Energy Overview

• Energy cannot be created or destroyed; it can only change forms (Law of Conservation of Energy).

• Energy arises from different forces: gravitational, thermal, nuclear, etc.

• Work (W) is the transfer of energy via force acting over a distance.

• Work is measured in joules (J) where 1 J = 1 N·m.

Work

• Definition: W = F * d (when force is parallel to the direction of motion).

• Work is a scalar quantity but can be positive, negative, or zero

Work at an Angle

• Formula: W = Fd * cos(θ) (uses the component of force parallel to displacement).

• Perpendicular Force: Always results in zero work.

Kinetic and Potential Energy

• Kinetic Energy (KE): The energy of motion, defined as KE = (1/2)mv².

• Potential Energy (PE): Energy stored due to position. For gravitational potential energy: PE = mgh

Work-Energy Theorem

• The work done on an object equals the change in its kinetic energy: W = ΔKE.

Conservation of Mechanical Energy

• If only conservative forces act, then initial mechanical energy = final mechanical energy: KE_initial + PE_initial = KE_final + PE_final.

Power

• Defined as the rate at which work is done: P = W/t.

• Measured in watts (W), where 1 W = 1 J/s.

Summary of Important Equations

• Work: W = Fd * cos(θ)

• Kinetic Energy: KE = (1/2)mv²

• Potential Energy: PE = mgh

• Power: P = Fv = W/t

• Conservation: KE_initial + PE_initial = KE_final + PE_final (if no nonconservative forces).

Key Points

• Positive work increases energy in a system; negative work decreases it.

• Mechanical energy remains constant in a closed system without nonconservative forces.