Introduction to Work, Energy, and Power

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

• Kinematics and Dynamics: Concerned with change, and energy plays a critical role.

Overview of Energy

• Different forms include:

  • Gravitational energy

  • Kinetic energy (related to speed)

  • Elastic energy (stored in springs)

  • Thermal energy (heat)

  • Nuclear energy

• Law of Conservation of Energy: Energy in a closed system remains constant.

• Work Definition: Work is the transfer of energy via force applied over distance.

Work

• Formula for Work: W = Fd (where F is force and d is distance).

• Units of Work: Joule (J), where 1 J = 1 N·m.

• Positive, Negative, Zero Work: Depends on direction of force relative to motion.

Work at an Angle

• Formula: W = Fd cos(θ) to account for angled force.

• Key Concept: Perpendicular forces do zero work.

Kinetic Energy

• Defined as: K = 1/2 mv², where m is mass and v is velocity.

• Increases with positive work done on the object.

Potential Energy

• Defined as: U = mgh, where h is height above a reference level.

• Types include gravitational potential energy and spring potential energy.

Conservation of Mechanical Energy

• In the absence of nonconservative forces, total mechanical energy (K + U) remains constant: Ki + Ui = Kf + Uf.

• Energy transformations: as potential energy decreases, kinetic energy increases and vice versa.

Power

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

• Formula: P = W/t (Power is in watts, W = J/s).

• Units: 1 watt = 1 J/s, with 1 horsepower = 746 W.

Summary

• Work relates to energy change; can be positive or negative.

• Energy is conserved in a closed system: initial energy = final energy.

• Mechanical energy can be calculated through various means, offering flexibility in problem-solving.