Lesson 4.4

Conservation & Transformation
of Energy

Energy transformation in systems helps us to make work easier. In a closed system, energy is never created or destroyed. It only transforms.

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Core Concepts

Click on the cards to reveal the definitions.

System

A specific group of interacting parts we are studying.

Transformation

Energy changing from one specific form to another.

Conservation

Staying the exact same total amount; never lost or created.

Mechanical Energy

The total combined energy of an object's motion and position.

The Two Main Forms of Mechanical Energy

Potential Energy (Ep)

Stored energy based on position or shape.

Gravity: Ep = mgh

(Mass × Gravity × Height)

Elastic: Ep = kx² / 2

(Stiffness × Deformation² / 2)

Kinetic Energy (Ek)

Active energy based on motion.

Motion: Ek = mv² / 2

(Mass × Velocity² / 2)

The Law of Conservation of Mechanical Energy

In a closed system, initial energy equals final energy.

Ek1 + Ep1 = Ek2 + Ep2

Visualizing the Law: The Free-Falling Ball

Move the slider to drop the ball. Watch how Potential Energy (Height) transforms entirely into Kinetic Energy (Speed) as it falls, while Total Energy remains constant.

10m
0m

Energy Levels

Total: 100 J
100
Ep
0
Ek

At max height, all energy is Potential.

The Problem-Solving Blueprint

Step 1: Given → Step 2: Equation → Step 3: Solution

Level 1 Direct Transformation

The Problem: A 2 kg ball is dropped from 10 meters. What is its kinetic energy right before it hits the ground? (g = 9.8 m/s²)

1. Given

  • m = 2 kg
  • h = 10 m
  • v1 = 0 m/s

2. Equation

Because it starts at rest, Ek1 is 0. All Ep1 becomes Ek2.

Ep1 = Ek2

3. Solution (Your Turn)

Ek2 = m × g × h

J

Level 2 Solving for Velocity

Level 3 Elastic Deformations