Work, Energy, and Power

• Definition: Energy cannot be created or destroyed, only transformed (Einstein).

• Introduction: Kinematics and dynamics deal with change, incorporating energy over time.

Energy Overview

• Definition of Energy: Difficult to define precisely; exists in various forms (gravitational, kinetic, potential, thermal, etc.).

• Law of Conservation of Energy: Energy in a closed system must remain constant; can only change form.

• Role of Forces: Forces cause change in energy, while work transfers energy between systems.

Work

• Definition of Work: Work occurs when a force acts on an object over a distance.

  • Formula: W = Fd (if force and distance are parallel)

• Units of Work: Joule (J), where 1 Joule = 1 Newton-meter.

• Types of Work:

  • Positive Work: Increases energy (object speeds up).

  • Negative Work: Decreases energy (object slows down).

  • Zero Work: Force perpendicular to movement.

Work Calculation

• Example 1: Lifting a book. Work done = Fd = (20 N)(3 m) = 60 J.

• Work at an Angle: When force is applied at an angle,

  • Formula: W = Fd cos θ.

Variable Forces

• When force varies, calculate work using the area under a force versus displacement graph.

• Example 5: Calculate work done in a spring system using geometry (trapezoid, triangle areas).

Kinetic Energy

• Definition: Energy due to motion.

  • Formula: K = (1/2)mv².

• Work-Energy Theorem: Work done on an object equals the change in kinetic energy.

Conservation of Energy

• Conservation Principle: Total mechanical energy (K + U) remains constant in the absence of non-conservative forces (like friction).

  • Equation: Ki + Ui = Kf + Uf.

Potential Energy

• Definition: Energy due to an object's position or configuration, often translatable to kinetic energy.

• Gravitational Potential Energy: U = mgh.

  • Work done against gravity = -Wby gravity.

• Examples of Potential Energy: Springs, electric fields, etc.

Power

• Definition: The rate of doing work or transferring energy.

  • Formula: P = W/t = Fv.

• Unit: Watt (W), where 1 W = 1 J/s.

• Example: Mover pushing a crate: P = W/t.

Summary Points

• Work results from force across a displacement.

• Energy transformations are key; energy conservation prevails in closed systems.

• Kinetic and potential energy relate inversely; understanding their conservation aids in solving problems in physics.