Sunday 31 May 2015

Tower of Brahma OR Tower of Hanoi Problem

The 'Tower of Brahma' or 'Tower of Hanoi' is a very interesting problem. There will be a stack of rings on a rod with the largest one at the bottom and the smallest at the top. All the rings in the stack have to be moved to another rod such that the order of the rings remain the same (biggest at the bottom and the smallest at the top). A third rod will be provided for the transfer. Find out the minimum number of moves needed to transfer the stack from one rod to another.


Rules to be followed during the stack transfer are :
  1. Only one ring can be moved at a time.
  2. Move is allowed only if a smaller ring is placed on a larger ring.
Kids Play
This is a problem that needs logic and calculations for college students but its some exciting fun time for kids. They really enjoy moving the stacks from one rod to another. Parents just need to tell the rules of the problem and see how your little one engages himself/herself in the puzzle.
 
Solution
number of rings        minimum number of moves
        1                     1
        2                     2x2-1
        3                     2x2x2-1
        4                     2x2x2x2-1
        5                     2x2x2x2x2-1


Video : Moving a stack of 4 jar lids from one plate to another with a minimum number of moves.


Wednesday 27 May 2015

Pinhole Camera


        A solar eclipse occurs when the moon passes between the sun and the Earth. During an eclipse the Sun, Moon and Earth are in the same line. The Moon partially, or fully blocks the Sun. A total solar eclipse occurs when the Moon completely covers the Sun's disk.
        It is very dangerous to see the sun through naked eyes or even any kind of filters. During Eclipse time it would be a wonderful experience if only you could see how the moon covers our sun partially or completely. To make it possible, we need to know how to construct a pin hole camera so that we can safely see the image of the sun on a butter paper.

How to make a pinhole camera

Things required : a long tube about 1meter in length, pin, butter paper / oil smeared paper, a shoe box/ wide box, a sheet of dark paper.

Step 1 : Cover one end of the tube with dark paper and prick a pinhole in the center. Cover the other end with butter paper so that we can see the inverted image of the sun.

Step 2 : make a circular hole in the box so that the tube fits in tightly. This box acts as a protection to the eye and also increases shade so that the pinhole image looks more brighter.


Observing partial Solar Eclipse that occurred in Bengaluru in 2009 through pinhole camera.



Ball Bearing Experiment


        A machine that works requires energy. Part of the energy is lost due to friction. Friction is a force that opposes motion. It is caused by the moving parts of a machine when they rub against each other. Reducing friction allows machines to run smoothly and efficiently and consume less fuel and energy. Bearings are supports that reduce friction. They help a moving part to roll rather than rub on its support. It consists of small metal balls over which the rotating part rolls over.

Ball Bearing Experiment
Let us build a simple ball bearing and see how it enables objects to spin easily.

Things we need
2 jar lids (one of which closely fits into another), marbles/ metal balls, pencil, clay, A wooden block, sticky tape.

Step 1 : Stick the smaller jar lid upside down on a wooden block.

Step 2: Place two equal blocks of clay on the ends of the pencil and stick the middle of the pencil to the larger lid.

Step 3 : Put the larger lid over the smaller lid and spin it sharply. Note how long it spins.
Step 4 : Remove the top lid and put marbles into the smaller lid. There should be enough marbled to form a ring and they should be able to move freely. Now replace the larger lid over the smaller lid and spin the pencil sharply. Note how long it spins. 
Observation
We observe that the pencil spins faster and longer when the two lids are separated by marbles. Thus the marbles or metal balls act as ball bearings and reduce friction between the rotating top lid and its support. Here is an example where ball bearing is put to practical use.



 Ball Bearing Experiment Video

How cable car works


How Submarine Works


Spring Balance

        Spring balance is a type of weighing machine. Weighing machines and scales are used to weigh quantities. A spring balance contains a spring (stretching material) that stretches in proportion to the weight of the object being weighed. The spring moves a pointer on a graduated scale.

Things Required
Spring (or a stretchable material like a flexible rubber band), a hook , a pointer, thread/rope, container, a strip of paper, objects of known weight.

Step 1 : Tightly secure one end of the spring to the hook. Fix a pointer horizontally to the other end of the spring. Tie a long rope to the same end of the spring.

Step 2 : Make 4 holes to the container and tie equal length ropes to each hole. Then knot all the ropes together and secure it to the free end of the rope hanging from the spring.


Step 3 : Hang your set-up freely from a height with the help of the hook. Stick the strip of paper to the wall or to the hook.

Step 4 : Take a pen and mark 0g on the paper strip when there are no weights in the container. Now add known weights (50g,100g,200g etc) to the container one by one. As weights are added the spring stretches and the pointer moves down the scale indicating the weights on the paper strip.


Your Spring balance with the graduated scale is now ready to weigh unknown weights. How much does your alarm clock weigh?


My Alarm clock weighs 80g.

Spring Balance Video

Zeotrope - An Early Animation Device

Question 1 : What is Animation?
         Animation is the process of displaying still images in a rapid sequence to create the illusion of movement. 
 
Question 2 : What is a movie?
            A movie is pictures in motion.

Question 3 : How does the picture you see on cinema screen move?
           The fact is that the pictures only appear to move. A movie film is a long strip of still pictures or frames that are projected on to a screen one after the other at a rate of 24 pictures a second. As each picture disappears from the screen, it persists in your eyes for a little longer and you continue to see it until the next picture appears. These pictures appears to merge together forming the illusion of motion in our brain. Since each picture is slightly different from the previous one, the image on the screen appears to move.

Zeotrope Experiment

         A Zeotrope is one of several animation devices that produce the illusion of motion by displaying a sequence by drawings and photographs showing progressive phases of motion. It consists of a cylinder with slits cut vertically. On the inner surface of the cylinder is a band with images each slightly different from each other. As the cylinder spins, the user looks through the slits at the pictures. This scanning of slits allows the user to see the pictures in motion.

Things required
Craft paper, packaging box, scissors, glue, scale, pencil and color pencils.

Step 1 : Take a big craft paper and cut a rectangle of length 65cm and breadth 15cm. The length is divided into 16 parts each of 4cm and 1cm for flap. The breadth measurements are : 1cm to 5cm slit length, 6cm to 12 cm images, 14cm to 15cm cuts/ flaps.

 
Step 2 : After making the measurements, here are some things to check.
  1. There should be 16 frames (Zeotrope can be made with 12 frames but not less than that) 
  2. There should be same number of slits as the number of frames. Each slit should be 4cm length and 3mm width.Cut out the slits with the help of a pen-knife.
  3. In the picture section, draw sequential pictures of a bouncing ball, bending tree, rotating hour hand of a clock or anything. 
Step 3: Glue the side flap and stick it behind the first frame thus making a cylinder shape with the pictures on the inner surface of the cylinder.

Step 4 : Trace the cylinder circumference on to the hard cardboard/packaging box and cut out a circle with a small hole punctured in the center.

Step 5 : Cut the bottom edge of the cylinder with 8 or 16 cuts of 1cm each. Fold the flaps inwards and stick them one by one on to the hard cardboard base such that the hollow cylinder sits firmly on to the circular base. 

Step 6 : Insert a rod through the hole and fix two nuts on the inner and outer side of the Zeotrope so that it should be able to rotate freely but not fall off the rod. Rotate the zeotrope briskly and view a picture through the slit. The picture appears to move.

You can also place the Zeotrope onto a disc that rotates with the help of a toy car motor and automate the movie experience. Adjust the speed of the Zeotrope so that the motion of the picture is smooth and continuous.

Zeotrope Video


Pulley Experiment

        
    A Pulley is a simple machine. It is usually used to lift things by pulling down a rope that passes over the pulley. In a single pulley the amount of effort or force needed to rise the load is equal to the weight of the load. In a multiple pulley system there are two or more pulleys and the effort needed to rise the load is much less than the weight of the load.

How to make a pulley?

Method 1 - Pulley made from corrugated cardboard

Step 1: Cut 2 bigger circles and a slightly smaller circle from a corrugated cardboard. Make a hole in the center of every cardboard circle.

Step 2 : Sandwich the smaller circle in-between the two larger cardboard circles with glue. Pass a pencil (any axle) through the hole so that the pulley wheel rotates freely. Your pulley is ready!

Step 1
Step 2 
Method 2 : Smooth and Stronger pulley

Things Needed : Craft paper, glue, pencil, packaging box

Step 1 : Cut thin and long strips of paper about 4mm width. Roll as many strips of paper on to a pencil depending on the size of the pulley you want to make.


Step 2 : Cut 2 circles from a packaging box, make holes in the center and sandwich the paper roll between the 2 circles. Your pulley is ready.

 Step 1
Step 2

Single Pulley Experiment - A Well

Things Needed : A pulley, rope, a toy bucket, a plastic container, 3 pencils, sticky tape, paper.

Step 1 : Draw and paint bricks on the sheet of paper and stick it around the plastic container such that it looks like a well.
 
Step 2 : Stick two pencils to the inner side of the container so that 70% of the pencil protrudes above the container. Then insert the pulley into the third pencil and then bind the third pencil horizontally to the two pencils with a thread or sticky tape.

Step 3 : Fill half of the container with water. Tie a bucket to a rope and then sling the rope on to the pulley. Fill the bucket with water and pull it out with the help of a pulley wheel. Have a nice time drawing water from the well ! Observe that lifting a bucket of water using a pulley is easier than lifting it directly from the well.

  
Multiple Pulleys

A multiple pulley system consists of two or more pulleys. There are 2 blocks of pulleys namely the upper block and the lower block (tackle). The upper block pulleys are fixed where as the lower block pulleys are attached to the load and moves along with the load. A rope is wound around both the sets of pulley wheels. As the number of pulleys increases a smaller effort is sufficient to pull a heavy load; but the load need to be pulled over a longer distance. The figure shows 1,2,3,4 and 6 pulley system respectively.

Experiments for multiple pulleys

A simple 2 pulley experiment to test whether the effort required to lift a load of 30 units is half its weight (i.e 15 units). Repeat the experiment with 3-pulleys, 4-pulleys and so on. When 3-pulleys are used the effort should be 1/3 rd and when 4-pulleys are used it should be 1/ 4 th the load.


Elevator Experiment

The Elevator technology uses two or more pulleys for lifting the Elevator. Heavy elevators can be easily lifted using a smaller counter weights and motors. A working model of an elevator can be built using cardboard boxes, LEGO blocks or other building materials. The upper block pulley should be fixed at the top and the lower block pulley should be attached to the elevator so that it moves along with the elevator. Tie a rope to a beam from the upper block and wind the rope over the lower and upper pulleys. Pull the free end of the rope to lift the elevator. Building and executing the elevator technology is left to the creativity of the child.

We have used LEGO blocks for the construction of elevator and its support. For the pulleys we have used the wheels by removing the outer rubber of the wheels. We are manually pulling the rope to lift the elevator. Instead you could use a smaller counter weight (½ the weight of the elevator in a 2 pulley system) or a motor to wind the rope on to a bobbin.

Video of the working model of our elevator

Tuesday 26 May 2015

Crafts for Kids

Making 3D models
Kids love to play with things they can hold and feel. They understand 3D shapes better through solid models and seeing them play with it is a feast to the eyes. So why not make some educational toys for your little ones?


Clock 
Learning about time will not be complete without a clock in your child's hand. Rotating 'Hour hand' and 'Minute hand' gives a lot of fun to those little hands.


Story props and masks
Make your story telling attractive by using story props and masks. Older kids can make such props for their Story telling competitions.


A Fruit Vendors Cart
A fruit vendors cart is an enjoyable toy for children especially boys. Putting stuffs on to the cart and pushing it around is a lot of fun.


Pot Painting
I have used acrylic colors to paint the pots. The light glass work gives an attractive look to the pot. Do use gold and silver powder colors to enrich your pot painting.


Home made Polymer clay
Polymer clay can be easily made at home using all purpose flour and fevicol. Mix all-purpose flour with some fevicol and very little water if required and bring it to the consistency of play dough. Make your model immediately and keep it aside for a few hours to set. Once the model dries up you can paint it using Acrylic colors.


Stage Decorations

Krishna Theme


Nursery Rhymes Theme


Story Time Theme


Ocean Theme


Treasures from Trash

Packaging-box bags
 
How to Make : Cut the packaging/carton box into half and wrap it with decorative paper. Punch two holes at the sides and attach a handle. Cute return gift bags are ready for your kids birthday.

 

Yakult Dolls
How to Make : Wrap the Yakult bottle with colorful craft paper or design a paper dress of your choice. Cut out a thermacol circle for the head and stick/draw eyes, nose and mouth. Take an ice-cream stick and fix the head to it. Insert the ice-cream stick into the Yakult bottle. Yakult dolls are ready!




Gift envelops from invitation cards
Why throw away the beautiful wedding invitation cards when gift envelops can be made from them.


Pencil Sketches

Lord Krishna teaching Bhagavad-gita

Swami Vivekananda

Vyasa narrating Mahabharata and Lord Ganesha writing it down

Ekalavya - The great archer

Sri Krishna

Mother Cauvery