Work, Power, Energy & Conservation

What is Work (Everyday vs Science)

• In science, work is done only when a force moves a body in the direction of the force. Reading, or holding a heavy bag still, is effort but zero work.
• Work is a scalar; its SI unit is the joule (J): 1 J is the work done when 1 N moves a body 1 m in its own direction (1 J = 1 N·m).

Formula and Units of Work

• Force along the motion: W = F × s. Force at angle θ: W = F × s × cos θ, since only the component along the motion counts.
• Dimensional formula of work: [ML²T⁻²].

Positive, Zero and Negative Work

• Positive work: the force helps the motion (θ < 90°) and gives energy to the body.
• Negative work: the force opposes the motion (θ > 90°), like friction, or gravity on a rising body, and takes energy away.
• Zero work: the force is perpendicular to the motion (θ = 90°, cos 90° = 0).

• Angle and Sign of Work

Energy – Capacity to Do Work

• Energy: the ability of a body to do work (to push, pull, lift or move something).
• Its unit is the joule, like work; it is a scalar, dimensions [ML²T⁻²]. 1 kJ = 1000 J; 1 calorie ≈ 4.18 J.

Different Forms of Energy

• Mechanical energy = kinetic + potential energy.
• Chemical energy is stored in food, fuels and batteries; nuclear energy is locked inside the nucleus of atoms.
• Energy changes continually from one form to another, and every form can be expressed in joules.
• Forms of Energy

Kinetic Energy (Energy of Motion)

• Kinetic energy: energy a body has because it is moving. KE = ½ m v² (m in kg, v in m/s).
• KE is never negative, since v² cannot be negative. Examples: a moving hammer driving a nail, wind turning a windmill.

Work–Energy Theorem

• Work–energy theorem: the net work done on a body equals its change in kinetic energy: W = ΔKE = KE_final − KE_initial.
• Positive net work speeds a body up; negative net work (friction) slows it down.
• A body of mass m at speed v can do work ½ m v² before stopping, which is why a fast car is harder to stop.

Potential Energy (Stored Energy)

• Potential energy: energy stored because of a body's position or shape (configuration).
• Gravitational PE of a body lifted to height h: PE = m × g × h.
• Elastic PE is stored in a stretched spring, bent bow, catapult or wound clock-spring.
• Rock layers at fault lines store PE like compressed springs and release it as earthquakes.

Kinetic vs Potential Energy

• Kinetic energy needs motion; potential energy needs position or shape. Both are measured in joules, dimensions [ML²T⁻²].
• A falling stone turns its potential energy into kinetic energy.
• Kinetic vs Potential Energy

Mechanical Energy & Conservation of Energy

• Mechanical energy = KE + PE, the energy of motion and position together.
• Law of conservation of energy: energy can change form but is never created or destroyed; the total energy of an isolated system stays constant.
• If only gravity acts, KE + PE stays constant: as PE falls, KE rises by exactly the same amount.

Energy Conservation in Free Fall

• A freely falling body's PE continuously decreases as it loses height and turns into kinetic energy, so it speeds up.
• At the top: maximum PE, zero KE. Just before landing: maximum KE, minimum PE.

Power – Rate of Doing Work

• Power: the rate of doing work (or of transferring energy): P = W / t.
• SI unit the watt (W): 1 W = 1 J/s. 1 kW = 1000 W; 1 horsepower ≈ 746 W.
• Power is a scalar, dimensions [ML²T⁻³].
• Power and Energy Units

Energy Conversions & Friction

• A windmill turns the kinetic energy of wind into electrical energy; a battery turns chemical energy into electrical; a bulb turns electrical energy into light and heat.
• Rubbing hands, or brakes, show kinetic energy turning into heat through friction.
• Friction always does negative work: it opposes motion and produces heat (energy lost).
• Energy Conversion Devices