Energy Notes

What is Energy?

• Definition: Energy is hard to define simply; various attempts at definition are presented throughout the lecture.
• Activity: The lecture begins with an exercise: define energy, draw a picture, with the condition that if your answer seems right, it's considered wrong.

Energy and its Manifestations

• Energy's Role: Energy allows things to happen, especially movement.
• Examples:
  • Energy powers Tony Stark's suit.
  • Energy powers everything around us.

Nature of Energy

• Definition Attempt: Energy is a power, source, or property used to heat up a body or physical system.
• Fuels: Energy can be derived from fuel, like food, or chemicals.
• Multiple Forms: Energy is not of a single type; there exist:
  • Solar energy
  • Nuclear energy
  • Sound energy
  • Chemical energy
  • Gravitational energy
  • Thermal energy
• Ubiquity: Energy is everywhere and dictates the existence of everything.
  • Example: A stress ball named Princess.

Energy as Currency

• Metaphor: Energy is the currency of our world.
• Principle: Everything we do uses the principles of energy.

Unit Overview

• Objectives: The unit will investigate:
  • What energy is
  • How we use energy
  • Why energy matters to us

Defining Energy

• Formal Definition: Energy is the ability to do work (acknowledged as a "lame" definition).

Defining Work

• Formal Definition: Work is the product of the component of force in the direction of motion times the distance through which the force acts.
• Formula: W = Fd \cos \theta

Work Equation Breakdown

• Variables:
  • W: Work
  • F: Force
  • \theta: Angle between the force and displacement
  • d: Displacement of the object
• Unit: Measured in Joules [J]

Work Example

• Scenario: Calculating work done on a lawn mower.
• Problem: A person exerts a constant force of 75.0N at an angle 35^\circ below the horizontal and pushes the mower 25.0m on level ground. How much work is done?

Maximizing and Minimizing Work

• Question: Under what circumstances is work maximized? When is it minimized?

Energy Types

• Concept: Different scenarios produce different kinds of energy.

Potential Energy (PE)

• Definition: Energy that is “stored” due to an object’s position (not movement).

Energy Stored in Position

• Scenario 1 - Gravity: A 25kg object is lifted 2m off the ground.
  • Work done: W = Fd \cos \theta where \theta = 0 so \cos(0) = 1
  • W = F_g h
  • Since F_g = mg, then Gravitational Potential Energy (GPE) can be expressed as:
  • GPE = mgh
• Scenario 2 - Springs: Energy stored in springs depends on how much the spring is compressed or stretched.
  • Hooke's Law: F = Kx
    • K: Spring constant [N/m]
    • x: Displacement from equilibrium [m]
  • Work Done: W = Fd \cos \theta
  • W = Kx \cdot x
  • W = \frac{1}{2} Kx^2
  • Elastic Potential Energy (EPE): EPE = \frac{1}{2}kx^2

Kinetic Energy (KE)

• Definition: Energy of