W&E

Introduction to Work, Energy, and Power

Definition of Work

Common vs. Scientific Definition:

• Common understanding: Any physical or mental labor is considered 'work'.

• Scientific understanding: Work = force × displacement (only when displacement occurs due to applied force).

Conditions for Work:

Two conditions must be met:

1. A force acts on the object.

2. The object must be displaced.

Mathematical Expression of Work:

• Formula: W = F × s (where W = work, F = force, s = displacement in direction of F).

• Unit of work: Joule (J), where 1 J = 1 N × 1 m.

Negative Work:

Negative work occurs if displacement is opposite to the applied force. Example: An object slowed down by an opposing force.

Forms of Energy:

• Energy: Capacity to do work, measured in Joules. Forms include:

  • Mechanical (kinetic + potential energy)

Kinetic Energy:

Defined as energy due to motion.

• Equation: E_k = 1/2 mv² (where m = mass, v = velocity

Potential Energy:

Based on position or shape.

• Gravitational potential energy equation: E_p = mgh (where m = mass, g = gravity, h = height).

• Example: A 10 kg object at 6 m has potential energy of 588 J.

Law of Conservation of Energy:

Energy can change forms, but total energy remains constant. Example: A falling object converts gravitational potential energy into kinetic energy.

Power Definition:

• Power: Rate of doing work.

• Formula: P = W/t (where P = power, W = work done, t = time).

• Unit of power: Watt (1 W = 1 J/s).

Summary:

Work is scientifically defined as the product of force and displacement. Energy, which can take various forms and convert between them, shares the same unit as work. The law of conservation of energy states energy is neither created nor destroyed, while power measures the rate of work done.