Work, Energy, and Power Notes

Key Concepts

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

• Work: Work is done when a force acts over a distance, expressed as W = Fd (cos θ).

• Energy Types: Includes kinetic, potential, and internal forms, affected by different forces (gravitational, elastic, etc.).

Work

• Definition: W = Fd, where F is the force and d is the distance moved in the direction of the force.

• Units: 1 Joule (J) = 1 Newton-meter (N·m).

• Work Calculation:

  • For constant force: W = Fd

  • At an angle: W = Fd (cos θ)

  • Positive work increases energy; negative work decreases energy.

Examples

• Lifting a Book: W = (force)(distance) = (20 N)(3 m) = 60 J.

• Work Against Friction: Often results in negative work when forces act in opposite directions.

Energy Types

1. Kinetic Energy (KE): Energy of motion, given by KE = (1/2)mv².

2. Potential Energy (PE): Energy stored due to position, typically gravitational PE = mgh.

Conservation of Energy

• Total mechanical energy (E = KE + PE) is conserved in a closed system without nonconservative forces:

  • E_initial = E_final

  • Changes in energy can be calculated through work done due to external forces.

Power

• Definition: Power is the rate of doing work, given by P = W/t, where t is time.

• Units: 1 Watt (W) = 1 Joule/second (J/s).

  • Example Calculation: If 1800 J of work is done in 20 s, the power output is P = 90 W.

Summary Highlights

• Work can change energy states; positive work adds energy while negative work removes it.

• Conservation of energy principles allow for the transition between kinetic and potential energy.

• Efficiency of systems can be assessed using power calculations to ensure work is done effectively.