The Coolie Work Done Problem

The Problem

In schoool level science boooks it is often stated that coolies (porters) who carry your baggages on their heads scienntifically don't do any work. The question is, Is it reallly so? The answer is both YES and NO.
Let us see what the real answer is to this intriguing problem.

The Solution

Let us start by understanding the concept of work done.
Let us say that force acting on an object in such a way that it is moving in the same direction as the force itself.

Now the mathematical equation for work done is given as
W = F . S = F.S. cos(theta) where (theta) is the angle between force and displacement.

So in the above case force and displacement are in the same direction which means (theta) = 0 degree and hence cos(theta) = 1. Hence work done W = FS which will be meximum for the given situation.

In the above figure the force applied is at 90 degree to the displacement. In this situation (theta) = 90 and cos(theta) = 0. Hence work done W = FSx0 = 0. Hence no work done.

Now the situation for a coolie under the action of gravity terms is exactly like the second case. The cooolies has to apply force to push the weight (Force) in the upward direction and has to move (displacement) in the perpendicular direction. Hence his work done is zero.
So under the condition that the collie is moving horizontally only his work done would come out to be zero.

But wait !!!!

Don't rush to tell a coolie that he is not doing any work for he actually is doing.
The total work done by a coolie is as follows.

Work (coolie) = Work (gravitation) + Work (friction)

That means there are two aspects of the work done by the coolie. The work (gravitation) as we saw can be zero. So everything boils down to

Work(coolie) = Work(friction)

As we know friction is a non-conservative force. Which means it depends on the actual path taken. So let us try to understand the work done by a coolie through an example.

Example:

Let a coolie of mass 60 kg is carrying a load of 15 kg on his head. He goes horizontally from one place to another at a distance of 250 meters. Let the coefficient of friction between the coolie's shoes and the road  is 0.8. Now lets see what happens.

Solution

Work(coolie) = Work(gravity) + Work(friction)

Work(gravity) = F.S. cos(theta)
Since theta = 0 therefore     Work(gravity) = 0.(This is what is given in books)

Weight of coolie + Weight on his head = (60+15) kg x 10 m/sq.s = 750 N  (g = 10 m/sq.s approx)
Force of friction = mu x weight = 0.8x 750 N = 600 N approx = 600 N

This means to walk the coolie needs to exert a force of at least 600 N on the ground to move ahead.
Work(friction) = Force x Displacement
                        = 600 N x 250 m = 15000 J.

So the work done by a coolie is actually

Work(coolie) = Work(gravity + Work(friction)
                      = 0                    +  15000 J
Hence the total work done is not zero but 15000 J.

This means the books teach you only about Gravitational work done and nothing else. Hence never ever tell a coolie that he has done no work.

Life of a Huge Star v/s a Smaller Star

The Problem:

It has been found both theoretically and observationally that in comparison to smaller stars the bigger more massive ones die out earlier. Analgously it is like if two cars of same make A and B have fuels such as A has 10 liter of petrol and B has 50 liters then common sense tells us that B will go longer than A in distance but in case of stars it is exactly the opposite, which means that A will survive longer than B if A is less massive than B. The question is HOW and WHY?
So let us see logically how.

The Solution:

Let us first understand that when a star is born it is almost completely made up of  Hydrogen which sets off a fusion reaction to produce heat, light and huge outward pressure. This huge outward pressure is countered by the gravitational force inward. This gravitational force is responsible for the starting of the fusion reaction at the first place and then maintaining it.
Now let us assume two stars A and B. A starts with 100 units of Hydrogen and B with 100000 units. Automatically their masses differ by 1000 times with B being more massive. This means that the gravitational pull of A will be 1000 (approx) times less than B and hence when the respective fusion reactions begin A will burn much, much slower than B.
In a reverse way we can say that since B has a gigantic mass its gravitational force will also be massive and so will be the outward pressure due to reaction. More fuel will have to  burnt more rapidly to counter the inner gravitational pull and to keep the star stable. So that will lead to a rapid usage of fuel leading to a smaller life span in comparison to the smaller star.

Krackling of Knuckles

The Problem:

We all, almost on a daily basis, stretch our fingers and create a krackling sound out of the knuckles. We exclaim in hindi, "haddiyan chatak rahi hain". Meaning, "the bones make the sound". But is it really so? Not exactly. It has hardly anything to do with the bones. Read on.

The Answer:

Our bone joints of the body are lubricated using a lubricating liquid which is, of course, naturally existent in our bodies at those joints. So is the case with our finger joints too. These lubricating liquids get filled with nitrogen which seeps into them from our blood capillaries. When we suddenly stretch these joints the pressure inside the liquid falls rapidly thereby converting the dissolved gasses into bubbles which soon after explode creating shockwaves which are heard as krackles. This process is known as Cavitation. 

So next time someone says, "haddi chatkana" or "crackling BONES" you can very well correct him that it is called cavitation. 

Comment

Why do the astronauts seem to be floating inside the space stations and shuttles?

The Problem:

You must have seen, on TV shows, that astronauts seem to be floating inside the space station or the space shuttle. It seems that they are weightless. And they actually are. But the question is how and why are they in that condition?

The Solution:

This is a classic question and one of my favorites which I have asked to numerous people and I usually get one of the following answers:

1. There is no gravity in the space. (90-95% people give this answer).
2. The gravitational pull is balanced by centrifugal force. (Some more learned guys give this answer).

Unfortunately both are wrong. Lets us see why.

1. The force of gravitation is inversely proportional to the square of distance. The space stations are at a height of nearly 400 kms. Now at a height of 400 kms, if you so dome calculations, you would find that the acceleration due to gravity is 90% of that on Earth's surface. So if you weigh 100 N on Earth then on space station it would be 90 N and not zero as you might think. SO it is definitely not ZERO GRAVITY out there.

2. Take a stone attached to a string and whirl it around. Do you really think that the stone would feel weightless? Think for yourself.

SO the question is what is the real answer. 

Weight is a force with which the Earth attracts everything towards itself. The acceleration imparted by Earth is 9.8 m/s^2. Now if you are in an elevator and it accelerates upwards at an acceleration of 9.8 m/s^2 then your weight will double out.This is because the weight tends to add up only when there is a normal reaction being imparted by the surface on which you are standing. In case of falling down the surface on which you are standing also tends to be in free fall with the same acceleration due to gravity. This means there will be no normal reaction and hence the apparant weight of yours will be zero.

This is precisely what happens inside a spacecraft. It is continuously freely falling towards the center of the Earth. Which leads to a weightless condition. The only catch is that the spacecrafts have a tangential velocity of nearly 25000 km/h which tends to make them go around the Earth in an orbit.

It is like the spacecraft is falling towards the Earth and the Earth is curving away from it thereby forcing the spacecraft to never really reach the Earth's surface.

Comments

Does string telephone work? If yes, then how?

The Problem:

As a child we all have made our very own string telephone and talked to our friends with most of the time with very disappointing results. Sometimes we could hear the voice of the friend and most of the times we couldn't. The question is why sometimes we could hear a faint voice and at other times no voices at all? And how does it work at the fundamental level? 

Read on.

The Answer:

Let us start the answer from answering the last question first. How does the telephone actually work? If you remember the telephone would look like the following. 

Now there are two components to this entire system. Two pieces of cups, better if it is metallic. And one strong string, again better if it is metallic. 

They are connected as shown. 

So this was all about the construction. The second part is tricky and it is here why most of us never got to make these work.

If you look at the first figure the string attached to the cans has to be as tout as possible. The reason is given below.

When we speak in the can the can vibrates with the sound vibrations that we produce. These vibrations in turn are passed off to the string attached to the can. The vibrations then travel through the string and does the reverse process of vibrating the can and letting the other person hear what you say. 

For this entire process to be successful it is important that the strings be tout so that the tension along the string is evenly distributed and the sound/vibrations can travel properly without much resistance. 

So if you really want to make a string telephone make it using metal cans and keep the string tout. And ya you will need to practice a bit to find out what pitch of your voice will reach the other end as the cans may not properly vibrate thereby rendering the entire thing useless.

Comments

Why do chalks squeal when writing on the chalk boards??

The Problem

You all must have seen that chalks make a squealing sound when teachers use them to write on the black boards. It is an usual phenomenon which as a student and, now, a teacher I have always hated. Can this be corrected? Read on to find out. 

The Answer

As a teacher when I hold the chalk in a wrong position or orientation with the board the chalk tends to stick to the board. Then when I try to push it forward to write on the board the chalk "slips" on the board and vibrates along it. While vibrating it hits the board several times per second creating the squealing sound. As the chalk moves faster the squeal tends to die down and the chalk starts to "stick" back on to the board preparing for the next round of squealing. 

Better quality non-dust chalks can reduce the squealing considerably.

Comment

Introduction to HOWs and WHYs of Science in General and Physics in Particular.

Hi all.
I have been thinking for a long time to start a blog for everyone, but specially my students, who would love to know the answer to some intriguing problems or observations that one might come across in day to day life.
My answers are strictly based in Physics (Science) and some are borrowed from various sources which includes books as well as websites.
I hope you will find it interesting.
Do leave a comment if you like it.
Thanks.