Dynamics I

Unit 2: Force and Translational Dynamics

  • 2.1 Systems & Center of Mass

  • 2.2 Forces and Free-Body Diagram

  • 2.3 Newton’s 3rd Law

  • 2.4 Newton’s First Law

  • 2.5 Newton’s 2nd Law

  • 2.7 Kinetic & Static Friction

  • 2.8 Spring Forces

Table of Contents

  • Introduction to Dynamics

  • Newton's First Law of Motion

  • Newton's Third Law of Motion

  • Free Body Diagrams

  • Friction

  • Net Force

  • Newton's Second Law of Motion

  • Mass, Weight, and Normal Force

  • Tension

  • Springs

Galileo vs. Aristotle

  • Aristotle's View:

    • Objects require a force to maintain motion.

    • Pushed objects must be continually pushed to move (based on 'Physics' by Aristotle, 2400 years ago).

  • Galileo's Perspective:

    • Proposed a thought experiment demonstrating that motion could continue without force in an ideal environment.

Thought Experiment Description

  • Smooth Ramps Experiment:

    • A ball rolled down a ramp reaches the same height on another ramp without external forces.

    • When the second ramp is less steep, the ball rolls farther but reaches the same height, illustrating conservation of energy.

    • If the ramp is flat, the ball continues indefinitely.

  • Implications: In the absence of friction and other forces, motion is sustained.

Newton's 1st Law of Motion

  • States that an object will maintain its velocity unless acted upon by a nonzero net force.

  • Inertia (Law of Inertia):

    • Objects resist changes in their motion; mass measures this resistance.

Inertial Reference Frames

  • Valid for frames that are not accelerating or rotating.

  • Earth’s surface is considered an inertial frame despite its motion through space.

Newton’s 2nd Law of Motion

  • Defines how an object's velocity changes when influenced by a net force.

  • Relationship among acceleration, force, and mass:

    [ F = ma ]

    • Describes how acceleration is directly proportional to net force and inversely proportional to mass.

Forces and Free-Body Diagrams

  • Free Body Diagrams (FBDs) represent all forces acting on an object:

    • Use arrows to show magnitude and direction.

    • Critical for problem-solving in physics.

Net Force

  • The sum of all forces acting on an object is represented by ΣF.

  • Example:

    • A 5.0 kg object acted upon by 20 N and 30 N forces to the right:

      [ ΣF = F_1 + F_2 = 20 N + 30 N = 50 N ]

    • Direction established from the FBD.

Mass, Weight, and Normal Force

  • Mass: A scalar quantity that reflects an object's inertia.

  • Weight: A force given by gravity acting on mass:

    [ F_g = mg ]

    • Defines equilibrium in scenarios like resting objects on a table where FN equals weight.

Tension in Physics

  • Tension is a force transmitted through a string or rope when it pulls an object.

  • Calculated using FBDs; requires balancing forces:

    • Example: Load suspended will equal tension in the rope (with acceleration considered).

Friction Forces

  • Kinetic and Static Friction:

    • Kinetic friction acts on moving objects; static friction resists the initiation of motion.

    • Coefficient of friction varies based on surface pairs; e.g., rubber on concrete has high coefficients.

  • Static friction can be modeled as a maximum force before motion starts:

    [ F_f ≤ μ_s FN ]

    • Where μs = coefficient of static friction.

Spring Forces and Hooke's Law

  • Hooke's Law describes the force exerted by a spring when compressed or stretched:

    [ F = -kx ]

    • Where k = spring constant and x = displacement from equilibrium.

  • The relationship is linear; a steep slope indicates a stiffer spring.