he probably did not drop balls from atop the tower but rolled them along inclined planes.
Galileo notwithstanding, astronauts in the 20th century did repeat a similar experiment on the surface of the moon, where there is no air. They dropped a feather and a coin simultaneously and verified that they fell together.
I would like to describe here an easy to do experiment which verifies the same law.
Take a moderately heavy book in one hand and a piece of paper in the other. The paper should be smaller in size than the cover of the book. Raise them to the same height and then release them at the same time. The book will hit the ground much before the paper. Now to get rid of the air resistance, put the paper on the book and repeat the experiment. This time they fall together. If the acceleration of the lighter paper were not equal to that of the book they would not have fallen together. The simplicity of the experiment may be deceptive but a moment’s reflection will tell us that it does vindicate Galileo’s law which says that all bodies fall with equal acceleration under gravity.
Pressure of moving air
Take two books almost equal thickness and place them about 10 cm apart so that there is a 10 cm wide uniform channel between them. Place a sheet of paper (A4 size, say) symmetrically above the channel and then, bringing your mouth close to one end of the channel blow air through it as hard as you can. Common sense would expect the paper to blow out. But actually it will be sucked into the channel.
This is a demonstration of Bernoulli’s principle which implies that moving portions of a fluid has a lower pressure than its static parts. (The higher the velocity lower is the pressure.) Air is static above the paper but is moving below it. Higher pressure presses the paper into the channel. The shape of the wing of an aeroplane – called an aerofoil – is designed to utilize the difference in velocity of the air above and below the wing to generate upward lift.
Here are some more fun experiments with soap bubbles and soap films – things you can do at different levels, right from class I to class X
The physics of soap films and soap bubbles is fascinating. Their size and shape are determined by surface tension and appearance and colour by the laws of optics. Here we will be concerned mostly with the former.
The guiding principle in understanding the behaviour of soap films can be stated this way: it always tries to minimize its surface area. In fact any liquid tries to minimize the area of its open surface because by doing so it minimizes its potential energy. A surface molecule has more potential energy than a molecule in any other part of the liquid. Now, for a given volume, a sphere has minimum surface area: that is why the natural shape of a liquid drop or a soap bubble is spherical. (Nature is a geometer: so goes the saying.) A circle, on the other hand, encloses the MAXIMUM area for a given perimeter.
Now let us see how nature makes use of these facts. Take a circular metal ring with a handle. A wire bent in that shape will do. Tie a string across it. Dip it in soap water so that a circular film is formed. The string will not have a definite shape. Prick the film on the right side of the string with a pin so that it breaks. On the left side, the film remains but the string takes a semicircular shape. If the film on the other side was broken, the string will again become circular but bent the other way.
If you carefully drop a small loop of the string on the film without breaking it, it will float around maintaining its irregular shape. If the film inside this loop is broken, at once the loop becomes a perfect circle. Why so?
In order to minimize the area of the film, one has to maximize the vacant area. For a given perimeter, i.e., length of the string, it is a circle or part of a circle.
A film formed at the end of a funnel contracts by itself for the same reason.
Thus, just one guiding principle is able to explain all the phenomena reminding us once again of the unity and beauty of physics. For soap bubbles one may refer to the sources mentioned.
Here is how you make stable soap films:
Things you will need:
1 cup of water
1 cup of liquid detergent
1 cup of glycerine
A big plastic bowl
A stiff wire
Mix the water, detergent and glycerine in a jar. Pour the mixture into a pan or cookie sheet. Bend the wire so that it forms a closed shape – a loop, a square or a circle – with a handle. This is your bubble frame. Dip the frame into the bubble mix and slowly pull it out at an angle, so a film of liquid stretches across it. Wave the wire through the air and then give your wrist a flick to set free a giant bubble.
Physics at work
A water bubble without soap lasts only a fraction of a second. A soap bubble lasts much longer. A soap bubble is a bubble of water with soap concentrated on the inside and outside surfaces. The soap molecules reduce the normal surface tension of the water. This allows the water molecules to stretch apart enough to form a longer lasting bubble. With the glycerine, the soap on the inside and outside surfaces of a bubble also helps keep the bubble in the water from evaporating and bursting.
Here are some more experiments with soap bubbles
Colours of a soap bubble
Blow a soap bubble using the soap solution and a paper straw. It should be of such a size that it remains stable for a reasonably long time. Observe the play of colours on its surface; the pattern keeps changing. One can see almost all the colours of the rainbow.
The soap film is very thin – thinner than a human hair in fact. Moreover, the thickness is not uniform all over the bubble. The colours emerge due to a phenomenon called “thin film interference”. Without getting into technical and mathematical details, one can describe this in the following way: a ray of light gets reflected both from the upper and the lower surface of the film. The two rays interfere to generate colours. The colour depends on thickness of the film.
Regions with same thickness show the same colour. But as the thickness of the bubble varies with time due to various factors such as gravity, air flow, etc., we see transient patterns of colour on the surface of the bubble.
Bubbles big and small
Consider that the water levels in the two tubes are unequal when the tap is closed. But as soon as the tap is open water moves from the right to the left column and the levels become equal.
Nature in this case seems to favour equality!
Now let us consider two soap bubbles – one bigger than the other. If they are connected by a hollow tube what will happen?
Common sense would expect the bigger one to shrink and the smaller one to blow up till they become equal. But defying our common sense just the opposite happens. The small one will contract and eventually collapse while the big one will grow bigger at its cost. Apparently Nature is on the side of inequality in this case.
It happens that way because the excess pressure inside a spherical soap bubble is INVERSELY proportional to its radius. Consequently the pressure inside the smaller bubble is greater and air flows from the smaller to the bigger bubble. This further reduces the radius and increases the pressure inside the smaller bubble. The process goes on till it collapses.
BOX
Strength of paper
Take a piece of A4 size bond paper. It is about 20 cm by 30 cm in size. Tear off a 20 cm by 10 cm strip out of it. Keep two books of nearly the same height some 6-7 centimetres apart. Place the paper symmetrically over that gap. Now place a pen on the paper above the gap. The paper will not be able to support the weight and will collapse.
Now fold the piece of paper to make a 10 cm X 1 cm strip. Do not tear. Fold it once more in the reverse direction. Repeat as many times as needed to make a corrugated sheet out of it. Put it back over the gap as before. Place the pen on top once again and note that this time its weight is supported. Put one more pen. That too will be supported.
A paper strip (or a meter scale, for that matter) is stiffer when the breadth is vertical than when it is horizontal. This is because the geometrical moment of inertia changes with configuration and alters the bending moment of the beam shaped object. Corrugation is used to increase the effective strength of a material.
Sources
https://www.youtube.com/watch?v=7Tsy_XfswhQ
https://www.youtube.com/watch?v=IUIurv5L_mM
The author is an Associate Professor of Physics (Retd), City College, Kolkata. He can be reached at pbandyo@gmail.com.
