4_PHYS_200_Dynamincs

Dynamics Overview

• Work ( ( W ): Work done by a constant force can be calculated using the formula:( W = F \cdot d \cdot \cos \theta )

  • Mechanical Advantage: Consideration in forces affecting motion.

  • Kinetic Energy Theorem: Connects work done with energy changes in objects.

  • Conservative Forces: Forces like gravity that do not dissipate energy.

• Energy Formulas:

  • Kinetic Energy ( ( KE ): ( KE = \frac{1}{2} mv^2 )

  • Potential Energy (PE):

    • Gravitational: ( PE = mgh )

    • Spring: ( PEet = 1/2kx² )

  • Conservation of Energy: Total energy within a closed system remains constant.

Forces

• Newton’s Laws:

  • First Law (Inertia): An object at rest stays at rest; an object in motion stays in motion unless acted on by a net force.

  • Second Law: ( F = ma ) – The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

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

• Friction: Static versus kinetic friction, which opposes motion depending on interaction surfaces.

• Center of Mass & Equilibrium: Analyze systems for stability and force distribution.

Learning Outcomes: Forces

1. Definition of Force: A push or pull that can change an object's state of motion.

2. Characteristics: Force is a vector with magnitude, direction, and components.

3. Types of Forces:

• Contact Forces: Friction, tension, normal force, drag.

• Non-contact Forces: Gravitational, electrostatic, magnetic.

4. Conservative vs Non-Conservative Forces: Conservative forces, like gravity, only depend on position; non-conservative forces depend on the path taken.

5. Weight vs Mass: Mass is a scalar property; weight is the force due to gravity, always directed downward.

6. Free-Body Diagrams: Illustrate all forces acting on an object.

Work and Energy

• Work Definition: Energy transferred by a force acting through a distance; work can be positive or negative based on direction relative to force.

• Power: Rate of doing work; can be calculated as average power over a time interval or instantaneous power using force and velocity components.

• Energy and Its Forms: Includes kinetic, potential, thermal, chemical, gravitational, mechanical, and sound energy.

• Principle of Conservation of Energy: Energy is neither created nor destroyed; it only transforms from one form to another.

Momentum and Collisions

• Momentum: The quantity of motion; linear momentum ( p = mv ). Properties and calculations based on mass and velocity.

• Impulse: Change in momentum resulting from a force applied over time.

• Conservation of Momentum: In isolated systems, the total momentum before and after collisions remains constant.

• Types of Collisions:

  • Elastic: Kinetic energy remains constant; objects bounce off each other.

  • Inelastic: Some kinetic energy converts to other forms; total momentum conserved, but not kinetic energy.

  • Real-world collisions are typically inelastic.