Dynamics

2.1 Forces and Free-Body Diagrams

Understanding Forces

  • Importance: Understanding forces is crucial for technology design, e.g., ancient trebuchets that launch projectiles using gravity.

  • Linear Actuator: Modern device that converts motor power into motion, reducing strain of repetitive tasks.

Common Forces

  • Force Definition: A push or pull, measured in Newtons (N).

  • Types of Forces:

    • Contact Forces: Act when two objects touch.

    • Non-Contact Forces: Act at a distance (e.g., gravity).

Forces of Gravity

  • Gravity: An attractive force between masses, generally stronger for larger masses (e.g., Earth).

  • Normal Force: Balances gravity, acting perpendicular to contact surfaces; prevents objects from moving under gravity.

  • Example: 30.0 kg desk versus 1.0 kg textbook shows small gravitational attraction compared to Earth's.

Other Common Forces

  • Tension (F > T): Pulling force in ropes, strings; remains uniform even with changes in direction (e.g., pulleys).

  • Friction (F > f): Resists sliding; can be static (no motion) or kinetic (in motion).

    • Static Friction: Resists motion until a certain threshold force is overcome.

    • Kinetic Friction: Acts on moving objects, opposite to direction of motion.

    • Air Resistance: A specific form of kinetic friction affecting light and fast-moving objects.

Free-Body Diagrams (FBD)

  • Purpose: Illustrates all forces acting on an object at a moment.

  • FBD Components:

    • Dot represents the object.

    • Arrows show direction and magnitude of forces.

  • Example Use: When pushing a stationary object, forces can be visualized through an FBD to understand dynamics better.

2.2 Newton's Laws of Motion

Newton’s Laws Overview

  • Newton's First Law of Motion: An object at rest stays at rest, and a moving object continues moving at constant velocity if the net force is zero.

  • Inertia: Resistance to change in motion; greater mass means higher inertia.

Newton’s Second Law of Motion**:

  • Formula: a > = SF > /m

    • Indicates acceleration is proportional to net force and inversely proportional to mass.

  • Force Calculation: Net force determined by sum of all acting forces.

Newton’s Third Law of Motion**:

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

Applications in Problems**:

  • Examples include calculating forces acting on objects and determining resultant accelerations.

2.3 Applying Newton’s Laws

Equilibrium**:

  • An object is in equilibrium (not accelerating) when the net force is zero (SF > = 0).

  • Break forces into components for complex situations.

Problem-Solving Tutorials**:

  • Analyze forces in two dimensions: Use free-body diagrams to organize forces and determine net forces in both x and y directions.

2.4 Forces of Friction

Importance of Friction**:

  • Essential for motions like walking and driving. Without friction, objects would slide uncontrollably.

  • Friction can be static (preventing movement) or kinetic (opposing motion).

Coefficient of Friction**:

  • Determined experimentally, different for various materials, dictates how surfaces interact.

  • Examples: Ice on ice has a low coefficient (~0.03), while rubber on dry asphalt is higher (~0.5).

Types of Friction**:

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

  • Kinetic Friction: Resists motion of already sliding objects.

Overcoming Friction**:

  • When applying a force to move an object, the effect of static vs. kinetic friction should be considered to calculate acceleration and required force.