People originally discovered physics and other sciences by asking how and why questions. Recently I read the book How Everything Works by Louis A. Bloomfield. This book teaches physics by answering the how and why questions on everyday objects that we see and use. In this post I will be explaining about Newton’s three laws of motion.
Newtons first law of motion is about inertia. Let us understand inertia intuitively from Richard Feynman. In the book The Pleasure of Finding Things Out he writes
One day when I was playing with what we call an express wagon, which is a little wagon which has a railing around it for children to play with that they can pull around. It had a ball in it – I remember this – it had a ball in it, and I pulled the wagon and I noticed something about the way the ball moved, so I went to my father and I said, “Say, Pop, I noticed something: When I pull the wagon the ball rolls to the back of the wagon, and when I’m pulling it along and I suddenly stop, the ball rolls to the front of the wagon,” and I says, “why is that?” And he said, “That nobody knows,” he said. “The general principle is that things that are moving try to keep on moving and things that are standing still tend to stand still unless you push on them hard.” And he says, “This tendency is called inertia but nobody knows why it’s true.” Now that’s a deep understanding – he doesn’t give me a name, he knows the difference between knowing the name of something and knowing something. which I learnt very early.
The line above that is marked in bold is newtons first law. Watch the video, which is taken from the movie Infinity in which Feynman’s father explains inertia to Feynman.
Now its time to look at the official definition of first law: An object that is not subject to any outside forces moves at a constant velocity, covering equal distances in equal times along a straight line path. In order to understand this definition you need to understand five important physical quantities relating to motion and look at their relationships to one another. The physical quantities are (1) position (2) velocity (3) acceleration (4) mass (5) force. I am going to use the image given below to explain these physical quantities
Position: It is a vector quantity. A vector has both magnitude and direction. The first picture of the boy is his position. At t=0 seconds the boy is standing 1m away from the tree in the east direction. A position has a magnitude, direction, and a reference point. In this case the reference point is a tree.
Velocity: At t=1 second the boy moves from 1m to 2m. He changed position. Velocity measures how quickly your position changes. It is a vector quantity and consists of the speed at which you are moving and the direction in which you are heading. In this case the boy is moving at a velocity of 1 m/s in the east direction.
Acceleration: At t=2 seconds the boy moves from 2m to 4m. He changes velocity from 1 m/s to 2 m/s. This change in velocity is called as acceleration and it is also a vector quantity. In this case the boy is accelerating at 1 m/s2 in the east direction. If the velocity does not change then its acceleration is zero and the object is undergoing a constant velocity.
Mass: It is a measure of inertia and it resists changes in velocity. Almost every object in the universe has mass. At t=2 seconds the boy changes velocity from 1 m/s to 2 m/s. For this to happen the boy has to experience an external force to overcome his mass. The standard unit of mass is kilogram.
Force: It is a push or pull on an object causing it to change its velocity i.e. to accelerate. It is also a vector quantity. The standard unit of force is newton. A newton is equal to the force that would give a mass of one kilogram an acceleration of one meter per second2.
Let me given an analogy to explain mass and force. I want to exercise every day. But I do not. Whatever prevents me from exercising is the mass. After reading this article I came to know that exercise boosts brain power. After that I started exercising regularly. This article is the force which made me to overcome my mass. Mass in physics is similar to status quo bias in psychology. Force in physics is similar to incentives in psychology. Now reread the official definition of newtons first law and you should be able to understand it easily. Many common activities depends on inertia. For example food processors, blenders, and coffee grinders can dice or puree foods that are held in place by their own inertia.
If I apply the same unit of force to a tennis ball and a bowling ball which one will accelerate faster? Your intuition should tell that that the tennis ball will accelerate faster. Why? The reason is because the mass of a tennis ball is lesser than the mass of a bowling ball. From this logic we can come up with the following formula.
acceleration = force / mass
For the same unit of force, larger mass results in smaller acceleration and smaller mass results in larger acceleration. This is newtons second law. The official definition is: The force exerted on an object is equal to the product of that object’s mass times its acceleration. The acceleration is in the same direction as the force. This is given by the formula shown below. Both the formulas are the same. The former is cleaner as it separates cause (force and mass) and effect (acceleration) cleanly. But the latter is used often in the textbooks.
force = mass * acceleration
Now try to answer the following question: If I drop a bowling ball and a tennis ball at the same time from the Empire state building which ball will hit the ground first? We will assume that there is negligible air resistance. Aristotle a famous greek philosopher told that the heavier object will hit the ground faster than the lighter object. If we take Aristotle words then the bowling ball will hit the ground first. People believed this for 2000 years. But this is not true. Why nobody cared to verify Aristotle statement? It is because of Authority Bias and Social Proof. In the year 1589 an Italian physicist named Galileo proved that both the balls will hit the ground at the same time.
Let us find out why this is the case. In order to answer this question we need to understand what gravity is. Gravity is a downward force which Earth exerts on any object near its surface. That object is attracted directly toward the center of the earth with a force called as weight. Earth exerts 1 newton downward force on a mass of 102 grams. Hence for 1 kilogram of mass earth will exert 9.8 newton force (1000 grams / 102 grams). From this we can derive the relationship between mass and weight. Remember that mass is a fundamental measure of the amount of matter in the object. Mass of an object will be the same anywhere in the universe. The standard unit of mass is Kilogram. The weight of an object is the force of gravity on the object. Depending on which planet the object is in its weight will vary. The standard unit of weight is newton.
weight = mass * acceleration due to gravity
weight = mass * 9.8 m/s2
Now we have all the information we need to answer why both the ball’s will hit the ground at the same time. As you can see that weight and mass are proportional to each other by a factor of acceleration due to gravity. Hence for every object weight and mass cancel leaving acceleration due to gravity which is a constant. Hence all the objects hit the ground at the same time. We resolved 2000+ years of misunderstanding.
Acceleration = Force / Ball Mass [Newton 2nd law] We know that the only force acting on a falling object is the Ball's Weight. Acceleration = Ball Weight / Ball Mass Acceleration = (Ball Mass * acceleration due to gravity) / Ball Mass Acceleration = 9.8 m/s2
Imagine a piano resting on a sidewalk outside your house. According to newtons second law, earth should be pulling the piano with a downward force which should cause the piano to fall down. But the piano is standing still on the sidewalk. Did the gravity disappear? No the gravity is still there. You can verify that by putting your foot underneath the piano. The pain resulting from that will tell you that gravity is still there. Newtons third law will answer why the piano is not falling down. The third law is: For every force that one object exerts on a second object, there is an equal but oppositely directed force that the second object exerts on the first object. The weight of the piano is balanced by an equal but oppositely directed force from the sidewalk. Hence the piano does not fall down.
Newtons third law is misunderstood by a lot of people. When you push on an object the object pushes back on you. Since these are equal and opposite forces they cancel out each other perfectly and hence there will be no effect on you or the object. Is this understanding correct? No. Given below is the explanation from the book How Everything Works
The two forces described by Newton’s third law always act on two different things. Your push acts on the object while the object’s push acts on you. Since the object accelerates in response to the net force it experiences – the sum of all individual forces acting on it – it is affected only by your force on it, not by its force on you. If you are the only thing pushing on it, it will accelerate. And if the object is the only thing pushing on you, you’ll accelerate, too!
Watch the video which clearly explains our misunderstanding of newtons third law.