What if we simulated Galileo's Leaning Tower of Pisa Experiment?

We've heard about Galileo's famous Leaning Tower of Pisa experiment. As mentioned earlier, we won't take part in the debate as to whether he actually conducted the experiment or not. How does it matter anyways.We should let it be, mainly because, Galileo was a great guy of his time, helped us understand a lot of things, and also because, true or not, the experiment helped us remember the fact, "Acceleration due to gravity doesn't depend on mass". Good enough for me. What do you say? However, please stay with me through this post where we think about the consequences of doing the experiment on our own (actually watch someone do it for us). Would we learn something new? something worth the 'Aahaaaa'.


We start with a moment of reflection. When we dropped the ball and the feather, the ball won the race. Race between the crumpled and the non crumpled sheet, the crumpled one won. What happens when we drop a shoe and a ball? They fall at the same time. Hmmm.. maybe the surface area not much of a difference? maybe ... Let's make it more obvious now. How about a watermelon and a muskmelon? Try dropping them. They fall at the same rate too? What are we missing out here? Now's the time. Imagine it's your birthday and I give you a present, all wrapped in red paper with a lovely white ribbon and ask you to wait till it's 12 to open it. No no.. Don't open it yet. Read on!

At this point, I would like you to see the lovely and interesting video about a tower and dropping melons from it, present in this website. For those of you who can't wait till the end, check it out till 3:20. What you see is the watermelon actually falls faster than the muskmelon given a considerable height. (is all you need to grab from that video for now) What does height change, how does it affect their behaviour? You hear Derek from the video attribute it to air friction. He's right. Let's think. Why didn't air friction show up when I dropped it from my hands while I was standing on the ground? There was air there too.

Let's look at the melons and their falls closely. Two forces acting on them. Gravity which is a downward pull, Friction which is an upward pull. Two forces. Acting on the same object. Different magnitude. The force of gravity acting on the melons doesn't change during their journey. However, the friction changes. It keeps increasing. Why? The melon is falling down with an acceleration. Which means, its speed is increasing. More speed, more particles bombard against the melon, more friction. To get a feel of this, imagine you sticking your hand out from a car that's moving at 20kmph. Now compare that to the force on your hand when the car is moving at 80kmph. More force isn't it? (Not to try at home. Sticking hand out of the car is definitely not advisable and you know why)

As the melon falls down, the friction or the drag force they call it, keeps increasing and keeps opposing the downward gravity force. And at one point of time, they equal and cancel out each other.Now, the muskmelon, smaller mass, smaller must be it's gravity force and as it falls down sooner will the airfriction force equal the gravity force (as compared to the watermelon).Isn't it? Just to make things clear here, let's assume some random numbers (argument sake). Let's say the gravity force on the watermelon is 40N and the gravity force on the musk melon in 20N. Before they start falling both their drag forces equal 0.After the drop, say after 10 seconds, the airfriction force builds up to 20N, which equals the muskmelon's gravity force. At this point both the forces cancel out for the muskmelon, but for the watermelon, the gravity force is still the better force. Crystal clear.

Another super question. Equal opposite force acting on the muskmelon. Will it stop in mid air now ? Ofcourse not. In the absence of any force, an object will continue its state of motion or state of rest. So the melon will fall at a constant speed. ( Meaning zero acceleration, which adds up, because that would mean zero force, and that's exactly our scenario now)

We said, zero acceleration, meaning constant speed. Meaning , the muskmelon will stop accelerating and will fall down at the same speed till it reaches the ground. This speed is called terminal velocity. While the muskmelon has acquired its terminal velocity, the water melon is still accelerating. Which implies, the watermelon will reach the ground before the musk melon.Explains what happens in the video isn't it?

Try and apply this new concept, terminal velocity to our earlier questions. The shoe and the ball dropped from my hand. The watermelon and the muskmelon dropped from my hand. It so happens that the distance from my hand to the ground is not sufficient enough for the objects to reach their terminal velocity. In the event that both the objects don't reach their terminal velocity, both of them accelerate at the same rate and reach the ground at the same time.Wonderful isn't it! I like the feeling when things fall in place in my head.

At this point, let's sum up quickly. Falling objects in the absence of a medium fall at the same rate. In the presence of a medium, we need to take into account the upward drag force acting on the falling object. Upward drag force increases with the speed of the falling object. In the duration of the fall, if the drag force equals and cancels out the gravity force, a constant velocity called terminal velocity is reached. From then on the object doesn't accelerate. So in any race, if the object reaches its terminal velocity before the other object, it falls slower.

I would like to quote a good application of this terminal velocity, to help you appreciate the newly learnt concept. Terminal velocity is what aids the parachute.

Imagine a sky diver jumping off his plane. At first, drag force is zero, and it slowly increases as he falls. At some point, the drag force equals the gravity pull, and he attains a terminal velocity. Now, when he opens his parachute, a sudden gush of drag force is created. Which leads to deceleration, meaning, reduction in speed. As the speed reduces, the drag force also reduces and finally equals the gravity again. But this time, attaining a much lower terminal velocity, thereby protecting him from his fall. Checkout this video I found on the internet to help your understanding of the above said.

What a beauty isn't it, this 'Terminal velocity'. That my friends, is the gift that I promised earlier in the post. Happy Birthday and wish you many more ( of these gifts!!)

Race between the ball and the feather!

Today's discussion is going to be real simple. As in, a real simple everyday scenario for which we all know the answer to. Take a ball, any kinda sorta ball. Take a feather. Any kinda sorta feather. Ball in one hand and the feather in the other. Hold both the arms at the same height. And drop the items. Who do you think wins the race ? I know. I know. It's definitely the ball. And that would be right. I'm sure everyone who's reading this could've come up with that. Let's talk about the why-factor now. Why did the ball reach the ground first and why did the feather come floating down? Time for the thinking hats ...

The simple explanation is, heavier things fall faster? I would ask you - "Why is that so my friend?" Well, some of you might say "That's how it is." Some of you might say - "You know, the heavier the object is, the more it gets pulled by the Earth's gravity and the faster it falls towards the Earth." And I would say "No no my friend. Adjust your thinking hats, time to think a little deeper." And would give you a new simple experiment to try on, that might change your world upside down!

Take two A4 sheets of paper. Tear one into a half, and if you have a 3 year old, ask him to crush it into a ball (believe me, he would love to do that) . So now, you have two things with you. One in each hand again. A sheet of paper as is, and half a sheet of paper crushed into a ball. Obviously, the full sheet of paper is bigger and heavier than half a sheet of paper. Obvious isn't it? Now drop both of these things at the same time, from the same height. And tell me which one reaches the ground first. Was it the half sheet or the full one? It was the half sheet wasn't it? Doesn't it mean that the lighter object fell faster this time? Does this defy your earlier assumption that heavy objects always fall faster? Yes it does. Before we go on to the why-factor and the explanation that would follow, I want to mention two great people from long long ago and so long ago.

Aristotle

Aristotle is one. He's from 384 BC. He said "Heavier  things fell faster, the speed being proportional to the weight". Before we judge him, we should know that how he saw the world  back then was completely different from the world we see now. Back then, not much of man made stuff, I mean cars, machines that could move, so the only thing they saw moving back then, was animals, birds, people. Hence, he believed, things moved to fulfil their purpose. Birds moved to some place they would rather be, due to some reason, and that motion was governed by will. And people followed his thoughts (this is just tip of the iceberg, he did a lot of contribution to science his time) for like 200 years till another person called Galileo came along.

Galileo ... where do we know him from? Yeah.. yeah.. the telescope guy isn't he? What did he do? We have documentation to believe that this guy said something like, objects fall at the same rate and the rate of fall is

Galileo

independent of their masses. That is to say, that both heavier and lighter objects fell at the same rate. And like how Mr Newton had his apple-on-the-head-eureka-moment, Galileo had this Leaning-Tower-of-Pisa-drop-balls experiment story.That is, it seems he went to the top of the Leaning Tower of Pisa and dropped two balls of different masses at the same time and from the same height and observed that they reached the ground at the same time, thereby defying Aristotle's claim so far! Well, there's a lot of controversy over if Galileo actually climbed the tower and if he actually dropped the balls or was it a thought experiment. I say friends, that's not important. What's important here is, he's given us food for thought. Let's chew in to the food or simply hold on to the thought, and give the man some credit and listen to his further explanation.

He says, let's take two balls. One heavier than the other. Let's tie them to each other with a string. Now let's drop them together from a building. What should we expect ? From what we know, from Aristotle, the heavier ball must fall faster, but this time, it is tied to the lighter ball by a string, so the slowly falling lighter ball should be hindering the heavier ball's motion by pulling it back. (That is, the string holding them together would be taut now) Which is to say, the heavier ball now should fall a little slower because the lighter one is holding it back. Now, coming to think of it, we've tied the balls together. Now the combined system of balls is heavier than the heavier ball alone isn't it? Which according to Aristotle should fall faster than the heavier ball alone. If you think of it this way, then, the balls should fall faster than if it were just the heavy ball alone. So, if we follow Aristotle's theory with the heavier-ball-tied-to-the-lighter-ball-system-of-balls, we end up with two contradicting outcomes. Something should be wrong isn't it?

Newton

Amongst all the new confusions that I've helped create in your mind today, I know you are wondering something else. How come today there's mention of two new guys and not a word about Mr.Newton. Well well friends, let's use our favourite man Newton's theory or laws of motion to come up with our conclusion about heavy and light balls and their motions.

We are talking about balls and their falling towards the ground. Bring on the one word that looks like it can answer everything, 'gravity'. Next, bring on, our man's gravity equation .

F = m1 * m2 * K / r2
(Read it as , m one into m two into K divided by r squared)

Next, I want to know the rate of fall of the object. Which means I want its acceleration. Bring on our man's formula for that.

F = m * a
(Read it as , force equals mass into acceleration )

Strap on your seat belts and get ready for your 'Ahaa' moment. Let's try and analyse the heavy ball. What is the force of gravity on the heavy ball? Using the first equation,

Force on heavy ball = mass of heavy ball * mass of the Earth * K / distance between their centres squared.  
F = m * M_earth * K/ r2     ---- equation 1

I want to find the acceleration of the heavier ball when it falls towards the earth.

F = mass of heavy ball * acceleration of heavy ball.
F = m * a
a = F/m  -- equation 2

Looking closely, we know that the force acting on the ball is gravity. So substituting the value of F from the equation 1 into equation 2, we get this :

a = M_earth * K / r2

What do we have here?  We are talking about the acceleration of the heavy ball. But, nowhere in the equation do I see the mass of the heavy ball. Hey, Galileo is right after all. The mass of the ball doesn't play a role at all in the acceleration of the ball towards the earth. Well that explains the A4 sheet experiment that we've done at the start of this post. Mass doesn't matter. It's 'Ahaaa' time. Say it. Feel it. Let everyone know !

Hold on, hold on. Another question rearing its ugly head. Why did the feather fall at a slow rate then? and in the A4 sheet experiment, why didn't they both fall at the same time? There must be another invisible force. Who is he/she? It's air friction. When an object falls, or moves for that matter, it collides against the air particles and bombards into them, thereby disturbing their state.  And they resist. Wouldn't you if someone pulls the ground beneath you? I would. As it is a resistance to the motion, it opposes the motion. This force must depend on the shape of the object then, right? Depending on how much of the object/surface area of the object pushes the air particles, should govern how much air friction. That explains the feather and the ball behaviour. The feather has more surface area than the ball. That explains the A4 sheet experiment. The full A4 sheet has more surface area in contact with the air than the crumpled up half sheet. (Taaaadaaaa !)

So, acceleration due to gravity is the same for all objects, but in the presence of a medium or air in this case, we see a difference in acceleration. That is to say, in the absence of air and its particles, the objects should fall at the same rate right? Yes, absolutely. In vacuum, the ball and the feather will fall at the same rate. Would you believe the astronauts actually tried this experiment on the moon. See it for yourself here. I have goosebumps. Do you?

What do you call a prologue that's a little late !

Hey, sorry, I'm not going to answer the question in the title. I don't even know if something like that exists. A prologue that doesn't precede the story! Defies its very purpose isn't it. However, I heard some wise man/woman say, "Better late than never" , so I'm going to write the prologue now. Better now than never right ?

An ordinary day, my friends and I meet up in our usual hangout spot to discuss the nitty gritty details around which each of our lives revolve. No no, not gossip. Definitely not. I would call it exchange of 'useful' information and 'life lessons' !!

One such day, my dear friend says "I read a page from the kids encyclopaedia to my elder one everyday. Some simply amazing stuff you know". I said ,"Wow. that's something nice. Tell me about it." She said about Earth's gravity, it's pull on the moon and many other things and how her 6 year old was able to understand and make correlations. She seemed thrilled. I was too. We wanted to make correlations and apply what we'd learnt too. Thus started our discussion. Very basic questions. Why does the moon go around the earth and not stick onto it like how we all manage to stay grounded. Why didn't the Sun pull the moon to it's side and how it lost the moon to the Earth ? Did it actually lose the moon to the Earth ? Does the moon have gravity? Why doesn't it make the Earth go around it ? And so on and so forth. We went back home with many such basic questions.  I'm sure we all faced these questions in school either with multiple choice answers or in the essay-questions. I've come beyond schooling now.Way way beyond. I knew all the concepts. But something was missing. Something. Like a missing link maybe ! Point to note here would be , both of us knew that gravity would answer almost all the questions above.We weren't satisfied. Needed to dig deeper. Thus started my quest for these basic but beautiful things that we often take for granted.

Just a day later, I went for a train ride with my 3 year old. His first train ride. He diligently spotted the stones on the train tracks and asked me with wide eyes " Ma, why didn't they clean the tracks? It's full of stones. Or did they put it there for some purpose?" For a minute, I was dumbstruck. Not because I didn't know the answer to his question, what bothered me more was that, why didn't I think of that question? I'm bigger, I understand things better, and hence that question should've come to me first. Then I realised, maybe that's the problem. I'm bigger! I take things for granted. I've lost the need to question. That precise moment is when I realised that I should definitely encourage my son and make sure he doesn't lose that wonderful habit of questioning things (the why-factor I call it), in the process of "growing-up". I immediately appreciated him for having come up with that wonderful question, I quietly did a google from my phone ( many thanks to the google guys and the fact that technology could save me from a little embarrassment) and explained him the 'ballast' in words he would understand. He gave me a huge smile and that filled up my heart!

The day I went home with both these feelings, is the day I gave the search engines so much work, so much work, looking for all related articles on the internet. I read, I read and I read extensively. I also have this obsessive compulsive disorder where I have to impart my newly learnt knowledge to someone, (sometimes it is the first random friend/acquaintance I see ) as soon as my mind has absorbed it. No wonder I have a very few and handful of them !! The point I'm trying to make here is that , my urge to let people read and understand what I just learnt was so huge that I completely skipped this small piece of post and went straight on to the explain the Moon's behaviour first, wherein I should've explained mine !!

Anyways, that's the story today. The articles that precede the prologue(!!?) and the articles that follow are all very simple and basic physics/science questions, which I didn't have time to enjoy when I was schooling. But, which I find absolutely amazing. Gives me the 'aahaa' moments. Read on and say "Aaaahaaaaaaaaaaa " !

Is the moon pulling the earth towards it ?

We said earth has gravity. We also said sun has bigger gravity pull. Does the moon have one too? If so is it pulling us in? You know, Newton, when he had his famous eureka moment, sitting under the apple tree and watching an apple fall ( you know the rest ) he said, even the apple has gravity and exerts a pull on the earth! To understand this better, we need to dig a little deeper into gravity and the factors influencing it.

Let's start with wikipedia's definition of gravity. It is a natural phenomena by which all physical bodies attract each other. Well, there is our answer. Moon being a physical body, is pulling the earth too. But how much is the pull? Didn't Newton think of it ever ? Sure, he did. And has thought of it enough to come up with a theory and a formula for it (Hail Newton )

F = K *m1 * m2 / r2

(Read it as, m one times m two divided by r squared. K being some constant)

Please don't get intimidated. All that he means is, gravitational force depends on the mass of the two concerned bodies and is inversely proportional to the square of the distances between them. That means, more the mass of the objects involved, more the force. And lesser the distance inbetween them, more the force (kinda)

Let's try and apply this formula to both the Earth and the Moon. Lets say m1 is the Earth and m2 is the Moon and r is the distance inbetween them. Sounds simple. But wait, hey , if I subsitute their values I end up getting one value for f, or force. Does that mean the force exerted by the Earth on the moon is the same as the force exerted by the moon on the Earth? In that case, why dint the Earth go around the moon? Or even better question, equal and opposite forces, why didn't they cancel out each other. Hmm... bit of a puzzler isn't it?

It actually isn't that much of a puzzler if you already knew Mr.Force quite well ! Let's go to wikipedia again, this time for definition of force.
It is something that tends to change the motion of an object. Can be described by intuitive concepts such as push or pull. 

Let's handle the second question first, Equal and opposite forces should cancel each other, true. But when ? When they act on the same object. Here the forces act on different objects, that is, the Earth's gravity acts on the moon and the moon's gravity acts on the Earth. So two different objects. Cancellation is out of the question now isn't it?

The first question now. The same magnitude of force acts on both these huge bodies. Looks like how they react to it depend on them. That's it. That's the answer.Do you see it? The Earth being so huge, requires more force to make it move. The moon being comparatively smaller, is easier to be influenced, as in, the amount of force exerted by the Earth is sufficient to move the moon, but the same amount of force exerted by the moon is not sufficient to move the Earth, or atleast so we see! Let's just say the Earth is stronger than the moon.

Looking at it with the Force formula

F= m* a

(Force equals mass into acceleration )

This equation also says the same. Given the same force, the body with the bigger mass moves lesser than the body with a smaller mass. How much they move and do they move at all, will all come to you if you put in the numbers there, but hey, I always shy away from big number calculations. All I need is an understanding and I'm content.

So.. the moon does try attracting our Earth with the same force. But our Earth says, no Mr.Moon(/Ms.Moon), I want you to come to me!

Moon doesn't crash onto the Earth, ok! Why doesn't it crash onto the Sun!

Thanks to the previous post, we know why the moon doesn't crash into the earth. Like how we all know that the moon revolves around the earth, we all also do know that the earth and the planets revolve around the sun. ( with a similar kind of explanation , must be ) That said, the sun has its own gravity too. And the Sun is hugggeeeeee. No denying that ! So why didn't the sun pull the moon to revolve around it, and how come it gave the moon up to the earth? Time to put our thinking hats on!

This explanation is relatively simple this time. No need to brush up on newtons laws.  One could say, the moon is closer to the earth than the sun. So the moon feels the earth's pull more. There is more to the gravitational force than just distance. The mass of the objects involved matters too! And imagine the size of the sun with respect to the earth ( I'm not going to quote Googly numbers here, but you get it right, it's very very huge) so the sun's pull ends up being greater than that of the earth's. Still moon goes around the earth. Why??

Let's look at the big picture. Picture with the sun, earth and the moon. The moon goes around the earth and the earth goes around the sun. If you think over that statement carefully, the moon is eventually going around the sun. Normally the motion of the Moon around the Sun is drawn as a kind of Spirograph pattern, but its actual motion is basically the same orbit as Earth with a small wobble to it. Let's leave the calculation of how exactly the path would look like to our wonderfully able astronomers, let's just be content with the fact that the we understand that the moon is influenced by both the earth's gravity and the sun's and it moves accordingly !

Some of you could ask, why didn't it fly off the earth and just go around the sun? We've discussed at length in our previous post about why the moon couldn't fly off the earth. It needed the escape velocity which it didn't have. Maybe if the earth's gravity suddenly ceased to exist, among all other things that would happen ( like floating cows for example ) the moon could maybe run off and get around the sun . How weird. It's just a thought ! 

Ever wondered why the moon doesn't crash onto the earth?

All of us ( I can safely assume it's most of us)  love looking at the moon. It looks stationary isn't it ? We've heard that it goes around the earth. Ever wondered why? Well, you ask any adult , and pat comes the reply - "it's earth's gravity man, elementary my dear Watson " . Well, if u look a little deeper, earth exerts gravity pull on the moon. Ok... But like how we stay grounded to the earth, why doesn't the moon crash into the earth because of gravity? How does it orbit the earth ? Now that's something we could think about .

To understand this, we need a fair understanding of gravity or rather the gravitational force. To be more precise earth's gravitational force . What is gravity? A pull exerted by the earth on objects. And for an understanding of force, we need to know newtons laws of motion ( they really go a long way in helping us understand. Thank you Newton ! )

Let's dig into gravity a little later. For now let's say, it's a "force exerted by the earth pulling objects closer to it or towards it " ( crude explanation for now ) let's try and analyse force. And so, let's look at newtons law of moving objects or the first law of Newton .
"An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force"

That having said, imagine I have a ball with me and I hold it in my right hand and just drop it. It goes down . That's not new. We've seen it many times. Now I do something little different. Instead of just dropping it onto the ground, I throw it forward. Point to note here is that I 'throw' it, that is, exert a force on it. Now what happens? The ball moves a little forward and then takes a curve and hits the ground. Easy peasy. Again, nothing we haven't seen before .

A good point to think about here would be, in both the cases, gravity exists. Why did one ball fall right down and the other move forward and fall ? The only difference was the force we exerted on the ball in the second case when I 'threw' it forward. Gravity , tried pulling it towards the earth. But the ball already had some speed/velocity here because of the throw. The ball moved forward because of it. And because of air friction ( that's another discussion totally, let's do it later. Let's assume friction hurts the motion or opposes the motion of the ball ) the ball lost its velocity and gravity got better of it, thereby eventually pulling it to the ground. So, gravity force tried altering the path of the moving object.

Let's extend the experiment a little further.( I better give Newton the credit. It was his experiment or theory rather ! I just read it in the internet ) so what he did,  he got on to a mount ( or so says the Internet ) with a cannonball in hand  and first like we did, dropped the ball. It went down. Then threw the ball. It took a forward motion and fell down in a curve. Now , he threw the ball with a little more force. The ball went further and fell down.  Little more force, the ball would fall further away. The earth is not a rectangle but a sphere. Imagine if u threw it away with little more force this time . It would not fall off the earth because of gravity, but will fall near the equator ( say ) . More push, the ball might fall near the South Pole. More push, the other side of the equator this time. A little more push and it might finish one whole circle and hit u at the back of your head !!! Isn't that something ?
[ Note : please read 'newton's cannonball' from wikipedia for exact details and an animation of the cannon ball and its outcomes. The above para is a simplified version ]

What is happening all this while is that, the gravity is altering the path of the ball which wanted to move in a straight line. And how far the ball went depended on the speed it had with it earlier.  Let's try and apply this to the moon. Moon wants to move in a straight line, but because of the gravity, it is constantly falling towards the earth. And goes one full circle. I know I know, you have a million more and new questions popping into your head now. Keep it mum just for a little while longer. I would like to take a small detour now.

Imagine I have a ball tied to a string and I fling it into a circle. The centre of the circle being the start of the string or my hand. The ball moves in circles. If at any point I cut the string, will the ball fall down? No? It will fly away tangential to where it is while I cut the string , and then eventually fall down.  Now the string is gravity. The ball is the moon. If the gravity one day disappears then the moon would go flying away. So far so good ?

In the ball example,  the ball keeps on moving coz of my exerting a force. In the example before that the ball completed one big circle and hit the back of my head and fell down. But the moon keeps going round and round. What's different ? Air friction.  The air particles bombard against the moving object and slow it down . In the absence of air or otherwise in vacuum, no opposing force and we could keep the ball moving on and on.

In the example above , I gave the ball its initial speed by giving it a fling. Who gave the moon its speed? Our explanation forces us to assume that the moon has a velocity of its own. Right ? That maybe, the moon was already moving in a straight line after it was born or because of some complicated spatial parameters. And it happened to come near the earth and got drawn into an orbit because of earth's gravity! Seems like an explanation isn't it ?

The velocity with which the moon goes round the earth is called orbital velocity.  That's how we send man made satellites into space. Like how I could make the ball move one complete cycle can I make the ball fall off the earth? Or escape the gravity pull?  That's possible too. Give it so much force or velocity that ( in the absence of air friction to slow it down ) it could be so much greater than the pull of the earth that it could go flying away. That's the escape velocity.

To sum up, the points to take back home from this post will be, the combined effect of the moon's own speed and the gravity pull of the earth together makes it go into an orbit around the earth. The speed the object(here the moon) possesses when it orbits another object(here the earth) is the orbital velocity. The speed required to escape the orbit is escape velocity.

We've given ourselves a new reason to feel happy. The moon is going to be with us for while ( touch wood ) and better so, we know why :)