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.