Untitled

Energy Overview

• Definition of Energy: Capacity to do work.
• Examples:
  • Wound watch spring: Converts stored energy to mechanical energy to move watch hands.
  • Car battery: Chemical energy transformed into electrical energy to run engines.
  • Mechanical energy: Energy gained by objects when work is done.
  • Applications: Design of engines, bridges, tools, parachutes, buildings.

Forms of Mechanical Energy

• Potential Energy (PE)

• Energy at rest, dependent on arrangement and position.

• Equations:

  • Gravitational Potential Energy: $PE_{grav} = mgh$
  • where:
    • $m$ = mass of the object
    • $g$ = acceleration due to gravity
    • $h$ = height or elevation
  • Elastic Potential Energy: $PE_{elas} = \frac{1}{2}kx^2$
  • where:
    • $k$ = spring constant
    • $x$ = compression or extension length

• Kinetic Energy (KE)

• Energy associated with moving objects and waves.

• Equations:

  • $KE = \frac{1}{2}mv^2$
  • where:
    • $m$ = mass
    • $v$ = velocity

• Forms of kinetic energy: Motion, Radiant, Sound, Thermal, Wave.

Energy Transfer and Transformation

• Energy Transfer: Movement of energy from one location to another (e.g., electricity from socket to battery).
• Energy Transformation: Change of energy from one form to another (e.g., potential energy to kinetic energy).
• Conservation of Energy: Total energy is always conserved during transfers and transformations.

Examples of Energy Conversion

• Human body converts chemical energy in food to mechanical energy for movement.
• Electric fan transforms electrical energy to kinetic energy.
• The Sun converts nuclear energy into heat and light energy.
• Lightning transforms electrical energy into light, heat, and sound energy.

Law of Conservation of Energy

• Energy cannot be created or destroyed; it is transformed from one form to another.
• In mechanical energy, the sum of potential and kinetic energies remains constant:
• $ME<em>1 = ME</em>2 = ME<em>3…, ext{ where } PE</em>1 + KE<em>1 = PE</em>2 + KE<em>2 = PE</em>3 + KE_3$

Activity: Riding on a Pendulum

• Goals: Understand and relate the concepts of potential and kinetic energy; apply these concepts in an experiment.
• Procedure:
• Materials: Stopwatches, masking tape, string, weight, calculator.
• Measure and record height at equilibrium and swing points.
• Calculate potential energy at swing points.
• Synchronize stopwatches for timing.
• Questions for Analysis:
• Identify locations of maximum potential and kinetic energy, analyze the period of pendulum motion.

Example Calculation with a Free-Falling Object

• Given: 1 kg stone dropped from a height.
• Equations Used:
• Height calculation: $h = \frac{1}{2}agt^2$
• Potential Energy at height:
  • $PE = mgh = (1 ext{kg})(9.8 ext{m/s}^2)(44.1 ext{m}) = 432.18 ext{J}$
• Kinetic Energy starts at zero when dropped: $KE = 0$
• Total Mechanical Energy (TME) at release: $TME = PE + KE = 432.18 + 0 = 432.18 ext{J}$
• As it falls, potential energy decreases while kinetic energy increases.
• Energy conservation observed with totals remaining constant at each interval.