Work, Energy, and Power

• Fundamental Principle of Energy:

  • "Energy cannot be created or destroyed; it can only be changed from one form to another." - Albert Einstein

  • Energy is a central concept in physics, integrated into all its branches.

Understanding Energy

• Definition of Energy:

  • Energy is difficult to define precisely and has various forms, including:

    • Gravitational energy

    • Kinetic energy (due to motion)

    • Elastic energy (stored in springs)

    • Thermal energy

    • Nuclear energy

  • Law of Conservation of Energy:

    • Energy remains constant in a closed system; it only changes forms.

  • Force and Work:

    • Force is the means of energy change, and work is how energy is transferred.

Work

• Definition of Work:

  • Work (W) is done when a force (F) acts over a distance (d): W = Fd

  • Units: Joules (J or N·m)

  • Work can be positive, negative, or zero depending on direction and interaction.

Examples of Work

• Example 1: Lifting a book (mass = 2 kg) a distance of 3 m:

  • Force required: F = mg = (2 kg)(10 m/s²) = 20 N

  • Work done: W = Fd = (20 N)(3 m) = 60 J

Work Done at an Angle

• Work at Angles:

  • When force is applied at an angle, W = Fd cos(θ)

  • Positive work increases object speed; negative work decreases speed.

  • Example 2: Moving a crate with a force at 30°:

    • Work done by the worker: W = (FT cos θ)(d)

Negative Work and Components

• Work Done by Non-Parallel Forces:

  • Normal Force: Always does zero work (perpendicular to motion).

  • Friction Force: Does negative work (opposes motion).

Energy and Forces on an Inclined Plane

• Example 4: A box sliding down an incline:

  • Work done by gravity, normal force, and friction calculated using respective angles and forces.

Variable Forces

• Work Done by a Variable Force:

  • Calculated by area under the force vs. displacement graph.

Kinetic Energy (KE)

• Definition: Energy an object has due to its motion.

  • KE formula: K = 1/2 mv²

  • Positive work increases kinetic energy.

The Work-Energy Theorem

• Theorem: Work done (W) = change in kinetic energy (ΔK): W = K_final - K_initial

  • Negative work done by gravity when an object rises.

Potential Energy (PE)

• Definition: Energy stored due to an object’s position in a field (e.g., gravitational).

  • PE formula: U = mgh

  • Conservative Forces: Work done by gravity is independent of path taken.

Examples of Potential Energy

• Example of lifting an object and calculating the work done against gravity.

Conservation of Mechanical Energy

• Principle: In the absence of non-conservative forces, the total mechanical energy (E = K + U) remains constant.

• When energy changes, one form of energy (potential or kinetic) increases while the other decreases.

Power

• Definition: Rate at which work is done or energy transferred, given by P = W/t.

  • Units: Watts (W), where 1 W = 1 J/s.

• Power in practical examples shows how efficiently work is done.

Summary

• Work involves force applied across a displacement.

• Positive work adds energy to a system; negative work removes it.

• Energy conservation laws dictate total initial energy equals total final energy.

• Power as a measure of how quickly work is done.