4a._work_energy_power

Work, Energy, and Power

Overview

  • Energy Defined: Energy cannot be created or destroyed, only changed from one form to another (Einstein).

  • Key Concepts: Kinematics and dynamics involve change; energy plays a crucial role in understanding these changes.

Energy: An Overview

  • Definition: Energy is difficult to define precisely, with various forms including:

    • Gravitational energy

    • Kinetic energy (speed-related)

    • Potential energy (stored energy)

    • Thermal and nuclear energy.

  • Law of Conservation of Energy: Energy cannot appear or disappear in a closed system; it transforms into different forms.

  • Work: Force exerted over a distance causes energy change, defined as:

    • Work Formula: W = Fd (if force is constant and parallel to displacement)

    • Unit of work: joule (J).

Work and its Calculations

  • Work at Angles: When work is done at an angle, use the formula:

    • W = Fd cos(θ)

  • Positive and Negative Work:

    • Positive work increases speed; negative work decreases speed.

    • Perpendicular force does zero work.

Example Calculations

  • Example 1: Lifting a 2 kg book 3 m at constant velocity requires 60 J of work.

  • Example 2: Crate moved at a 30° angle does 600 J of work.

  • Example 3: Friction does -462 J of work on a crate.

Kinetic Energy (KE)

  • Definition: Kinetic energy is energy of motion, given by:

    • KE = (1/2)mv^2

  • Work-energy theorem: W = ΔKE, where work done transfers energy to the system.

Potential Energy (PE)

  • Definition: Stored energy based on position, e.g., gravitational potential energy:

    • PE = mgh (mass * gravity * height)

  • Change in potential energy: Important for calculating work done by gravity.

Conservation of Mechanical Energy

  • Total Mechanical Energy: E = KE + PE, conserved in absence of non-conservative forces.

  • Mechanical Energy Conservation Equation:

    • Ki + Ui = Kf + Uf

  • Example: A ball falling has constant mechanical energy when ignoring air resistance.

Power

  • Definition: Power is the rate at which work is done, expressed as:

    • P = W/t = Fv (for constant force and velocity)

  • Unit of Power: watt (W), where 1 W = 1 J/s.

Summary

  • Work causes changes in energy; positive work adds energy, negative work removes energy.

  • Kinetic energy and potential energy are conserved in closed systems under ideal conditions.