Hello there! Welcome to lecture five: Newton’s third law!
Newton’s third law describes the forces that exist between two objects when they interact. This helps us understand the physics of lots of everyday motion: why we move when we walk, how rockets are capable of propelling through space, and more!
Each of the following concepts will be discussed in this video: Newton’s third law, systems and external forces, and using Newton’s second and third laws.
Newton’s third law
Newton’s third law states that for every action, there is an equal and opposite reaction. Forces always come in pairs: action-reaction pairs. As I stand here recording this video, I am pushing down on the floor. The reaction force is that the floor is pushing up on me. How do I know the floor pushes up on me? Because I can feel it!
Any time two objects interact with each other, or exert forces on each other, there will be two forces: an action force and a reaction force. The two forces are equal in magnitude and opposite in direction.
If you high five somebody, there’s an action reaction pair. Both hands exert equal forces on each other in opposite directions.
Playing sports, if you hit a ball with a bat, your head, your feet, or another object, there’s an action reaction pair. In softball and baseball, the bat and ball both have equal forces exerted in opposite directions.
In this demo, I wanted to show that two objects in contact with each other will, by definition, experience equal and opposite forces. I connected two force probes together with a rubber band, causing them to be in contact with each other. One of the force probes is held stationary on a ring stand. As I push and pull one of the force probes, it exerts an equal and opposite force on the second force probe. Both of these forces is recorded in real time using Logger Pro. You can see from the computer readout that the forces are indeed equal and opposite.
This isn’t only true when one of the force probes is stationary. I repeated the demonstration while holding both force probes. Regardless of if the system is stationary, accelerating in one direction, or moving at a constant velocity, the two force probes exert equal and opposite forces on each other.
Any time two objects are in contact with each other, they will exert equal and opposite forces, regardless of the mass, size, velocity, speed, or acceleration of either of the objects.
While walking a dog, the dog exerts a force on the leash, which exerts an equal and opposite force on the dog. As we saw with the force probe demo, that means an equal force occurs between the person and the leash, and the reaction force to that is between the leash and the person. While walking, both the person and the dog push against the ground as they walk. The reaction: the ground pushes back against the person and the dog. Even in a seemingly straightforward scenario as this, we can identify quite a few action-reaction pairs!
Consider the game of tug of war. In this game, two teams stand at opposite sides of a rope. Both teams pull on the rope, attempting to pull the other team over to their side. Both teams are in contact with the rope.
Let’s say one team consists of lots of very muscular individuals, and the other team consists of just a few rather small individuals. Which team exerts more force on the rope? The large group of large folks? The small group of small folks?
The answer is: both teams are exerting exactly the same force on the rope! How do we know this is true? If both teams are in contact with the rope, then Newton’s law tells us that their forces will be equal and opposite. This is exactly the same as the dog and the person walking the dog.
So who wins the game of tug of war? The answer is: whichever team exerts the most force on the ground with their feet will win the game. If the team of very large people are standing on a slick floor wearing slippers, they will not be able to exert a lot of force on the ground, and will be moved around very easily. If the team of very small people are standing on asphalt wearing boots, they will be able to exert a lot of force on the ground, and will be harder to move.
Next time you play a game of tug of war, wear boots that give you a lot of traction with the floor, and make good contact. It doesn’t matter how hard you pull on the rope, as long as your feet exert a larger force on the ground than your opponents!
In general, if we know one force, we can determine the action-reaction pair by criss-crossing the two nouns. If the action force is that a baseball bat hits a ball, the reaction force is that the ball hits the bat.
If the action force is that my feet push down on the ground, the reaction is that the ground pushes up on my feet. If the action force is an airplane propeller pushing backward on air molecules, the reaction force is air molecules pushing forward on the propeller.
Let’s think about gravity. Gravity is a force where the Earth pulls me (and other objects) downward. What is the reaction force? Is the reaction force the support force between me and the floor? If we think about the support force as a push or a pull, we can say that the support force is the floor pushing up on me. We can see that these are NOT action-reaction pairs because the nouns are different.
What is the reaction force to gravity? The reaction force is that I am pulling up on the Earth. What is the reaction force to the support force? I am pushing down on the floor. Be careful: two forces that act on the same object cannot be action-reaction pairs.
Newton’s third law can be considered to be the reason why things move. A rocket works by creating a chemical reaction that causes exhaust gases to be pushed out of the bottom of the engine. The reaction force is thrust that causes the rocket to move upward. A jet engine also produces thrust by moving gases backward through a turbine engine.
Systems and external forces
A system is any collection of objects that we define. If there are two carts moving on a track, we can define a system as consisting of both carts, or of only one or the other cart. In other words, a system can be defined however we choose. This concept is important in understanding how external forces can act on an object to change its motion. What do we consider to be an external force? While the concept of a system can be somewhat arbitrary, it can be useful when determining how to analyze the properties of an object or collection of objects. We’ll see this to be true in lecture six when we discuss momentum.
Let’s consider a horse pulling a cart along a road. If we consider the system to be the cart, then the horse is considered external to that system. From the perspective of the system, the horse is an external force acting on the cart and causing it to move.
What if we expand our view and define the system as consisting of both the cart and the horse? What is the external force that causes the system to move? In this case, we have to look outside of the horse for the answer. The reason the system moves is because the Earth causes a friction force that allows the system to move.
But what if we continue to expand our view of the system to include everything: the cart, the horse, the Earth, everything? How can anything move if the definition of a system is arbitrary, and nothing is truly external? How can things move if every action has an equal and opposite reaction force? Why don’t all forces just cancel out and cause everything to be in equilibrium all the time? Let’s find out!
Using Newton’s second and third laws
If every force causes an equal and opposite counter force, why isn’t everything in equilibrium? The reason is that while all forces have equal and opposite reaction forces, the effect of those forces depends on the object they act on. We can use Newton’s second and third laws together to get an idea of why this is.
As you walk around, you are able to change your motion. It is possible to change your motion by pushing off the floor. The reaction force is that the floor pushes you as well. This reaction force causes us to move.
Why is it that we move when we walk and the floor does not move? Think about the floor: it is attached to a building that’s probably extremely massive and hard to move. It has a lot of inertia. Compared to the building, we are relatively small and don’t have much mass. While we experience equal forces, we do not experience equal accelerations, or changes in our motion, as a result of that force.
Let’s see how this example works by relating it to a ping pong ball and the Earth.
In this demo, I dropped a small yellow ping-pong ball that has a mass of 10 grams, or 0.01 kilograms. The Earth’s gravitational field causes the ping-pong ball to have an acceleration of 9.8 meters per second squared. We can use Newton’s second law to calculate the net force on the ball to be 0.098 Newtons. In other words, the Earth pulls down on the ball with 0.098 Newtons of force.
The reaction force is that the ball pulls up on the Earth with a force of 0.098 Newtons; equal and opposite. Why don’t we feel this upward force? The reason is that the Earth is extremely massive and its inertia makes it exceptionally difficult to move. Let’s use Newton’s second law to calculate the acceleration of the Earth due to the ball. 0.098 Newtons equals the mass of the Earth times the acceleration of the Earth. The Earth has a mass of six times ten to the 24 kilograms. When we divide both sides of the equation by six times ten to the 24 kilograms, we find the acceleration of the Earth is 1.6 times ten to the negative 26 meters per second squared, essentially zero.
Even if I were to have dropped something with a mass of thousands of kilograms, or a million kilograms, or a billion kilograms, the acceleration of the Earth would still be essentially zero. The earth is extremely massive; it’s massive on literally a planetary scale. So it would take an object of comparable mass and size to make any noticeable effect on the Earth’s motion.
Every object that the earth pulls down, pulls the Earth up with equal magnitude. You are pulling up on the Earth yourself, and do so all the time! Just because there are equal and opposite forces does not mean there is equal and opposite motion. The Earth can cause us to accelerate very readily, whereas we do not make even a tiny budge to the Earth’s motion.
Thanks for taking the time to learn about Newton’s third law! Until next time, stay well.