Work, Energy, and Power

• Energy Definition: Energy cannot be created or destroyed, only transformed. Key to physics in studying dynamics and kinematics.

Energy: An Overview

• Various forms: gravitational, kinetic, thermal, etc.

• Law of Conservation of Energy: Energy must convert into another form in a closed system.

• Work Definition: Application of force over a distance.

  • Work Formula: ( W = Fd )

  • Units: Joule (J) = N·m

Work at an Angle

• Work formula for angle ( \theta ): ( W = Fd \cos \theta )

• Positive work increases speed, negative work decreases speed.

Kinetic Energy

• Defined as energy of motion: ( K = \frac{1}{2}mv^2 )

• Link between work and kinetic energy established via the Work-Energy Theorem: ( W = \Delta K = K_{final} - K_{initial} )

Potential Energy

• Gravitational Potential Energy: Energy due to position in a gravitational field, given by ( U_g = mgh ).

• Important for understanding energy conservation in free-fall situations.

Conservation of Mechanical Energy

• Total mechanical energy ( E = K + U ) is conserved in the absence of nonconservative forces (e.g., friction).

• Energy transformations occur between kinetic and potential forms as motion occurs.

Nonconservative Forces

• Include friction and air resistance, modifying the conservation equation to account for work done by these forces: ( K_i + U_i + W_{other} = K_f + U_f )

Power

• Definition: Rate at which work is done or energy transferred.

  • Power Formula: ( P = \frac{W}{t} = Fv )

  • Units: Watt (W) = J/s

Summary of Key Concepts

• Work is linked to energy changes in systems:

  • Positive work adds energy; negative work removes energy.

• Mechanical energy conservation applies when nonconservative forces are absent.

• Power reflects efficiency in energy use.