Newton's Third Law of Motion: Study Notes

Ch. 05 – Newton’s Third Law

5.1 Forces and Interactions

Forces always occur as interactions between objects. When one object exerts a force on a second object, the second object simultaneously exerts a force back on the first object. These forces are equal in magnitude and opposite in direction.

• Force: A push or pull exerted on an object, resulting from its interaction with another object.

• Interaction Pair: The forces two objects exert on each other are called an action-reaction pair.

• Example: When a hammer strikes a nail, the hammer exerts a force on the nail, and the nail exerts an equal and opposite force on the hammer.

5.2 Newton’s Third Law

Newton’s Third Law states: "Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first."

• Law Statement: To every action there is always an opposed equal reaction.

• Action and Reaction: Forces always come in pairs—if object A exerts a force on object B, object B exerts an equal and opposite force on object A.

• Identifying Action/Reaction Pairs: The simplest way is to identify the two objects interacting and describe the force each exerts on the other.

• Example: When you sit in a chair, your body exerts a downward force on the chair, and the chair exerts an upward force on your body.

Table: Action-Reaction Pair Identification

Action	Reaction
Hammer hits nail	Nail hits hammer
Earth pulls on apple (gravity)	Apple pulls on Earth
Hand pushes wall	Wall pushes hand

5.3 Action/Reaction Pairs on Different Masses

Although action and reaction forces are always equal and opposite, their effects depend on the masses of the objects involved. The same force produces different accelerations if the masses are different, as described by Newton’s Second Law.

• Newton’s Second Law: $F = ma$

• Acceleration: $a = \frac{F}{m}$

• Example: When a cannon fires a cannonball, the force on the cannonball and the force on the cannon are equal in magnitude but opposite in direction. However, the cannonball (small mass) experiences a large acceleration, while the cannon (large mass) experiences a small acceleration.

Key Point: A given force exerted on a small mass produces a large acceleration, while the same force exerted on a large mass produces a small acceleration.

5.4 Vectors and the Third Law

Forces are vector quantities, meaning they have both magnitude and direction. When analyzing forces, it is often useful to break them into components, especially when dealing with inclined planes or multiple directions.

• Vector Components: Any vector can be resolved into two perpendicular components, typically horizontal ($F_x$) and vertical ($F_y$).

• Finding Components: Use the Pythagorean theorem to find the magnitude of the resultant vector: $F = \sqrt{F_x^2 + F_y^2}$

• Example: A skier on a slope experiences a gravitational force that can be split into a component parallel to the slope (causing acceleration down the slope) and a component perpendicular to the slope (balanced by the normal force).

Table: Forces on an Object on an Inclined Plane

Incline Angle	Normal Force (N)	Gravity Component Parallel to Incline ($mg\sin\theta$)	Gravity Component Perpendicular to Incline ($mg\cos\theta$)
0° (flat)	Maximum	0	$mg$
Increasing	Decreases	Increases	Decreases
90° (vertical)	0	$mg$	0

Additional info: The resultant of any two vectors can be found using the parallelogram rule.

5.5 Defining the System

When analyzing forces, it is important to define the system under consideration. Action and reaction forces act on different objects, so they do not cancel each other out within a single system.

• System: The object or group of objects being analyzed.

• Internal vs. External Forces: Internal forces (action-reaction pairs within the system) do not change the motion of the system as a whole. Only external forces can change the system’s motion.

• Example: If you consider an orange and a cart as a system, the force of the orange on the cart and the force of the cart on the orange are internal and do not affect the system’s acceleration. If an external force acts on the system, it can accelerate.

Additional info: Every force is a member of an action/reaction pair, and these pairs act on different objects.