Friction

Supposing you are holding a pen statically. The weight of the pen is acting downward which is opposed equally with an opposite upward force by the friction force (F). The perpendicular force that acts across the surface area of the pen will be the normal force (N). At any given time, the friction force will be the product of the normal force and the coefficient of static friction (µ). i.e., F = N * µ.

If the coefficient of friction is high, like in a rough surface, then the normal force required will be less. If the coefficient of friction is very low, like in silky smooth surface, then the normal force will be high to compensate for the slippage.

To put it in other words, the coefficient of friction will be the ratio of the friction force to the normal force. µ = F/N (parallel force/perpendicular force)

Migration of birds….

It is the winter – The ground is covered with a white carpet of snow. You cannot wander outdoors because of the bone-chilling cold and the freezing water. You sit inside your thermal regulated house, sipping piping hot coffee and lazing around in front of your fireplace. Now tell me, how many of you have wondered about the poor tiny little birds that used to flock your backyards in the spring? Are they still out in the cold or have they gone elsewhere?

Looks like except for a few residential species, most of the birds are vacationing in the warmer south. Can you believe, in North America alone, 5 billion birds annually leave their breeding grounds to go south for winter? So, why do they migrate? It’s for survival – to survive from food scarcity and the harsh winter. Migration is probably the most amazing, inspiring natural phenomenon – Imagine a tiny little bird against the most ferocious elements of nature – it has to overcome the inclement weather, heat exhaustion, fiery wind, and other natural disasters to reach its destination.

Let me show you some of the perilous journeys these birds take. The Arctic terns breed in the arctic summer. They follow the coastline of Africa to reach the Antarctic in November and enjoy the summer there – a total distance of 10,000 miles – they do it twice a year, every year till they perish.

Take the case of barn swallows. Have anyone seen a swallow? It such a teeny-weeny little bird that weighs only a mere 20 g. It nests in the British midlands and go all the way to South Africa, an epic journey of 6000 miles, crossing the formidable Sahara desert that itself stretches around 1000 miles. Of the 5-6 offspring that start the journey, only one will return, a mortality rate of 80%.

Or take the example of bar headed goose. They travel from central Asia to the winter grounds in India – they cross the Himalayas at a height of up to 29,000 feet.

Coming to North America, the tiniest bird that you see in your backyard, the ruby throated humming bird has come from the Yucatan Peninsula crossing the Gulf of Mexico to breed and spend its summer here in the east coast. For that matter, most of the colorful song birds that you see and hear their songs like warblers, thrushes, tanagers, and the birds of prey like hawks, eagles, falcons and ospreys have traveled between 1000 to 8000 miles to breed in the Northern hemisphere. Most of them have wintered in central or south America.

Now that we are in Delaware, can we witness this bird migration first hand? Yes you can. The best place to watch the spring migration of the shore birds is to go to the Delaware Bay in May. Thousands of exhausted shore birds like red knots, sander lings, sandpipers arrive here to feed on the horseshoe crab eggs before continuing their journey to their breeding grounds in the Tundra and Boreal forests of the north.

The best place to watch the fall migration is Cape May. Here you can observe the migratory hawks and millions of songbirds. Here they concentrate in huge flocks to wait for the right weather conditions to cross the Delaware Bay to go south.

Now, next time in spring when you see a colorful bird or hear a heart-rending melodious song, please remember, these tiny little heroes travel thousands of miles every year against all odds just to ‘survive’.

My encounter with elephants….

Before starting my encounter with elephants, let me give you a short introduction about the elephants. Elephants are social animals just like humans. They live in closely knit family groups that are led by the oldest female of the herd. Adult males are rebellious and solitary and associate with the herd only for mating. India holds the largest number of asian elephants – around 25,000, of which southern India is home to around 12,000 elephants. In addition to deforestation, disease and poaching, human-elephant conflict seems to be the most widespread and difficult issue to tackle in elephant conservation. Conflict often occurs when humans move into elephant habitat.

In 2004, when I was working in India, I had a strange request from a scientist friend of mine who works with elephants. He asked me to help him out in ‘elephant census’ in Bannerghatta National Park in southern India about 20 km from Bangalore. So I became a volunteer along with 20 other members for 2 days.

The park spreads around 25, 000 acres. It has hills and valleys with the valley containing moist deciduous forest habitat, while the rest of the park is dominated by dry scrubland and dry deciduous areas. For each of the volunteer 2 forest guards were assigned. I carried a binocular & a camera, while the forest guards carried a small drum, walkie-talkie, the maps, food and water, and two loaded rifles. That was the first time in my life I have actually touched the rifle. I asked naively ‘do u ever use the rifle? for which the foreste guard answered that just one month before a forest guard was trampled by a solitary elephant despite of having a rifle. The gravity of the situation was slowly sinking to me. I got the bottom line message that ‘u don’t take it easy with elephants’.

And so we set off for the elephant census.

The temperature was hovering around in the 90s. We were basically targeting water bodies and ponds where the elephant loves to hang out because of the heat. We were very particular in not going too near them to precipitate an anxiety attack from them. They are highly territorial. Anytime we came across a thick bamboo bush, the guards bellowed loudly at times beating even the drum when they were not quite sure what was lurking behind the bushes. Besides elephants, the Bannerghatta national park is also home to a wide variety of wild animals and reptiles like poisonous snake and scorpions.

We counted atleast five herds for the first day. We photographed the dung, and the footprint of the elephants. It was a productive and tiring day. One of the guards spotted a small honeycomb on our way back and he made a bold attempt to grab it from the few bees that were hovering around it. We plucked few broad leaves and used them as our container while the forest guard poked the honeycomb with a twig to extract the honey. Needless to say, that was the best fresh honey that I’ve ever tasted in my life!!

The next day we were not that lucky to spot a single herd. It was almost late afternoon, when we approached a valley. One of the range guards climbed a tree and spotted a herd at the bottom of the valley, wallowing in a flowing stream. Since we were not sure about the number of elephants in the herd we thought we could approach them a little closer. It was a difficult climb downhill with thorny bushes and no paths. We had to be careful about the reptiles too. After climbing down almost half of the distance one of the rangers told us to pause suddenly. He stood straight straining to catch some sound. There was an eerie silence. All I could hear was the gentle rustling of the trees and the shrubs and my own heavy breathing. Then I realized something was wrong. The ranger guard who was in front of me saw some 5-6 elephants that were coming towards us with their trunks lifted high and were trying to sniff our scents.

Thatz when I saw some 30 feet away a glimpse of a brown mass. I felt rooted to that place just like the tree… and that split second the guard grabbed my hand and started to run down hill on the other direction coz the wind will be in the opposite direction if we run downhill. I don’t know where we had that super human strength. We were bolting like winds and I couldn’t cope up with the speed of the guards where I stumbled and fell twice. That guy never left his grip he just dragged me till we reached the bottom of the valley. It was the mother of all runs. After reaching the valley the forest guard pulled out his rifle and fired a shot in the air. A deafening boom. My knees were shivering and my whole body was covered with dust, bruises and scratches.

By then the guards explained to me that probably that chase was a mock charge because calves were there in the herd. If the elephant were to chase us really they would have got us within no time.

Till this day this incident remains one of the most memorable events in my life….

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Radiocarbon and radiometric dating.

Radio Carbon Dating – Example for Exponential Decay

As cosmic radiation bombards earth’s atmosphere, nitrogen gets split into Carbon 14, an unstable isotope (C14 is called ‘radiocarbon’ because it is radioactive). Now because of lightening and other natural phenomenon, carbon 14 gets into the atmosphere that is taken up readily by the plants through photosynthesis. Now when we eat the plants, it gets deposited in our system. As long as we ingest carbon 14 till we die, the ratio of carbon 14 to carbon 12 remains stable in our body too, just like in the atmosphere. But the minute we die, whatever carbon 14 left in our system starts decaying. The half-life of carbon 14 is 5730 years. I.e., after 5730 years, the carbon 14 would have decayed half the amount when compared to the stable atmospheric ratio of carbon 14 to 12.

OK ….here is a simple problem to solve. In your backyard, when you are digging for your gardening work, you are coming across a mummified body ;). You are curious and determined that the ‘mummy’ belongs to B.C period. How will you find out the age of that ‘mummy’?

You can use the help of carbon dating to find out the ratio of carbon 14 to carbon 12 that is currently present in the mummified body. Let us presume it was 1.2 х 10 ^–12 grams. Then compare it with the atmospheric ratio of carbon 14 to carbon 12, that is 1.3 х 10 ^–12 grams.

Use the exponential decay formula. Check out the previous blog of exponential function.

A = C e ^kt

Where C is the initial amount, k is the rate of growth, t is the time, and A is the amount after time t.

We know half-life of carbon 14 is 5730 years. We need to find the rate of decay.

0.5 = e ^5730k

5730k = ln (0.5)

k =ln (0.5)/5730

Now substituting in our exponential decay formula, we have,

1.2 х 10 ^–12 = 1.3 х 10 ^–12 e ^{ln (0.5)/5730 t}

1.2 х 10 ^–12/1.3 х 10 ^–12 = e ^{ln (0.5)/5730 t}

ln (1.2 х 10 ^–12/1.3 х 10 ^–12) = ln (0.5)/5730 t

5730 ln (1.2/1.3) / ln 0.5 = t

t = 661. 69 years. So, this mummified body does not belong to B.C period. Nevertheless, it is an interesting 600 years old ‘mummy’.

Here, is a question for you. How long do u think that this radio-carbon dating be used to calculate the age? We know that every 5570 years, the radio-carbon in any given material is halved. So, if we keep computing, by the end of 60,000 years almost all the radio-carbon would have disappeared. So , radio-carbon dating would not be used to date anything that is beyond 60,000 years old!

Argon-argon dating (which has a half-life of  1250 million years) and other isotopes  are used to find the age of the rocks that are millions of years old and from that the age of the dinosaurs are calculated. This process is called as radiometric dating.

Constant Error, Variable Error, Absolute Error and Root Mean Square Error – Labview

Imagine a target where archer A and archer B are trying their luck for a good shot. The following figure is the outcome. Now let us try to figure out who has done the best. Again it depends on what you want to see. The common error measurements are as follows:

 

 

 

 

 

 

 

 

 

 

Constant Error:

 

Constant error measures the deviation from the target. The formula for it is: Σ (xi-T)/N, where T is the target and N is the number of shots. It comes with a positive or negative sign which points out the direction of the error. Absolute constant error will give the absolute value of CE alone without mentioning the direction.

 

Variable Error :

 

Variable error measures the consistency of the shots. It calculates the standard deviation of the total shots. Its formula is sq.root (Σ (xi-M)^2/N, where M is the average shot.

 

Absolute Error:

Absolute error is the overall deviation without considering the direction. In constant error there is a danger of cancellations of error because of direction. However, the error due to bidirection gets eliminated in absolute error. Its formula is Σ absolute ((xi-T)/N).

 

 

 

 

 

 

 

 

So here is a question for you? Among A and B, who is the better archer? Are you bothered about the deviationper se or concerned more about the consistency? I would say bet on archer B than A because he has lesser variablity.

Root Mean Square Error:

 

This measures both the deviation and the consistency of the shots. Its formula is sq.root (Σ (xi-T)2/N).

 

 

 

 

Coefficient of Variation:

It is nothing but standard deviation divided by mean. It gives a clear picture about the deviation. If there are lots of tremors, then the standard deviation increases and so the coefficient of variation.

Check:
Constant Error, Variable Error, Absolute Error & Root Mean Square Error

Ref:

Richard A. Schmidt, Timothy D Lee, (1999. Motor Control and Learning (Third Edition). Human Kinetics.

Click on the image to get a close-up view!

The explanations about all the errors are here. Click the link below.
Measurements of Error

Calculating Earth’s Circumference: Eratosthenus (276-195 B.C)

Eratosthenus was the first person to calculate the earth’s circumference with a fair accurate measurement. It took us another 2500 years to confirm his calculation!

His calculation is very simple and logical. He was intrigued that at Syene, a southern city of Egypt the sun was directly overhead at noon time (which means there were no shadows) on June 21 (summer solstice). At the same time, there was a considerable amount of shadow in Alexandria, a city 800 km from Syene. If earth were to be parallel this cannot be the case. At both places there won’t be a shadow from any pillar or building.

But in reality, in Syene there is not a shadow, but in Alexandria there is a shadow. He thought logically about this problem. He could  conclude that  only if the two places are not parallel that can happen, which means that earth is not flat but is curved or rounded!!!

He applied simple geometry and found the angle of shadow from the pillar to be 7⁰. He extended the angle to the center of the earth which corresponded to 800 kms, the distance between Syene and Alexandria. He then easily calculated the circumference of the earth to be 41, 000 kms which is very true with less than 1% of error!

Imagine he did this feat 2500 years back and it took almost 2000 years for the mankind to re-discover his calculation!

Generalized Motor Program – Schmidt

Motor program concept says that our movements are pre-programmed in an open-loop fashion. Imagine a seed which has a blueprint of what it wants to become in its core. Especially this motor program concept is applied to explain fast movements that are around 100-150 ms. If such were the case, would it then be possible to have programs/engrams stored in our brain for each and every action? Could this immense storage of the motor program in brain feasible? Another question that can come will be for novel movements. What about certain movements that we have never done before? Do you think that program is also imprinted on our brain?

Generalized motor program concept gives a solution for both the storage and the novelty problems. It says that by modifying the parameters such as force and timing of the movement you could have a single motor program that could be customized for different patterns.

A common example would be the walking pattern: you could walk slowly or fast, trot or run slowly or fast. Shapiro (1981) in his experiment showed the ratio of timing of a single step (100%): See the diagram. Now this ratio was unperturbed when the subject was walking or running. What does it mean? In slow walking the timing parameter was slower and for running the timing parameter was faster in the common motor program that oversees both walking & running! Another example to think about is a familiar song one could sing quickly-slowly or loudly-in whispers. You can make out the original song due to its fixed ratio of the timing and note of the song. Here all you have done is changed the parameters of that song with respect to time and audibility. The same thing applies for the handwriting, whether you write in your right or left hand or with foot or manipulating a pen between your teeth. One could make out the unique pattern of an individual’s writing style!

Ref:

Schmidt, R.A. (1988). Motor control and learning: A behavioral emphasis. Champaign: Human Kinetics.
Shapiro, D.C., Zernicke, R.F., Gregor, R.J., & Diestel, J.D. (1981). Evidence for generalized motor programs using gait-pattern analysis. Journal of Motor Behavior, 13, 33-47.

Posture Biomechanics

Supposing you weigh 50 kg in your weighing machine, then what is your force when you are standing on the weighing machine?

We know, f= m*a, so your force is 50 * 10 m/s2 (approx. of gravity which is 9.8m/s2) = 500 N.

So, even though you weigh 50 kg on earth or moon, your force on earth is 500 N and your force on moon would be different as the gravity of moon is lesser than earth!

Another point to ponder is you are exerting 500 N on earth and the earth is exerting that equal amount of force (500 N) as a ground reaction force on you. Both the forces cancel out and you are standing blissfully unaware of whatever is going on. If the ground is not exerting an equal amount of force on you then you would pierce against the ground with your force like a metal coin in a glass of water.

So, what exactly is a force?

Remember Newton’s I law? Force is that which alters the state of rest or of uniform motion of an object.

Balanced forces result in equilibrium.

Here comes another interesting question. What is then a moment?

Whenever a force acts at a distance from a joint/pivot, then it creates a torque or moment that tends to rotate the object around that joint/pivot.

Moment = force * distance

The classical example would be a seesaw. You tend to rotate with respect to the pivot up or down. Going back to our previous example, when you are standing on the ground, you are exerting your force (in this case 500 N) to the ground. Where exactly are you exerting? Is the force goes throughout the whole feet or hypothetically at some point? Remember center of mass of an object? Brush up your center of gravity and line of gravity before you read the following paragraphs. Supposing the center of mass or center of pressure of your foot is mid-point between the foot and your nearest joint/pivot is your ankle joint, then you do have a moment generated here, isn’t it? The force is say, 3-4 cms away from your ankle joint, and then the moment that is created would be

M=500 N * .03m = 15 N.m.

i.e., a moment of 15 N.m is trying to rotate your ankle joint up (dorsiflexion). But again there you are, standing blissfully unaware of what is happening at your foot. So, what is preventing your rotation? The action of your plantarflexors! Yes, that’s right; they produce an opposing plantar flexion moment that opposes your ankle rotation up.

Next time when you are standing for a long time and wondering why you get calf pain, you know the answer at least…

Now, coming out of the foot segment, let us concentrate on the whole body. Where do you think you have your center of gravity and line of gravity? The center of gravity is approximately located anterior to S2. And following are the moments that result due to the position of the LOG either in front or behind the joint, which are opposed by the moments developed by the opposite groups of muscles/ligaments.

Newton’s Laws of Motion

1. Law of Inertia:

An object tends to remain in its state of rest (or of uniform motion) unless it is disturbed by an external force.

Therefore, al objects tend to resist their change of state.

Example, if the driver applies a sudden brake, you tend to fall forward with a jerk because your body still wants to move in the same speed and direction of the car.

2. Law of Acceleration:

The acceleration of an object is directly proportional to the force of the object and inversely proportional to the mass of the object.

Accleration = force/mass or

F=m*a

F is expressed in Newton. One Newton is defined as the amount of force required for a mass of 1 kg to accelerate 1 m/s2.

3. Third Law of motion:

For every action there is an equal and opposite reaction.

For example, if you slap the ground with your hand, you get pain in your hand. With whatever force u exert on the ground, the ground hits u back equally 🙂

Another example is when you are swimming or paddling, you are using your arms to push the water behind. What does the water do to you? It propels you forward.

Another common example is when you are walking. You place your foot on the ground and push it backward. The ground exerts an equal and opposite force to push you forward!

Index of all my blogs

Click on ‘read full post’ at the end. You can see the links!!!!!

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Basic Statistics

Basic Statistics
Variability – Standard Deviation and Error
Z Scores
Pearson’s correlation
Common Statistical Tests
Linear Relationship and Linear Regression
Regression Basics
T-Test Basics
ANOVA Basics
post hoc
Two Way Independent ANOVA
One Way Repeated Measures ANOVA
Degrees of Freedom (df) in Statistics”

Everyday Math
Logarithmic Function
Exponential Function &amp
Doubling Time
Radio-Carbon & Radiometric Dating
arithmetic-geometric series
Linear Relationship and Linear Regression

Intellectuals of the past
Zeno’s paradox: 495 b.c
Calculating Earth Circumference: Eratosthenus: 276-195 b.c

Labview
Save_Data_with_Header
Labview-To read column from 2-dimensional array
Constant Error, Variable Error, Absolute Error & Root Mean Square Error

MotorControl
Measurements of Error
Speed Accuracy (Spatial) Trade Off: Fitts Law
Linear Speed (Spatial) Accuracy Trade Off-Schimdt
Speed Accuracy (Temporal) Trade Off
Generalized Motor program – Schmidt

Personal
My encounter with elephants
Migration of birds

Physics
Electromagnetic Radiation
Newton’s Laws
Velocity and Acceleration – Basics
diffusion-osmosis
Friction-Basics
Posture Biomechanics