Work, Energy, and Power
Work done by constant forces (W = F · s cos θ), work-energy theorem, gravitational and elastic potential energies, mechanical energy conservation, and power.
Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.
Learning Objectives
- Calculate work done by forces inclined to displacement and understand zero-work scenarios.
- Apply conservation of mechanical energy (E_k + E_p = constant) to conservative gravitational and elastic systems.
Core Theory & Concepts
Energy is the capacity to do mechanical work. Work quantifies energy transferred by a force acting over a displacement. In the absence of non-conservative dissipative forces like friction, total mechanical energy is conserved.
Work-Energy Theorem
The net work done on an object by all forces equals the change in its kinetic energy: W_net = ΔE_k = ½m v² - ½m u².
Mechanical Power
Power is the time rate at which work is performed: P = W / t. When force F produces velocity v: P = F · v.
Common Misconceptions
Believing centripetal force does work on a particle in uniform circular motion.
Syllabus Topic Outline
- 1Work definition W = F · s · cos θ
- 2Work-Energy Theorem: W_net = ΔE_k
- 3Gravitational potential energy (mgh) and elastic potential energy (½kx²)
- 4Power as rate of work P = dW/dt = F · v