Work, Energy, and Power

• Definition of Energy

  • Energy cannot be created or destroyed, only transformed.

  • Key players in energy concepts: force (creating change) and work (transfer of energy).

Energy: An Overview

• Forms of Energy

  • Gravitational, kinetic, nuclear, thermal, elastic (spring), etc.

  • Each form obeys the Law of Conservation of Energy, meaning it can change forms but not vanish in a closed system.

• Key Concepts

  • Force causes changes in energy.

  • Work is the measure of energy transfer.

Work

• Definition of Work

  • Work (W) is done when a force (F) acts over a distance (d).

  • Formula: W = Fd (when F is parallel to d).

  • Measured in joules (J), where 1 J = 1 N·m.

  • Work can be positive, negative, or zero.

• Calculation Example (Positive Work)

  • Lifting a 2 kg book by 3 m:

    • Weight (F): F = mg = 20 N

    • Work: W = Fd = (20 N)(3 m) = 60 J.

• Work at an Angle

  • For angles, use: W = Fd(cos θ).

    • Perpendicular force does zero work.

• Calculation Example (Angle)

  • 15 kg crate, force at 30°:

    • W = (FT(cos θ))(d) = (69 N)(cos 30°)(10 m) = 600 J.

Work and Friction

• Normal Force

  • Normal force does zero work since perpendicular to motion.

• Friction Force Example

  • Work done by friction (negative work):

    • W = -μkFN·d

    • Negative work indicates an opposing action.

Kinetic Energy

• Definition

  • Kinetic energy (K) is energy of motion: K = (1/2)mv².

  • Work done transfers energy to an object, increasing its kinetic energy.

• Example

  • Kinetic energy of a 0.10 kg ball at 30 m/s: K = (1/2)(0.10 kg)(30 m/s)² = 45 J.

Potential Energy

• Definition

  • Potential energy (U) is energy by virtue of position.

  • Example: U = mgh (gravitational potential energy).

• Example

  • Work done lifting a 2 kg ball to height 1.5 m: W = -Fwh = -mgh = -30 J.

    • Change in potential energy during this lift is +30 J.

Conservation of Mechanical Energy

• Principle

  • Total mechanical energy (E): E = K + U

  • Mechanical energy is conserved without nonconservative forces acting.

• Equations

  • Ki + Ui = Kf + Uf

  • Example of energy change calculated through height and speed changes.

Power

• Definition

  • Power (P) is the rate of doing work: P = W/t.

  • Unit: Joule/second (Watt).

  • Example: Moving a crate with 300 N force over 6 m in 20 s results in P = 90 W.

Summary of Key Concepts

• Work: W = Fd cosθ

• Energy Conservation: Ki + Ui ± W = Kf + Uf

• Power: P = W/t = Fv.

• Understanding of energy changes, work done, and the relationships among forms of energy is crucial for problem-solving in physics.