Topic 1 | Space, Time, and Motion

Introduction

This section introduces the foundational concepts of classical mechanics, focusing on the nature of space, time, and motion. The study of motion (kinematics and dynamics) is central to understanding how objects behave under various forces.

Part 11 | Newton's Laws of Motion

Concepts of Mass and Force

• Mass: The mass of an object is the quantity of matter that the object contains. It is a scalar quantity and is measured in kilograms (kg).

• Force: A force is a push or pull acting on an object. It is a vector quantity, measured in newtons (N).

• Mass vs. Weight: Mass is an intrinsic property of matter, while weight is the force exerted on that mass by gravity. Weight depends on the gravitational field strength.

• Formula for Weight: where is weight, is mass, and is acceleration due to gravity ( on Earth).

Newton's First Law of Motion (Law of Inertia)

Newton's First Law states that an object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity unless acted upon by a net external force.

• Inertia: The tendency of an object to resist changes in its state of motion.

• Natural State of Motion: In the absence of friction, the natural state is constant velocity, not necessarily rest.

• Equilibrium: A body is in equilibrium if the net force acting on it is zero.

• Example: A sloth at rest remains at rest unless disturbed; a block on a frictionless surface moves with constant velocity.

Newton's Second Law of Motion

Newton's Second Law quantifies the relationship between force, mass, and acceleration. It states that the acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass.

• Mathematical Formulation: where is the net force, is mass, and is acceleration.

• Proportionality: and

• Unit of Force: 1 Newton () is the force required to accelerate 1 kg of mass by .

• Examples:

  • If a 10 kg cart is pushed with a force , it accelerates at ; with , ; with , .

  • For a constant force, increasing the mass decreases the acceleration.

Newton's Third Law of Motion

Newton's Third Law states that for every action, there is an equal and opposite reaction. When one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.

• Mathematical Formulation: where is the force exerted by object A on B, and is the force exerted by B on A.

• Examples:

  • When you kick a soccer ball, your foot exerts a force on the ball, and the ball exerts an equal and opposite force on your foot.

  • When you walk, your foot pushes backward on the ground, and the ground pushes forward on your foot.

  • When a hammer hits a nail, the nail exerts an equal and opposite force on the hammer, causing it to stop.

  • Rocket propulsion: The rocket pushes exhaust gases downward, and the gases push the rocket upward.

Equilibrium and Vector Addition

Equilibrium occurs when the sum of all forces acting on a body is zero. Forces are vectors and must be added using vector addition.

• Equilibrium Condition:

• Vector Addition: Forces acting at angles must be added using vector diagrams or components.

• Example: If three forces act on a point and their vector sum is zero, the point is in equilibrium.

Applications and Examples

• Why aren't you falling right now? The normal force from the chair balances your weight, resulting in equilibrium.

• Why do you feel the ball when you kick it? The ball exerts an equal and opposite force on your foot.

• Why does a hammer stop when hitting a nail? The nail exerts a force back on the hammer, stopping its motion.

• Walking: The ground pushes forward on your foot as you push backward.

• Rocket Launch: Demonstrates Newton's Third Law in space; the action of expelling gases produces an equal and opposite reaction, propelling the rocket.

Summary Table: Newton's Laws of Motion

Additional info: The notes include visual demonstrations and everyday examples to reinforce the understanding of Newton's Laws. The concept of equilibrium and vector addition is essential for solving problems involving multiple forces.