4a._work_energy_power.pdf
Work, Energy, and Power Notes
Overview
Energy is defined as the capacity to do work and change forms.
Law of Conservation of Energy: Energy cannot be created or destroyed but can change from one form to another.
Energy
Different forms include gravitational, kinetic, potential, thermal, and nuclear energy.
Work is the transfer of energy, defined as the application of force over a distance.
Work
Formula: W = F * d * cos(θ)
Scalar quantity measured in joules (J or N·m).
Positive work adds energy; negative work removes energy.
Example: Lifting a 2 kg book 3 m against gravity does 60 J of work.
Work at an Angle
When force is applied at an angle, only the component of force along the direction of motion does work.
Example: A 15 kg crate pulled at 30° with 69 N over 10 m does 600 J of work.
Kinetic and Potential Energy
Kinetic Energy (KE): Energy due to motion, defined as KE = (1/2)mv².
Potential Energy (PE): Energy stored due to position, primarily gravitational PE: PE = mgh.
Total mechanical energy (E) = KE + PE; mechanical energy is conserved in closed systems.
Work-Energy Theorem
The work done on an object equals its change in kinetic energy: W = ΔKE.
Example: A ball of mass 0.10 kg moving at 30 m/s has KE = 45 J.
Conservation of Mechanical Energy
In the absence of nonconservative forces (like friction), total energy remains constant:
( Ki + Ui = Kf + Uf )
Example: A stuntwoman at 40 m has PE = 24,000 J; if she jumps, this PE converts to KE upon landing.
Power
Power is the rate at which work is done: P = W/t.
Measured in watts (1 W = 1 J/s).
Example: A mover applies 300 N over 6 m in 20 s, resulting in a power output of 90 W.
Summary
Work: W = Fd cosθ; work can change energy states.
Energy Conservation: Total initial energy = total final energy.
Kinetic and Potential Energy: KE = (1/2)mv²; PE = mgh, energy can transform between forms.
Power: P = W/t is the efficiency of work done.