4a._work_energy_power (1)

Work, Energy, and Power

• Definition of Energy: Energy cannot be created or destroyed, only transformed.

• Change: Kinematics and dynamics revolve around change in states of objects.

Energy: An Overview

• Energy forms: Types include gravitational, kinetic, potential, thermal, nuclear.

• Conservation of Energy: Energy in a closed system remains constant; it converts from one form to another.

Work

• Definition: Work (W) is done when a force is exerted over a distance—W = Fd.

• Units: Measured in joules (J); 1 J = 1 N·m.

• Positive, Negative, Zero Work:

  • Positive work increases kinetic energy.

  • Negative work decreases kinetic energy.

  • Perpendicular force = 0 work.

• Work Done At an Angle: W = Fd(cos θ).

Examples of Work

• Lifting a Book: Calculated by W = Fd, with F = mg.

• Crate on Horizontal Floor: W = (FT cos θ)d for inclined forces.

Kinetic Energy (KE)

• Definition: KE = (1/2)mv^2; energy of motion.

• Work-Energy Theorem: Work done on an object is equal to the change in KE.

Potential Energy (PE)

• Definition: PE depends on an object's position; specifically gravitational potential energy: U = mgh.

• Conservative vs Non-Conservative Forces:

  • Conservative forces (like gravity) depend on position change.

  • Non-conservative forces (like friction) depend on path taken.

Conservation of Mechanical Energy

• Total mechanical energy (E = KE + PE) is conserved in the absence of non-conservative forces.

• Example: A ball dropped from a height transforms potential energy into kinetic energy on impact.

Power

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

• Units: 1 W = 1 J/s, horsepower also used.

• Applications: Example of a mover exerting force and calculating power output.

Summary

• Work leads to energy changes. Positive work adds energy; negative work removes energy.

• Conservation laws: Total initial energy = Total final energy in closed systems.

• Key formulas: W = Fd cosθ, KE = (1/2)mv^2, PE = mgh, P = W/t.