Chapter 1 paterns of Motion and Equilibrium

Chapter 1: Patterns of Motion and Equilibrium

Overview of Motion Concepts

Lecture covers key concepts:

• Aristotle on Motion

• Galileo’s Concept of Inertia

• Mass — A Measure of Inertia

• Net Force

• The Equilibrium Rule

• Support Force

• Dynamic Equilibrium

• The Force of Friction

• Speed and Velocity

• Acceleration

Aristotle on Motion

• Classification of Motion:

  • Natural Motion: Straight up or straight down.

  • Violent Motion: Imposed motion due to external push or pull.

Galileo’s Concept of Inertia

• Demolished Aristotelian Assertions: In absence of a force, objects in motion remain in motion indefinitely.

• Inertia: Resistance to Change.

  • Example: Leaning Tower of Pisa experiment with dropped objects.

  • Galileo demonstrated that all objects fall at the same rate without air resistance.

  • Horizontal Motion: In absence of friction, no force is necessary to keep a moving object in motion.

  • Experiments with Inclined Planes: Balls rolling down and up inclined planes demonstrating inertia — returning to original height.

Mass and Inertia

• Definition of Mass: Quantity of matter that composes an object.

  • Greater mass results in greater inertia, and vice versa.

• Weight: Amount of gravitational pull on an object; proportional to mass.

  • Relation: Twice the mass = twice the weight.

• Mass vs. Volume:

  • Mass: How much matter is contained.

  • Volume: How much space an object occupies.

Key Concepts of Inertia

• Units of Measurement for Mass: Kilogram (kg) is the standard; 1 kg = 10 Newton on Earth.

  • Mass remains constant regardless of location (e.g., Moon).

Net Force

• Definition: Net force combines all forces acting on an object; it is crucial for understanding how motion changes.

  • It determines changes in an object’s state of motion by indicating whether or not an object will accelerate.

• Vector Representation:

  • Force vector: Magnitude and direction represented as an arrow.

  • Resultant: Net result of combined vectors (forces).

  • To calculate net force, one must sum all forces acting on an object considering their directions, where forces acting in opposite directions subtract from each other.

• Gravitational Pull:

  • Gravitational pull is the attractive force exerted by the Earth (or another massive body) on an object, pulling it towards the center.

  • This force is calculated using the formula: Weight (W) = mass (m) × gravitational acceleration (g).

  • On Earth, g is approximately 9.8 m/s², meaning for every kilogram of mass, there is a gravitational pull of about 9.8 Newtons.

  • The gravitational pull is a constant force acting on all objects, contributing significantly to their net force when combined with other forces.

The Equilibrium Rule

• Definition: State of no change; rest or constant velocity indicates equilibrium.

• Mathematical Notation: ΣF = 0 (vector sum of forces equals zero).

• Conditions: An object can only be in equilibrium under multiple forces (net force cannot be zero under a single force alone).

Support Force

• Definition: Normal force acting upward against gravity; it is equal and opposite to the gravitational force on an object resting on a surface.

Dynamic Equilibrium

• Condition: Object moving at constant velocity; forces cancel to zero.

• Friction: Resistive force acting opposite to motion, can occur in fluids, air, or solid surfaces.

Speed and Velocity

• Speed: Distance covered per unit time.

  • Formula: Speed = Distance / Time.

• Velocity: Speed with a direction specified.

  • Average vs. Instantaneous Speed: Average speed is total distance/time.

  • Instantaneous speed is at a specific moment.

Acceleration

• Definition: Rate at which velocity changes over time.

  • Formula: Acceleration = (Change in Velocity) / Time Interval.

• Free Fall: When falling under the influence of gravity alone, experiencing gravitational acceleration (g = 9.8 m/s²).

Key Terms to Remember

• Inertia: Property of resistance to changes in motion.

• Mass: Quantity of matter; a measure of inertia.

• Weight: Force due to gravity on an object.

• Force: A push or pull.

• Friction: Resistive force opposing motion.

• Equilibrium Rule: ΣF = 0 for non-accelerating objects.

• Acceleration: Rate of change of velocity with time.

• Speed: Distance/time measurement.

• Velocity: Speed with directional component.