Understanding the Fundamentals of Newton's Laws of Motion

Mechanics is a vital area within physics that focuses on the study of forces, mass, and motion. This tutorial aims to provide a clear introduction to the fundamental concepts!

Topics Included:

Definitions of force, mass, velocity, acceleration, and weight
Vector representation in diagrams
Newton's three laws of motion and the behavior of objects under force
Action and reaction forces
Friction and its implications
Kinematic equations of motion
Vector addition and resolution
Work and kinetic energy
Momentum concepts
Moments, couples, and torque
Angular velocity and power

Essential Quantities in Mechanics

The International System of Units (SI), derived from the French Système International d’Unités, serves as the standard for engineering and scientific calculations, essentially unifying the metric system.

Among the seven base quantities in the SI system, three—mass, length, and time—are pivotal in the study of mechanics.

Mass

Mass is a characteristic of an object, representing its resistance to motion. It remains constant regardless of the object's location, whether on Earth, another planet, or in space. The SI unit for mass is the kilogram (kg).

Length

In mechanics, length refers to the distance an object travels or the distance over which a force acts. The fundamental unit of length is the meter (m).

Time

Time measures the duration for an event to occur, such as the time it takes for an object to cover a specified distance. The SI unit for time is the second (s).

Derived Quantities

These quantities emerge from combinations of mass, length, and time. The key derived quantities include:

Velocity

Velocity defines the speed of an object in a specified direction, measured in meters per second (m/s). Average velocity equals the distance covered divided by the time taken.

Acceleration

Acceleration occurs when a force is applied to a mass, resulting in an increase in velocity. This acceleration is proportionate to the force and inversely related to the mass, measured in meters per second squared (m/s²). Average acceleration is computed as the change in velocity over the time interval during which the change happens.

Force

Force can be viewed as a "push" or "pull." It can be either active or reactive. The relationship is defined by the equation: force = mass × acceleration. The unit of force is the newton (N).

Note: In US English, "meters" is spelled as "metres."

Examples of Forces

Lifting an object demonstrates an active force exerted upwards.
The gravitational force, known as weight, pulls objects downward.
A bulldozer applies considerable force to move materials.
Rocket engines produce substantial thrust to propel vehicles into orbit.
Reactive forces can be observed when pushing against a wall or compressing a spring—both scenarios illustrate equal and opposite reactions.

Understanding a Newton

In the SI system, force is quantified in newtons (N), where one newton equates to a weight of approximately 3.5 ounces or 100 grams.

What is a Vector?

A vector is characterized by both magnitude and direction, while quantities like mass lack a directional component and are termed scalars. Velocity exemplifies a vector as it possesses both speed and direction. Similarly, force is also a vector quantity. In diagrams, vectors are represented as arrows, with the angle relative to a reference line indicating direction. Mechanics problems can often be simplified by drawing vectors to scale, aiding in the determination of unknown forces.

What Are Vector Diagrams?

In mechanics, free-body or force diagrams visually represent the forces acting within a system. Typically, a force is depicted by an arrow, with its direction indicated by the arrowhead.

An Example of a Large Force

Types of Forces

Effort

Effort refers to the force applied to an object that may cause it to move, such as pushing a lever or pulling a load.

Weight

Weight describes the gravitational force acting on an object, which is influenced by its mass and position relative to the Earth’s center.

Tensile or Compressive Reaction

When a rope is pulled or a spring is stretched, the material experiences strain, resulting in a reactive force that counters the applied force.

Static Friction

Friction opposes motion and can be either beneficial or detrimental. It can make it difficult to slide objects, yet it enables walking without slipping.

Viscous Friction or Drag

This type of friction arises when objects move through fluids, such as air or water, resulting in resistance.

Electrostatic and Magnetic Forces

Charged objects can attract or repel each other, while magnets demonstrate similar behavior based on their poles.

What is a Load?

When a force acts on a structure, it is termed a load, such as the weight of a roof on walls or the force exerted by wind.

Newton’s Laws of Motion

In the 17th century, Isaac Newton formulated three laws of motion to describe the dynamics of bodies in the universe.

Newton’s First Law of Motion

"An object remains in its state of rest or uniform motion unless acted upon by an external force." This implies that a stationary object will not move unless a force is applied.

Newton’s Second Law of Motion

"The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass." This can be expressed as F = ma, where F is force, m is mass, and a is acceleration.

Newton’s Third Law of Motion

"For every action, there is an equal and opposite reaction." This means that forces always occur in pairs; when one object exerts a force on another, the second object exerts a force of equal magnitude in the opposite direction.

What is Dry Friction or “Stiction”?

Friction is a reactive force that opposes motion. When attempting to slide an object, friction acts against the applied force until the maximum limit is reached, leading to movement.

Kinetic Friction

Once motion begins, the friction opposing it decreases, characterized by a different coefficient.

Newton’s Equations of Motion (Kinematics Equations)

Three principal equations govern the relationships between distance, time, and final velocity during acceleration.

Let: - u = initial velocity - v = final velocity - s = distance covered - t = time taken - a = acceleration

For uniform acceleration: 1. v = u + at 2. s = ut + 1/2 at² 3. v² = u² + 2as

Examples

A force of 100 newtons accelerates a 5 kg mass for 10 seconds.
A 10 kg mass dropped from a height of 100 meters.

Mechanics

Applied Mechanics by John Hannah and MJ Hillier is an essential textbook for engineering students, covering various topics, including statics and dynamics.

Mathematics

Engineering Mathematics by K.A. Stroud is an engaging resource for understanding essential mathematical concepts relevant to engineering.

What is Momentum?

Momentum is defined as the product of mass and velocity. In collisions, momentum is conserved, meaning the total momentum before and after the event remains constant.

What is Work?

Work is defined as the product of force and the distance moved in the direction of the force. The unit of work is the joule.

What is Kinetic Energy?

Kinetic energy pertains to an object in motion and is calculated using the formula KE = 1/2 mv².

Moments, Couples, and Torque

A moment is produced when a force acts on an object, resulting in rotation about a point. Torque is the measure of this rotational effect.

Measurement of Angles in Degrees and Radians

Angles can be expressed in degrees or radians, with radians often simplifying mathematical calculations.

Angular Velocity

Angular velocity measures the rate of rotation, commonly expressed in radians per second.

Relationship Between Angular Velocity, Torque, and Power

Power can be calculated as the product of angular velocity and torque.

References

Hannah, J. and Hillier, M. J., (1971) Applied Mechanics (First metric ed. 1971) Pitman Books Ltd., London, England.

Disclaimer

This article is written to the best of the author's knowledge for informational and entertainment purposes only and should not be considered a substitute for professional advice.