Newton’s Laws and Types of Forces — Physics 140 Study Notes

Newton’s Laws and Types of Forces

Introduction

This study guide covers the foundational principles of Newton’s Laws of Motion and the various types of forces encountered in introductory physics. Understanding these concepts is essential for analyzing the motion of objects and the interactions between physical systems.

Force and Mass

Definition of Force

• Force is defined as a push or a pull exerted by one physical system on another.

• Forces can be classified as:

  • Contact forces: Require physical contact between objects (e.g., normal force, tension, friction).

  • Noncontact (action-at-a-distance) forces: Act without direct contact (e.g., gravitational force).

• Inertia is the property of a physical system to maintain its state of rest or uniform motion. It is measured by mass.

Newton’s First Law — Law of Inertia

Statement and Mathematical Formulation

• An object tends to maintain its state of rest or uniform motion (constant velocity) unless acted upon by a net external force.

• If the vector sum of all forces acting on an object is zero, the object experiences zero acceleration and is said to be in translational equilibrium.

Mathematical Expression:

• $\sum \vec{F} = \vec{F}_1 + \vec{F}_2 + ... + \vec{F}_n = 0$

• On the x-axis: $F_{\text{net},x} = \sum F_{i,x} = 0$

• On the y-axis: $F_{\text{net},y} = \sum F_{i,y} = 0$

Example: A book resting on a table remains at rest because the net force on it is zero (gravity is balanced by the normal force).

Newton’s Second Law — Force and Acceleration

Statement and Mathematical Formulation

• The vector sum of all forces acting on an object equals the mass of the object times its acceleration.

• This law quantitatively relates force, mass, and acceleration.

Mathematical Expression:

• $\vec{F}_{\text{net}} = \sum \vec{F} = m \vec{a}$

• Or, $\vec{a} = \frac{\vec{F}_{\text{net}}}{m}$

• On the x-axis: $F_{\text{net},x} = m a_x$

• On the y-axis: $F_{\text{net},y} = m a_y$

Example: If a 2 kg object experiences a net force of 10 N to the right, its acceleration is $a = \frac{10}{2} = 5$ m/s2 to the right.

Newton’s Third Law — Action/Reaction

Statement and Application

• If a physical system acts on another with a force $\vec{F}_{\text{ACTION}}$, the second system reacts with a force $\vec{F}_{\text{REACTION}}$ equal in magnitude and opposite in direction.

• These forces act on different objects, not on the same object.

Mathematical Expression:

• $\vec{F}_{\text{REACTION}} = -\vec{F}_{\text{ACTION}}$

Example: When you push against a wall, the wall pushes back against you with an equal and opposite force.

Types of Forces

Gravitational Force

• Gravitational force is a noncontact force of attraction between two objects with mass.

• Given by Newton’s Law of Universal Gravitation:

$|\vec{F}_G| = G \frac{m_1 m_2}{r^2}$

• Where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses, and $r$ is the distance between their centers.

• The weight of an object is the gravitational force exerted by the Earth on that object: $w = mg$.

Example: The gravitational force keeps planets in orbit around the Sun.

Normal Force

• The normal force is a contact force exerted by a surface perpendicular to the surface of contact.

• It balances the component of other forces (like gravity) perpendicular to the surface.

• By Newton’s Third Law, if object A exerts a normal force on object B, B exerts an equal and opposite normal force on A.

Example: A book resting on a table experiences an upward normal force from the table equal in magnitude to its weight.

Tension Force

• Tension is the force transmitted through a string, rope, cable, or similar object when it is pulled tight by forces acting from opposite ends.

• In an ideal (massless, frictionless) rope or pulley, the tension is the same throughout the rope.

• Tension always pulls away from the object it is attached to.

Example: In a hanging mass supported by a rope, the tension in the rope equals the weight of the mass if the system is at rest.

Action/Reaction Example (Book Example)

• When an apple rests on a table, the forces acting on the apple are gravity (downward) and the normal force (upward).

• The action-reaction pairs are:

  • Apple exerts a force on the Earth (downward), Earth exerts a force on the apple (upward).

  • Apple exerts a force on the table (downward), table exerts a force on the apple (upward).

• Action-reaction pairs always involve two different objects.

Summary Table: Types of Forces

Type of Force	Contact/Noncontact	Direction	Example
Gravitational	Noncontact	Attractive, along line joining centers	Earth pulling on a falling apple
Normal	Contact	Perpendicular to surface	Table supporting a book
Tension	Contact	Along string/rope, away from object	Rope holding a hanging mass

Additional info: Frictional forces, spring forces, and other types of forces are also important in Newtonian mechanics but are not detailed in these slides.