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 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
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?
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?
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 |
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 |
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?
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