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# What is Newton's third law?

Learn about the fact that forces come in pairs.

## What is Newton's third law?

You probably know that the Earth pulls down on you. What you might not realize is that you are also pulling up on the Earth. For example, if the Earth is pulling down on you with a gravitational force of 500 N, you are also pulling up on the Earth with a gravitational force of 500 N. This remarkable fact is a consequence of Newton's third law.
Newton's third law: If an object A exerts a force on object B, then object B must exert a force of equal magnitude and opposite direction back on object A.
This law represents a certain symmetry in nature: forces always occur in pairs, and one body cannot exert a force on another without experiencing a force itself. We sometimes refer to this law loosely as action-reaction, where the force exerted is the action and the force experienced as a consequence is the reaction.
We can readily see Newton’s third law at work by taking a look at how people move about. Consider a swimmer pushing off from the side of a pool, as illustrated below.
The swimmer pushes against the pool wall with her feet and accelerates in the direction opposite to that of her push. The wall has exerted an equal and opposite force back on the swimmer. You might think that two equal and opposite forces would cancel, but they do not because they act on different systems. In this case, there are two systems that we could investigate: the swimmer or the wall. If we select the swimmer to be the system of interest, as in the image below, then ${F}_{\text{wall on feet}}$ is an external force on this system and affects its motion. The swimmer moves in the direction of ${F}_{\text{wall on feet}}$. In contrast, the force ${F}_{\text{feet on wall}}$ acts on the wall and not on our system of interest. Thus ${F}_{\text{feet on wall}}$ does not directly affect the motion of the system and does not cancel ${F}_{\text{wall on feet}}$. Note that the swimmer pushes in the direction opposite to that in which she wishes to move. The reaction to her push is thus in the desired direction.

## What are other examples of Newton's third law?

Other examples of Newton’s third law are easy to find. As a professor paces in front of a whiteboard, she exerts a force backward on the floor. The floor exerts a reaction force forward on the professor that causes her to accelerate forward.
Similarly, a car accelerates because the ground pushes forward on the drive wheels in reaction to the drive wheels pushing backward on the ground. You can see evidence of the wheels pushing backward when tires spin on a gravel road and throw rocks backward.
In another example, rockets move forward by expelling gas backward at high velocity. This means the rocket exerts a large backward force on the gas in the rocket combustion chamber, and the gas therefore exerts a large reaction force forward on the rocket. This reaction force is called thrust. It is a common misconception that rockets propel themselves by pushing on the ground or on the air behind them. They actually work better in a vacuum, where they can more readily expel the exhaust gases.
Helicopters similarly create lift by pushing air down, thereby experiencing an upward reaction force. Birds and airplanes also fly by exerting force on air in a direction opposite to that of whatever force they need. For example, the wings of a bird force air downward and backward in order to get lift and forward motion.

## What do examples involving Newton's third law look like?

### Example 1: Fridge push

A person drives a cart, Cart 1, to the right while pushing another cart, Cart 2, that has a massive refrigerator on it. The total mass of Cart 2, cart plus fridge, is three times the total mass of Cart 1, cart plus person. If the person is driving with enough force that the two carts accelerate to the right, what can be said for sure about the magnitudes of the forces on the carts?

### Example 2: Third-law-force pairs

A box sits at rest on a table as seen in the image below. Various forces are listed in the table below the image.
Drag the forces in the right column so that they're lined up with their Newton's third law partner force in the left column.

## Want to join the conversation?

• For example, if a baseball ball is applying force on a ball of 1000N and ball moves away. If the ball is applying the same force on the bat why doesn't the bat moves away?
• Great question. There are two factors to consider.
First, the masses are different. The mass of a baseball is .145kg, while a bat has a mass of about 1.0 kg. So, from F = ma, this tells us that a = F/m, and so the acceleration of the ball will be about 7 times the acceleration of the bat. We know that the average acceleration is given by a = Δv/Δt, which tells us that Δv = a * Δt. Thus, since the Δt is the same for both, and the acceleration of the ball is 7 times bigger, the Δv of the ball will be 7 times bigger.
The Second factor is that the bat is already moving with a fairly high speed, and so its momentum is much greater than the momentum of the ball, at least in the frame of reference of the spectators. Thus, the bat is only slowed down, while the ball is turned completely around. Here is an example:
mass of bat = 1kg
mass of ball = (1/7)kg
initial velocity of bat = +35 m/s
initial velocity of ball = -35 m/s
final velocity of bat = +20 m/s
final velocity of ball = +70 m/s
You can see that the Δv for the bat = 20 - 35 = -15m/s, while Δv for the ball = 70 - -35 = +105m/s, which is 7 times as big as the Δv for the bat.

If you were to watch the collision from a car moving at v = +35m/s, you would see the bat initially at rest and finally moving at -15 m/s, so you would see it "moving away" from the collision.

One final factor is that the player keeps pushing on the bat during the hit, so although the ball pushes on the bat equal and opposite to the bat pushing on the ball, there is additional force on the bat that tends to counteract the ball pushing on the bat.
• how did newton figure out his third law?
• By noticing that an apple pushes downwards against his hand(because of gravity), as his hand pushes up on the apple(by holding it).
• Assume that I drop a ball from the 2nd floor to the ground. Why is it that the ball could not bounce all the way back to my position if Newton's third law state that the ground will exert an equal amount of force to the ball?
• Energy is lost every time the ball bounces because of the air friction. In a (hypothetical) perfect vacuum where nothing acts on the ball except for gravity, the ball would bounce all the way back to the 2nd floor every time, forever (or until stopped by an external force).
• How does one differentiate between an action force and a reaction force if they are both "reacting" to each other?
• Actually there is no difference between the two since they both occur at the same time. Action and reaction are just terms given for better understanding.
• Newton’s law states that if we apply force to an object, it will push back with the same amount of force in the opposite direction. So if I push a pen with 10 Newton it is supposed to push me back with 10 Newton too. And as the forces cancel out, the net displacement should be zero. Then how does the pen move?
• Forces can only cancel out on a single object. In this scenario you experience a force of 10 N in one direction and the pen experiences a separate force of 10 N in the opposite direction. The net force on the pen is 10 N. There is no reason to add the 10 N on you to the pen because those 10 N are being exerted on you, not the pen.
• what if two boxes equal is mass and force collided in space head on
(1 vote)
• The answer to this depends on how elastic the collision is, see Coefficient of restitution (https://en.wikipedia.org/wiki/Coefficient_of_restitution). If kinetic energy is conserved, they bounce back with equal speed. If the collision has loss (i.e. they make a noise, their surfaces heat, they plastically deform etc), they bounce back with lower speed.

Think of 2 cars in a head on collision. They crumple and don't bounce much at all - an inelastic collision.

Note that momentum is maintained in all collisions: 2 objects the same mass travelling equal speed along the same line in opposite directions have a sum of 0 momentum. For momentum to be conserved they must have equal speeds in opposing directions after the collision.
• Why is lying in bed not an example of Newton's 3rd law? My text book says its because the forces acting on you come from a different interaction pair but doesn't explain further.
• When you lie on your bed, you push on the bed and the bed pushes on you. That's Newton's third law.
At the same time, earth's gravitational force is pulling on you, and your gravitational force is pulling on earth. That's another example of 3rd law.
Note that 3rd law pairs have to be of the same type. contact force and contact force, in the bed/you situation. Gravity and gravity in the earth/you situation.
Now we can ask a different question: why are you stationary when you lie on your bed. That's because the contact force from the bed on you is equal to your weight. Here we have two different types of forces - the contact force and the gravitational force. The sum of those forces is zero, so you don't accelerate. That's Newton's 2nd law, F = ma.
• What would happen if Newton's Third Law didn't happen? Would a runner be able to run or would his force keep pushing at the ground with no result?