Fast and lazy, or slow and active

D. Leela, Chennai

"We had fun with the falling bottles last week-end, didn't we?" asked Leela. 
"Yes," said Maya, "and I also found out something nice in school."
"What is it?" asked Leela. 
"It was Amrit who found out. We had this ball with the rubberband attached to it. You are supposed to keep hold of one end of the rubberband and throw the ball and try and catch it."
"Yes, I know," said Leela impatiently. "We bought one in Delhi near the India Gate, don't you remember? I wonder where it is."
"Anyway," continued Maya. "We stapled the free end of the rubberband to the bottom of a paper cup. On the inside. Then we would hold the cup in our hands, try to throw the ball and then catch it back in the cup."
"It must be easy," said Leela at once.
"Wait, that's not it," said Maya. "Well, as I said, it was Amrit who was throwing the ball and he accidentally let go. That is, he let go the ball as well as the cup! When the ball started to fall, it fell right into the cup. Then the cup and ball fell down together!!"
"So I suppose all of you tried to repeat it," asked Leela.
"That was just it," said Maya. "Every time we tried to repeat it, it worked! I mean, we thought it was a coincidence that the ball fell straight into the cup the first time. But each time the ball fell, it always fell into the cup. It was very strange."
"I can't understand it either," said Leela. "Let's ask Mother."
Just then a familiar voice called out. "Leela! Maya! Are you there? Can you please bring me the paper that is under the paper-weight in your room?"
"Yes, Amma, I'll do it," said Leela. 
"No, me," shouted Maya, reaching out for the paper-weight. At that moment, Leela grabbed the paper and neatly yanked it out from underneath the weight. Both of them looked at the weight; it hadn't even moved.
Both of them forgot Mother and her paper. "Let's do it again!" they said.
Leela put the paper back under the weight and said, "OK, you try this time."
Maya gingerly caught hold of one end of the paper and pulled cautiously. The paper slid towards her, along with the paper-weight which moved along with the sliding paper. 
"No, both are moving," she said. 
"I think it had something to do with the speed," said Leela. "Try pulling it out faster."
Maya bunched up the ends of the paper and yanked hard on it. The paper-weight promptly rolled over.
"No," said Leela. "Don't fold or crease the paper. Here, let me try." She smoothed out the paper, put it back under the weight and yanked on it. The paper smoothly came out in her hand, while the paper-weight had again barely moved.
At that moment, Mother came in to the room, wondering why the children had not yet brought her the piece of paper. The children promptly showed her their discovery.
"Ah, yes, inertia," she murmured. 
"What's that?" asked Leela. 
"It just means that objects are like you, basically lazy! If you pull fast enough on the paper, there's not enough time for the paper to `tell' the weight that it is moving! So the weight just stays in place, since it prefers to stay at rest. It's just plain lazy. But if you do it slow enough, the weight has enough time to feel the motion of the paper and it decides to move along with it -- the friction causes them to move together."
Both children looked puzzled. "But what does inertia do?" asked Maya.
"I've learned about forces," said Leela. "If you apply so much force on an object, it will move so much distance. What does fast or slow have to do with it?" 
"Let's do another experiment," said Amma. She cut out one half of an old greeting card and placed it on a glass tumbler. Then she put a coin on the card.
"See, if you move the card slowly, the coin will come with it, but if you yank the card, or even flick it with your finger (like playing carroms), the card will fly off and the coin will drop into the tumbler."
The children played this for a while. Then Leela said, "I still don't understand what inertia actually means. How does it make the force larger or smaller?"
Mother said, "There are many things involved. For instance, take the paper-weight or the coin. They have weight because they are pulled down by Earth's gravity. In fact, weight is just a special force. Now Newton, a famous scientist, said that the action of every force has an equal and opposite reaction."
"That's Newton's third law," said Leela. 
"Yes," said Mother. Then she looked at Maya and said, "Think of it this way. If gravity pulled you to the centre of the Earth, why are you still here? Why are you simply not sinking through the Earth and going towards its centre?! That's because there is an equal and opposite reaction to the force of gravity. This is the solid ground pushing you upwards so that you don't fall through.
"What's pushing the Moon up then?" asked Maya.
"A very interesting question," said Amma. "But let us keep that for later and stick to inertia. I have one more fact to tell you. When you pull or push some object, for it to move it has to overcome friction."
"Yes, I know that," said Maya. "Rough surfaces cause more friction than smooth ones."
"Yes, but the interesting fact here is that the frictional force is proportional to the reaction force. It depends on the weight of the body and the smoothness of the surface but it doesn't really care whether the cloth is being moved fast or slowly."
"How is that fact going to help us here?" asked Leela. "After all, we are looking for something that differentiates between slow and fast motion."
"Perhaps it's not so easy to understand after all, but let me try," said Mother. "We have said that what is important is the frictional force, but what is really relevant is how long this force lasts."
"Ha!" said Leela. "At last we see the dependence on fast and slow: it's the time for which we pull that makes a difference."
"Exactly," said Mother. "If you pull slowly, the time duration is longer. In physics, you will say that the impulse (= Force X time duration) lasts longer. If the time is short, the impulse is small."
"Why is it that the impulse is important? Normally, we talk about forces and their effects," asked Leela.
"Do you recall how forces affect objects?" asked Mother.
"Yes, it's Newton's second law. Every object remains in a state of rest or uniform motion unless acted upon by an external force. I guess that means when a force acts on a body, it changes its speed. In fact, I know that it causes it to accelerate, or sometimes decelerate, since we write F=ma, where F is the force, m the mass and a the acceleration."
"Yes, that's the key point. Change in speed. Actually, velocity times mass is called the momentum of an object. So you can also say that a force causes an object to change its momentum."
"You will see that Force X time has the same dimensions as momentum. Hence it is the impulse that changes the momentum of objects and that is why impulse is what ultimately decides whether the coin will move with the card, or be lazy and fall into the glass. In general, this whole complicated explanation is simply replaced by the one word `inertia'!"
"Actually, I knew this stuff already," said Maya importantly. Then, as the others looked disbelievingly at her, she continued, "When I'm combing my hair in a hurry and yank on it, I notice it breaks off near the end, where the comb is. Perhaps that's because it doesn't have time to tell the rest of the hair to get pulled or stretched. But if I simply hold both ends of the hair and pull, perhaps it will stretch and stretch and finally break somewhere near the middle? Shall I try?!"
Both Leela and Mother laughed.
"I don't think you need to sacrifice your hair in the cause of science. Perhaps an ordinary thread would do. Also, you can knot beads into the string so you can easily tell exactly where it breaks off. Hold one end fixed or tie it to some support. Then try yanking on the string or else pulling it slowly until it can't stretch any longer and breaks."
"I think if you pull it slowly, it will break at the top end, because it's supporting the maximum weight of all those beads," said Leela. "Any way, let's do it and see."
The two children rushed off to get the beads and thread while Mother picked up the forgotten piece of paper and left the room smiling.