Pale blue dot Animation | Hindi | Translation by Arvind Gupta

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Juggling Force and Momentum - English

This incident happened many years ago when I was finishing my high school in Meghalaya, a state in India's northeast there are lush and dense forests everywhere. I used to walk to my school with my friend everyday through a narrow 2km long path. If I had taken the road the 2km walk would become a 20 km, 1hr bus ride. This was because the closest road-bridge was far away.
Also the path to my school had an amazing tree bridge which is now famously called the living tree bridges of Meghalaya. These bridges are made from aerial roots of rubber fig trees. It takes about 10 years for the roots to grow and the craftsmen have to ensure that the roots grow in a mesh so that they can take the weight of people crossing the bridge.

And one of those days I forgot my heavy school bag and so my parents promptly gave my bag to my classmate Gokul who now had to carry two bags 5 kg each. 
The weight limit of the tree was 50 kg. That was because the bridge was still 50 year young and roots tender. Over its life time of 500 years the bridge could take weight upwards of 200 kgs.
So there he was, Gokul weighing 45 kgs, at the mouth of the bridge with two bags 5kg each. Surely he couldn't carry the two bags with total weight of 55 kg on a 50 kg weight limit 
Gokul, smart with numbers, decided to juggle his way. That way with one bag in air the total weight would be 50. Perfect.
Well not really. The bridge broke, luckily Gokul got minor bruises. He was really confused though. Why the bridge break even though Gokul's Math looked all right.
The next day to solve the bridge breaking mystery, Gokul with two bags, went to a similar adjoining bridge. This time however, he reduced the weight of bags to 2.5 kg each. With 2 bags of 2.5 kg each, he carefully started juggling on the bridge but again he had a massive fall. This time though Gokul broke a couple of bones.
However what troubled him most (more than the broken bones) was the mystery of bridge and weight and math and science
Can you tell what went wrong? Gokul was a perfect juggler and this time the Gokul's weight and bag was 47.5 kg well below the 50 kg limit? 
As far as Gokul was concerned, he was enjoying his recovery to the fullest. He was really elated to miss school, and with broken bones, everything was served to him right in the bed. Not bad at all. Haan.

This work is supported by IUCAA (www.iucaa.in) and TATA Trust (www.tata.com/aboutus/sub_index/Tata-trusts)

Credits:,Ashok Rupner, Manish Jain, Pradnya Pujari, Shivaji Mane, Jyoti Hiremath, Arvind Gupta, Vidula Mhaiskar TATA Trust: Education is one of the key focus areas for Tata Trusts, aiming towards enabling access of quality education to the underprivileged population in India. To facilitate quality in teaching and learning of Science education through workshops, capacity building and resource creation, Tata Trusts have been supporting Muktangan Vigyan Shodhika (MVS), IUCAA's Children’s Science Centre, since inception. To know more about other initiatives of Tata Trusts, please visit www.tatatrusts.org

Animation by: Rosehub

Here is the Answer-

Mathematics and Mystery of the Cycle Track - English

This story more than 100 years old. In 1904 Sherlock Holmes the famous detective based in London investigates a murder. Next to the site of the murder are cycle tracks, on a muddy road from the school and the village. And only if they could figure out the direction of the cyclist based on the track, they can nab the culprit. Watson as usual is not sure. "This track, as you perceive, was made by a rider who was going from the direction of the school." "Or towards it?”

No, no, my dear Watson... It was undoubtedly heading away from the school."

That is because back wheel is deeply sunk in the mid because of weight and it crosses the other track and so the murderer is going away from village.

If you think about it, this is where Sherlock Holmes is wrong. We hate to acknowledge that super smart Holmes is wrong but actually he is. While the back wheel will cross the front wheel but that will be true in either direction of bicycle is going. If holmes would have said there were two murderers going on unicycle it might be a better answer. So how can we help Holmes or Arthur Conan Doye here?

So now let us investigate. And the answer to this is Elementary Watson. The back wheel follows the front wheel always. Unless of course you are driving the cycle backwards. Which you can't unless you have a BMX cycle which will be invented in future (this story happened in 1904). And the length of bicycle is constant. So the murderer is going towards the village. 

Huh.

OK let’s do the details.

The back wheel cannot turn. So the back wheel and frame point towards the front wheel or center of front wheel. Direction of the wheel at any time is just the tangent to the path. So if we draw the tangent on the back wheel path it should cut the front wheel at a distance which is the length of cycle. 

Now if we draw the tangent to green track here we see it does not cut the red track at cycle length. So green cannot be back wheel and is front wheel. While the tangent to red track cut the green track so it is back wheel. And now by drawing tangents at different locations we can see that in only one direction the distance is constant. So the cycle is going Left to right. So the murderer is Rueben Hayes living in the village. And now since we are all expert detectives. Is it possible to have a track where we cannot tell a direction? Well it is possible if you can ride a bicycle in a circle. The tracks will be two circles with same radius with back wheel with smaller radius. Since this is symmetric you cannot tell whether are going clockwise or anticlockwise. But since you are going in circles anyways it doesn't matter unless of course you are a MATHEMETICIAN. 

So I hope his story will inspire back to cycling and interested in the concepts of calculus a branch of math on which this story is based. Thank you. TATA Trust: Education is one of the key focus areas for Tata Trusts, aiming towards enabling access of quality education to the underprivileged population in India. To facilitate quality in teaching and learning of Science education through workshops, capacity building and resource creation, Tata Trusts have been supporting Muktangan Vigyan Shodhika (MVS), IUCAA's Children’s Science Centre, since inception. To know more about other initiatives of Tata Trusts, please visit www.tatatrusts.org

Animation by: Rosehub