Lecture3-24

Modelling in Physics

• Objects as Points

  • Model objects by ignoring their size and shape.

• Forces and Movement

  • Focus on forces that cause movement of the point object.

  • Movement is analyzed in a plane using vectors.

Learning Outcomes

• Understanding Force

  • Learn the concept of force in physics and its vector nature.

  • Explore the significance of the net force on an object.

• Equilibrium

  • What occurs when the net force is zero and the importance of inertial frames.

• Acceleration and Mass

  • Understand how acceleration is derived from net force and mass.

• Mass vs. Weight

  • Differentiate between mass of an object and its weight.

• Interactions of Forces

  • Explore the relationship between forces exerted by two objects on each other.

Introduction to Dynamics

• Kinematics Review

  • Recap of using kinematics to describe motion in various dimensions.

• What Causes Motion?

  • Dynamics explains the relationship between motion and the forces causing it.

• Newton's Laws

  • Newton’s laws of motion were derived from extensive experiments by other scientists.

Properties of Forces

• Definition of Force

  • A force is defined as a push or pull.

  • It is an interaction between two objects or an object and its environment.

• Vector Quantity

  • Forces have both magnitude and direction.

Types of Forces in Mechanics

• Normal Force

  • A contact force acting perpendicular to surfaces.

  • Counteracts the weight of an object resting on a surface.

• Friction

  • A contact force that opposes the motion of objects sliding over surfaces.

• Tension

  • A contact force experienced in cables or ropes when pulled taut.

• Weight

  • A long-range force acting downwards due to gravity.

Drawing Force Vectors

• Representing Forces

  • Vectors represent applied forces; their length corresponds to magnitude.

Superposition of Forces

• Combining Forces

  • The net effect of multiple forces acting at a point can be represented by their vector sum.

Decomposing Forces

• Component Vectors

  • Use perpendicular x- and y-axes to analyze forces.

  • Trigonometric methods can be employed to determine the components of a force.

Notation for Vector Sum

• Resultant Force

  • The net force is the total vector sum of all forces acting on an object.

Newton's First Law

• Equilibrium

  • An object remains at rest or in constant velocity unless acted on by a net force.

  • Net force must be zero for an object to be in equilibrium.

Net Force Causes Acceleration

• Example with a Hockey Puck

  • Accelerates in the direction of the net applied force.

Newton's Second Law of Motion

• Force and Acceleration Relationship

  • Acceleration of an object is directly proportional to net force and inversely to mass.

Object Under Uniform Circular Motion

• Centripetal Force

  • Acceleration directed toward the center of the circle requiring a net external force.

Mass and Acceleration

• Resistance to Acceleration

  • An object's mass determines its resistance to acceleration under a constant force.

Newton's Second Law in Detail

• Force and Mass Proportionality

  • SI unit of force is the newton (N).

Mass and Weight Relationship

• Weight Calculation

  • Weight is the gravitational force exerted by the earth on an object.

  • Relation: ( w = mg ) (weight = mass × gravitational acceleration).

Apparent Weight and Weightlessness

• Effects of Acceleration

  • Apparent weight changes with the acceleration of a reference frame (e.g., in elevators).

Newton's Third Law

• Action-Reaction Principle

  • For every action, there is an equal and opposite reaction.

Free-Body Diagrams

• Visualization of Forces

  • Diagrams illustrate forces acting on an object, highlighting actions and reactions.

Problem Solving in Dynamics

• Steps to Solve

  • Identify knowns and unknowns, create sketches, apply Newton's laws.

Frictional Forces

• Nature of Friction

  • Opposes motion; increases with the mass of the object.

Kinetic and Static Friction

• Types of Friction

  • Kinetic friction applies during movement; static friction acts at rest.

Static to Kinetic Friction Transition

• Behavior of Friction

  • Static friction is overcome to initiate motion; kinetic friction acts during sliding.

Free-Body Diagrams Consideration

• Forces on a Person Walking

  • Must account for static and kinetic friction in free-body diagrams.

Friction Example Problem

• Calculating Forces

  • Determine minimum force required to move an object on a surface.

  • Assess block’s acceleration with applied force.