Energy Conversion & Conservation
Understanding how energy transforms between different forms while following the Law of Conservation of Energy
The Law of Conservation of Energy
Energy Cannot Be Created or Destroyed
Energy can be transferred from one object to another, or transformed from one form to another, but the total amount of energy in a closed system remains constant.
Key Concept
When energy changes form, some energy may appear to be "lost" but it's actually transferred to the surroundings as thermal energy (heat). In real systems, energy conversions are never 100% efficient due to friction, air resistance, sound, and other factors.
Forms of Energy
Energy exists in many different forms. Here are the main types we'll focus on:
Gravitational Potential Energy (GPE)
Energy stored due to height: GPE = mgh
Example: Water at top of a dam, roller coaster at highest point
Kinetic Energy (KE)
Energy of motion: KE = ½mv²
Example: Moving car, falling object, flowing water
Elastic Potential Energy (EPE)
Energy stored in stretched/compressed objects: EPE = ½kx²
Example: Stretched spring, drawn bow, compressed trampoline
Thermal Energy
Energy due to particle motion: Q = mcΔT
Example: Heat from friction, warm objects, steam
Common Energy Conversions
Energy constantly changes form in everyday situations. Here are some important conversions:
GPE → KE
Falling Objects & Roller Coasters
Description: As an object falls, its height decreases (GPE decreases) and its speed increases (KE increases).
GPE
High, slow
KE
Low, fast
Formula: mgh = ½mv² (assuming 100% efficiency, no air resistance)
EPE → KE
Springs & Elastic Objects
Description: When a stretched spring is released, stored elastic energy converts to kinetic energy.
EPE
Stretched spring
KE
Moving object
Formula: ½kx² = ½mv² (assuming 100% efficiency)
KE → Thermal
Friction & Air Resistance
Description: When objects slide or move through air, friction converts kinetic energy to thermal energy (heat).
KE
Moving object
Thermal
Heat energy
Example: Brakes get hot when stopping a car. Rubbing hands together generates heat.
Interactive Roller Coaster Simulation
Watch how gravitational potential energy converts to kinetic energy and back again in a roller coaster!
Energy Calculations
At bottom: v = √(2gh × efficiency) = 29.7 m/s
The roller coaster shows energy conservation: GPE at top converts to KE at bottom, then back to GPE as it climbs again (minus losses to friction and air resistance).
Pendulum Energy Conversion
A pendulum demonstrates continuous conversion between GPE and KE:
Maximum GPE
Minimum KE (v = 0)
All energy is gravitational potential
Maximum KE
Minimum GPE (h = 0)
All energy is kinetic
Energy Efficiency
In real systems, energy conversions are never 100% efficient. Some energy is always transferred to the surroundings as:
- Thermal energy (heat from friction)
- Sound energy (vibrations in air)
- Light energy (sparks, glowing)
Efficiency Formula: Efficiency = (Useful Energy Output ÷ Total Energy Input) × 100%
Example: A car engine might be 25-30% efficient. Most of the fuel's chemical energy becomes waste heat!
Sankey Diagram: Energy Flow
Sankey diagrams show how energy is transformed and transferred in a system:
The width of each arrow represents the amount of energy. Notice how most energy becomes waste heat in real systems.
Solved Example Problems
Example 1: Falling Object
GCSE FoundationA 2 kg object is dropped from a height of 20 m. Calculate its speed just before it hits the ground, assuming no air resistance. (Use g = 10 N/kg)
Step 1: Apply conservation of energy
GPE at top = KE at bottom (assuming 100% conversion)
Step 2: Cancel mass from both sides
Since mass appears on both sides, it cancels out:
Step 3: Rearrange to solve for v²
v² = 2gh
Step 4: Substitute values
v² = 2 × 10 × 20 = 400
Step 5: Take square root
v = √400 = 20
Step 6: State the answer with units
Speed = 20 m/s
Step 7: Interpretation
All gravitational potential energy converts to kinetic energy. The speed doesn't depend on mass!
Example 2: Spring Launch
GCSE HigherA spring with constant 200 N/m is compressed 0.1 m and used to launch a 0.05 kg ball horizontally. Calculate the ball's speed as it leaves the spring, assuming 80% of the elastic energy converts to kinetic energy.
Step 1: Calculate elastic potential energy
EPE = ½kx² = ½ × 200 × (0.1)²
EPE = ½ × 200 × 0.01 = 1 J
Step 2: Account for efficiency
Only 80% converts to KE:
KE = 80% of EPE = 0.8 × 1 = 0.8 J
Step 3: Use kinetic energy formula
KE = ½mv²
0.8 = ½ × 0.05 × v²
Step 4: Rearrange to solve for v²
v² = (2 × KE) ÷ m = (2 × 0.8) ÷ 0.05
v² = 1.6 ÷ 0.05 = 32
Step 5: Take square root
v = √32 ≈ 5.66
Step 6: State the answer with units
Speed = 5.7 m/s (to 2 significant figures)
Step 7: Interpretation
20% of the spring's energy was "lost" as heat and sound during the launch.
Example 3: Energy Conservation with Friction
Grade 10A 10 kg box slides down a 5 m high frictionless ramp, then travels 20 m along a horizontal surface with friction before stopping. If the frictional force is 20 N, calculate the box's speed at the bottom of the ramp.
Step 1: Calculate initial GPE
GPE = mgh = 10 × 10 × 5 = 500 J (using g = 10 N/kg)
Step 2: Calculate work done against friction
Work = Force × Distance = 20 N × 20 m = 400 J
Step 3: Apply energy conservation
Initial GPE = KE at bottom + Work against friction
500 = KE + 400
KE at bottom = 500 - 400 = 100 J
Step 4: Use kinetic energy formula
KE = ½mv²
100 = ½ × 10 × v²
100 = 5 × v²
Step 5: Solve for v²
v² = 100 ÷ 5 = 20
Step 6: Take square root
v = √20 ≈ 4.47
Step 7: State the answer with units
Speed = 4.5 m/s (to 2 significant figures)
Step 8: Interpretation
Only 100 J of the initial 500 J became kinetic energy. 400 J converted to thermal energy due to friction.
Practice Problems
Test your understanding with these energy conversion problems:
Problem 1: Simple Pendulum
GCSE FoundationA 0.5 kg pendulum bob is lifted to a height of 0.8 m and released. Calculate its maximum speed at the lowest point, assuming no energy losses. (Use g = 10 N/kg)
Problem 2: Spring Efficiency
GCSE HigherA spring (k = 500 N/m) is compressed 0.2 m and launches a 0.1 kg ball vertically. If the ball rises to a height of 8 m, calculate the efficiency of the energy conversion.
Problem 3: Energy Transformation Chain
Grade 10 ChallengeA hydroelectric power station uses water falling from 50 m height. The water flows at 100 kg/s. The turbine-generator system is 80% efficient.
- Calculate the electrical power output in watts.
- If this electricity powers 20 W light bulbs, how many bulbs can it power?
Energy Conversion Calculator
Use this calculator to solve energy conversion problems: