3.3. Work, Energy, and Power

Page 1

Overview of Topic

• Introduction to Work, Energy, and Power

• Discussion of the OCR A Physics A-level content

Page 2

Work Done

• Definition: Work done is the transfer of energy when a force causes motion.

• Equation: Work done (W) = Force (F) × Distance (d) moved in the direction of the force.

• Key Points:

  • If force is at an angle, only the component of the force in the direction of movement is used.

  • Unit: Joules (J); 1 Joule is the work done when a 1 N force moves an object 1 m.

  • SI base unit: kg·m²/s².

Conservation of Energy

• Energy: Capacity to do work, scalar quantity measured in joules.

• Key Forms of Energy:

  • Kinetic Energy: Energy of moving objects.

  • Gravitational Potential Energy: Energy stored due to position in a gravitational field.

  • Elastic Potential Energy: Energy stored during reversible shape changes.

  • Electric Potential Energy: Energy from charge positions in an electric field.

  • Sound Energy: Energy from mechanical waves (movements of atoms).

  • Internal Energy: Total kinetic and potential energy of molecules.

  • Electromagnetic Energy: Stored energy in oscillating fields (waves).

  • Nuclear Energy: Energy stored and released during particle rearrangement in nuclei.

  • Chemical Energy: Energy in chemical bonds, released upon rearrangement.

• Principle of Conservation of Energy: In closed systems, energy cannot be created or destroyed, only converted.

• Example: Lifting a book transfers gravitational potential energy (GPE) when work is done against gravity; conversion occurs when the book falls, changing GPE to kinetic energy (KE).

Page 3

Kinetic and Potential Energies

Kinetic Energy

• Definition: Energy of an object due to its motion.

• Formula: KE = 1/2 mv²

  • Derived from the work done and Newton's second law (F = ma).

Gravitational Potential Energy (GPE)

• Definition: Capacity to do work due to position in a gravitational field.

• Formula: GPE = mgh

  • m = mass, g = gravitational acceleration, h = height.

• Key Points:

  • GPE increases when height increases (work done against gravity).

  • GPE decreases as an object falls back down.

Energy Exchange between Kinetic and Potential Energy

• In systems like roller coasters, KE and GPE exchange dynamically with no work against resistive forces.

• At maximum height, all energy is GPE; as it descends, GPE converts to KE, and vice versa.

Page 4

Object Speed and Energy Conservation

• Equation: mgh = 1/2 mv² leads to v = √(2gh).

  • Indicates that final speed is independent of mass (free fall acceleration).

Power and Efficiency

Power

• Definition: Rate of energy transfer.

• Formula: Power (P) = Work done (W) / Time (t)

  • SI Unit: Watts (W); 1 W = 1 J/s, SI base unit: kg·m²/s³.

• For constant velocity against resistive forces, net force must be zero, leading to:

  • P = F × v (F = force required).

Efficiency of Mechanical Systems

• Real systems experience energy losses (e.g., thermal energy).

• Efficiency Formula: Efficiency (%) = (Useful Output Energy / Total Input Energy) × 100

  • Greater efficiency indicates less energy waste.