Forces and Vectors

Definition and Types of Forces

Forces are physical quantities that characterize how hard (magnitude) and in what direction an external agent pushes or pulls on an object. Forces are vector quantities, meaning they have both magnitude and direction.

• Contact Forces: Forces that arise from physical contact between objects (e.g., friction, tension, normal force).

• Long-Range Forces: Forces that act over a distance without direct contact (e.g., gravity).

• Examples of Forces: Gravity, spring, tension, normal, friction, drag, thrust.

Newton's Laws of Motion

Newton's First Law (Law of Inertia)

An object at rest remains at rest, and an object in motion remains in motion with constant velocity unless acted upon by a net external force.

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

• Mass: A measure of an object's inertia.

Newton's Second Law

The acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass.

• Equation:

• Units: Newtons (N), where

Newton's Third Law

For every action, there is an equal and opposite reaction. If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.

• Action-Reaction Pairs: Forces always occur in pairs acting on different objects.

Free-Body Diagrams (FBD)

Free-body diagrams are graphical representations used to visualize the forces acting on an object.

• Purpose: To identify all forces and their directions for problem-solving.

Using Newton's Second Law

Constant Mass Systems

When mass is constant, Newton's second law simplifies to:

• For equilibrium:

Variable Mass Systems

When mass changes (e.g., rockets), Newton's second law must account for the rate of change of mass.

• Equation:

Spring Force, Gravitational Force, Weight, and Mass

Spring Force (Hooke's Law)

The force exerted by a spring is proportional to its displacement from equilibrium.

• Equation:

• k: Spring constant (N/m)

• x: Displacement from equilibrium (m)

Gravitational Force and Weight

• Weight:

• g: Acceleration due to gravity ( on Earth)

Friction

Types of Friction

Friction is a force that opposes the relative motion between two surfaces in contact.

• Static Friction: Prevents motion up to a maximum value.

• Kinetic Friction: Opposes motion once movement has started.

Friction Equations

• Static Friction:

• Kinetic Friction:

• Coefficients: (static), (kinetic)

Drag Forces and Terminal Speed

Linear and Quadratic Drag

Drag forces oppose motion through a fluid and depend on velocity.

• Linear Drag: (low speeds, small objects)

• Quadratic Drag: (high speeds, large objects)

Terminal Speed

Terminal speed is reached when the drag force equals the gravitational force, resulting in zero net acceleration.

• Equation (linear drag):

• Equation (quadratic drag):

Ropes and Pulleys

Equilibrium and Tension

Ropes and pulleys are used to transmit forces and change the direction of force application.

• Tension: The force transmitted through a rope or cable.

• Equilibrium: Forces must balance for the system to be at rest or move with constant velocity.

Uniform Circular Motion

Characteristics

Uniform circular motion occurs when an object moves in a circle at constant speed.

• Velocity:

• Centripetal Acceleration:

• Centripetal Force:

Circular Orbits

Gravitational Orbits

Objects in circular orbits are subject to gravitational force as the centripetal force.

• Equation:

• Orbital Speed:

Centrifugal "Force"

Apparent Force in Rotating Frames

The centrifugal force is a fictitious force observed in a rotating reference frame, directed outward from the center of rotation.

• Equation:

Non-Uniform Circular Motion

Changing Speed in Circular Motion

When speed changes, there is both centripetal and tangential acceleration.

• Total Acceleration:

• Tangential Acceleration:

Work and Energy

Work

Work is the transfer of energy by a force acting over a distance.

• Equation:

• Units: Joules (J)

Kinetic Energy

• Equation:

Potential Energy

• Gravitational Potential Energy:

• Elastic Potential Energy (Spring):

Thermal Energy

Thermal energy is the microscopic kinetic and potential energy of particles.

Conservation of Energy

Mechanical Energy Conservation

In the absence of non-conservative forces, the total mechanical energy (kinetic + potential) of a system remains constant.

• Equation:

Work-Energy Theorem

• Equation:

Dissipative Forces and Thermal Energy

When non-conservative forces (e.g., friction) are present, mechanical energy is not conserved, and some energy is transformed into thermal energy.

• Equation:

Summary Table: Types of Forces

Additional info:

• Some context and definitions have been expanded for clarity and completeness.

• Equations and units have been standardized for academic use.

• Table entries inferred from context and standard physics curriculum.