Classical Mechanics

The work-energy theorem states that the net work done on an object by all forces acting on it equals the change in its kinetic energy. When a force pushes an object, the total work performed throughout the displacement directly corresponds to how much the object's kinetic energy increases. This relationship provides a practical method to analyze motion without solving Newton's second law directly.

When an object is thrown upward, its potential energy increases while kinetic energy decreases. As the object rises, it slows down, converting kinetic energy into gravitational potential energy. When the object falls back to Earth, this process reverses: potential energy decreases while kinetic energy increases, demonstrating energy transformation under conservative forces.

Mechanical energy is the sum of kinetic and potential energies. It remains constant when only conservative forces act on an object, meaning no energy is lost to friction or other dissipative forces. By setting the change in kinetic energy equal to the negative change in potential energy, the total mechanical energy stays conserved throughout the object's motion.

Friction performs negative work on a moving object because it acts opposite to the direction of motion. This negative work reduces the object's kinetic energy, causing it to slow down. The work-energy theorem accounts for all forces, including friction, so the net work done equals the total change in kinetic energy from all sources combined.

Yes, the work-energy theorem works effectively for curved paths and irregular surfaces where solving Newton's second law directly becomes challenging. The theorem considers cumulative work done by all forces regardless of path shape, making it a versatile tool for analyzing motion in complex geometries without requiring detailed force calculations.

When an object's motion is known but the forces acting on it are unknown, the work-energy theorem allows you to derive valuable information about those forces. By examining the work done and the distance over which it acts, you can calculate the net force involved using the relationship between work and kinetic energy change.

Total work done by a force equals the sum of all infinitesimal amounts of work performed throughout an object's displacement. By integrating these small work increments and applying Newton's second law, the work-energy theorem emerges, connecting the cumulative work to the overall change in kinetic energy.