Copy of Conservation of Mechanical energy

February 20, 2025

  • Welcoming message to students: "WELCOME TO MY CLASS"

  • Inspirational note: "Learning Never Stops!"

February 27, 2025

Conservation of Mechanical Energy

  • Educator: Brench Lander G. Gemina

Content Standard

  • Learners demonstrate an understanding of the conservation of mechanical energy.

Learning Competency

  • Ability to explain energy transformation in various activities/events.

Learning Targets

  • At the end of the lesson, students should be able to:

    • Infer that the total mechanical energy remains the same during any process.

    • Perform activities to demonstrate the conservation of mechanical energy.

Key Notes

Energy in Objects

  • Every object has energy, regardless of its motion state (at rest or moving).

Energy Transformation

  • Energy can be converted from one form to another and is considered conserved in the process.

Mechanical Energy

  • Definition: Energy acquired by objects when work is done.

  • Relates closely to the definition of energy as the capacity to perform work.

Types of Mechanical Energy

  1. Potential Energy (PE)

    • Energy possessed by objects at rest.

    • Gravitational Potential Energy: Energy due to an object's position.

    • Elastic Potential Energy: Energy stored in deformed elastic materials (e.g., springs).

  2. Kinetic Energy (KE)

    • Energy possessed by an object in motion.

    • Potential energy is "waiting" and kinetic energy is "moving."

Energy Transformation Example

  • From Potential to Kinetic Energy:

    • The ball at the top has potential energy (stationary) and can convert it into kinetic energy as it falls.

    • When it hits the ground, all potential energy converts to kinetic energy until it stops.

Total Mechanical Energy

  • Formula: MET = PE + KE

    • MET = Total Mechanical Energy

    • PE = Potential Energy

    • KE = Kinetic Energy

Gravitational Potential Energy Equation

  • GPE = mgh

    • GPE: Gravitational Potential Energy

    • m: mass of the object

    • g: acceleration due to gravity (9.8 m/s²)

    • h: height from ground

Kinetic Energy Equation

  • KE = (1/2) mv²

    • KE: Kinetic Energy

    • m: mass of the object

    • v: velocity

G.U.E.S.S. Method for Problem Solving

  • G: Given

  • U: Unknown

  • E: Equation

  • S: Substitution

  • S: Solution

Sample Problems

  1. Gravitational Potential Energy:

    • A 2 kg ball is on a 5-meter-high shelf. Calculate its GPE.

  2. Kinetic Energy:

    • A 1,200 kg car is moving at 20 m/s. Determine its kinetic energy.

  3. Speed Before Hitting Ground:

    • A 3 kg rock falls from a 10-meter-high cliff. Determine its speed just before impact.

  4. Maximum Height Calculation:

    • A 50 kg student jumps and reaches a speed of 3 m/s before leaving the ground. Calculate the height reached.

Key Concepts

  • Energy is essential for performing work; it remains undetectable yet evident in physical transformations.

  • Law of Conservation of Energy: Energy cannot be created or destroyed but only transferred or transformed while the total energy remains constant.

    • Equation: ME_initial = ME_final (PE1 + KE1 = PE2 + KE2)

Example Problem Illustration

  • During a flood, a 100 kg tree trunk falls down a 5m-high waterfall. Calculate:

    • a. Its potential energy at the top of the waterfall.

    • b. Its kinetic energy at the bottom of the waterfall.

    • c. Its velocity as it reaches the bottom.

Check Problems

  1. Speed at Point B:

    • A 275 kg roller coaster travels at 12 m/s at a height of 10m at Point A. Calculate its speed at the bottom (Point B).

  2. Dropped Rock:

    • A 3 kg rock dropped from 10 meters high. Calculate:

      • a. Its potential energy before falling.

      • b. Its kinetic energy when 5 meters above ground.

      • c. Its speed just before it hits the ground.

  3. Dropped Ball Analysis:

    • A 2 kg ball dropped from 5 meters:

      • a. Calculate total mechanical energy before drop.

      • b. Calculate speed just before impact.