# Newton's Third Law of Motion

"Lex III: Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi."

''To every action there is always an equal and opposite reaction: or the forces of two bodies on each other are always equal and are directed in opposite directions''. [3]

In 1686, Sir Issac Newton presented his three laws of motion in the "Principia Mathematica

Philosophiae Naturalis." His third law, also known as the "Law of Reciprocal Actions", is most commonly described as "for every action, there is an equal and opposite reaction." This means that, if object A exerts a force on object B, object B exerts an equal and opposite, force on object A. These forces are known as action and reaction forces, which always come in pairs. In this sense, the Law of Conservation of Energy is applied, stating that "energy is neither created nor destoryed."

Principles of action and reaction forces can be applied with contact interactions, (such as friction or tension), as well as interactions from a distance, (such as gravity or magnetism). Issac Newton used the word motion in this principle interchangeably with the word momentum. Newton used this third law of motion to come up with the Law of Conservation of Linear Momentum, which goes much further in depth and sometimes provides exceptions to his third law of motion, such as with force fields or subjects in quantum mechanics.

## Forces and Interactions

 Image courtesy of Georgia State University
To say that every action has an equal and opposite reaction would be putting things very simply. There is much more detail involved in this law. The interaction between two objects is always involved in a force. There are two equations to express this:

FB = - FA

or

FA + FB = 0 [9]

Picture a hammer hitting a nail and driving it into a piece of wood. Most people would say that the hammer exerts a force on the nail, but this is only half of the process. The nail, in fact, exerts a force on the hammer as well. This is what stops the hammer and keeps it from going through the nail all together. By the direction of which the nail goes, you would say that the hammer exerts a stronger force. This is because the nail is small compared to the hammer, and also the worker behind the hammer. However, this law applies forces in mass. Even though the nail is much smaller than the hammer, it exerts a reaction force equal to the mass of the hammer's action force. [6,7,9]

## Identifying Action and Reaction

 Image courtesy of U.S. Centennial of Flight Commission
It can sometimes be difficult to distinguish between the action and reaction forces. Take a person on a skateboard, for instance. When he pushes himself forward, he exerts a force to the ground in the opposite direction. In the same sense, the ground pushes against him and the skateboard to propel him forward.

Thinking of this, one would also wonder about the forces of gravity when applying this law. Let's say that someone is sitting in a chair. The action force would be the gravitational pull of the Earth's core pulling the person down toward it. The person in the chair is applying an equal force to his or her mass back on the Earth, and also the chair, which is applying an upward force on the person to keep him or her from falling through to the ground. [6,7,8]

## Action and Reaction on Different Masses

 Image courtesy of Georgia State University
A lot of people tend to wonder how these actions and reactions work in gravity, more specifically with the planets. How can a person on the Earth possibly exert an equal and opposite force back on the Earth's gravitational pull of its core? The answer is mass. A force applied to an object is equivalent to the mass of that exerting force. In exchange, the reaction force is equivalent to the action force.

Refer to the picture on the right. We have a 50N block on top of a 200 N block, all on top of a spring-board scale. All of this is understood to be on Earth, which will pull these things down with the force of gravity. Taking it one step at a time, we see that the 50 N block exerts a force of 50 N down on the 200 N block. At the same time, the 200 N block exerts a 50 N force back up to the 50 N block as a support force.
The 200 N block is now supporting a 50 N force and applying a 200 N force on the spring-board scale. The scale now has to support both the 200 N and 50 N blocks, therefore, it much exert a 250 N force back up on the two blocks.
Now this whole contraption is sitting on the Earth itself. Depending on how much the scale weighs, the Earth much now exert a reaction force upon these objects in order to support them. The Earth will exert a force equal to the mass of these objects to keep them supported, but at the same time, the gravity of the core pulls these objects down in accordance to their mass. [8]

## Do Action and Reaction Forces Cancel?

This is perhaps one of the most difficult questions to answer in Newton's Third Law. In simplicity, action and reaction forces can never cancel each other. However, because of the two forces' characteristic of having opposite directions in respect to one another, they do cause the object in the system to stay at rest in some cases. For example, a person pushing on the wall is not in motion because the force by that person is being pushed back by the force exerted by the wall which is equal in magnitude and opposite in direction. It is possible for an action force to seem to be canceled with another action force, as long as both action forces are exerted on one object, which will exert a reaction force on both action forces.

Let's say that two boy, Jack and Michael, are playing soccer. If Jack kicks the ball, he exerts a force on that ball and makes it accelerate forward. If the ball comes and hits Michael's foot, the ball has exerted a force on his foot, and the reaction force from him makes the ball decelerate to a stop. Now, if this game suddenly gets competitive and the two boys try to steal the ball from each other, at some point, they might kick the ball at the same time with the same force in opposite directions. In that case, the action forces coming from the two boys would cancel, but the reaction force from the ball would still push both forces back, so there would be no acceleration.

# Presentation

## Vocabulary

• Action Force - One of the two forces, (the "cause" force), in Newton's Third Law.

• Interaction - A shared action between two objects in which both objects exert equal and opposite forces on each other.

• Newton's third law - Law stating that, when one force is exerted on an object by another object, the second, (or reaction), object exerts an equal and opposite force on the first, (or action), object.

• Reaction Force - One of the two forces, (the "effect" force), in Newton's Third Law.

• Acceleration - The act of changing, (usually increasing), velocity.

• Gravity - Force of action where objects tend to fall toward the Earth or around celestial bodies in space.

• Velocity - Rapid movement of an object; speed.

• Momentum - Measure of the motion of a moving object. Newton would commonly use the word motion in place of momentum.

• Motion - Action of a body moving or changing position. [11]

# References

1. National Aeronautics and Space Administration - Newton's Third Law Applied to Aerodynamics
2. The Physics Classroom - Newton's Third Law
3. Wikipedia - Newton's Laws of Motion.Newton's third law: law of reciprocal actions
4. Wikipedia - Conservation of energy
5. Wikipedia - Conservation of linear momentum
6. Prentice Hall Conceptual Physics Chapter 6 - Newton's Third Law of Motion Action and Reaction
7. How Stuff Works - Newton's Third Law (Law of Force Pairs)
8. Georgia State University HyperPhysics - Newton's Laws
9. Newton's Third Law of Motion - Andrew Zimmerman Jones, About.com
10. Physics at BHS
11. Dictionary.com