Work, Energy, and Power

• Energy cannot be created or destroyed, only transformed from one form to another.

  • Quote by Albert Einstein emphasizes the fundamental principle of energy conservation.

  • Kinematics and dynamics focus on the changes that require energy.

Energy: An Overview

• Defining Energy:

  • Challenging to provide precise definitions; energy can exist in various forms.

  • Forms of energy include:

    • Gravitational energy

    • Kinetic energy (due to speed)

    • Elastic potential energy (stored in springs)

    • Thermal energy

    • Nuclear energy

• Law of Conservation of Energy:

  • Energy is conserved in a closed system; it can only change form.

  • Work is the method of transferring energy between systems.

Work

• Concept of Work:

  • Work (W) is defined as the application of force over a distance.

  • Equation: W = Fd (when force F is constant and parallel to the distance d).

  • Units of Work: 1 Joule (J) = 1 Newton-meter (N·m).

• Scalar vs Vector:

  • Work is a scalar quantity, despite depending on the vector quantities of force and distance.

  • Can have positive, negative, or zero values based on direction.

Work Examples

• Example 1: Lifting a Book

  • Lifting a 2 kg book to a height of 3 m requires work.

  • Calculation: W = Fd = (20 N)(3 m) = 60 J.

• Work at an Angle:

  • Modified formula: W = Fd cos θ (when forces are at angles).

  • Important Notes:

    • Positive work increases speed; negative work decreases speed.

    • Perpendicular force yields zero work.

• Example 2: Moving a Crate

  • Scenario: A 15 kg crate pulled at a 30° angle with a force of 69 N over 10 m.

    • Calculation: W = (69 N · cos 30°)(10 m) = 600 J.

Work Done by Non-Negative Forces

• Work done by normal and friction forces:

  • Normal force does zero work if perpendicular to motion

  • Friction does negative work opposing motion.

  • Example 3: Work done by friction = -462 J.

Kinetic Energy

• Defined as energy of motion: K = (1/2)mv².

• Directly related to work done: positive work increases kinetic energy, negative work decreases it.

• Work-Energy Theorem: Wtotal = ΔK (total work is the change in kinetic energy).

Potential Energy

• Potential energy (U) depends on position:

  • Gravitational potential energy: U = mgh.

• When objects are raised in height, work is done against gravity:

  • Example: Lifting a 2kg ball to a height of 1.5m results in U = 30 J.

Conservation of Mechanical Energy

• Mechanical energy is conserved in ideal scenarios (no non-conservative forces like friction).

  • Total Mechanical Energy = K + U

  • For an object in free fall, the potential energy converts to kinetic energy as it falls.

Power

• Defined as the rate at which work is done or energy is transferred:

  • Units: 1 Watt (W) = 1 Joule/second.

  • Formula: P = W/t or P = Fv (for constant forces and velocities).

• Example: A mover doing 1,800 J of work in 20 seconds has a power output of 90 W.

Summary

• Work: W = Fd cos θ; can be positive, negative, or zero.

• Energy: Conserved; total initial energy equals total final energy in closed systems.

• Kinetic Energy: K = (1/2)mv², work done leads to changes in kinetic energy.

• Potential Energy: U = mgh; depends on position within a gravitational field.

• Power: Rate of doing work, P = W/t.