Law of Conservation of Energy Formula with Step-by-Step Example
The Law of Conservation of Energy is a fundamental principle in physics that states: energy cannot be created or destroyed; it can only change from one form to another. In a closed system, the total energy before and after any physical process remains constant, even if the energy transforms between different types. This concept is essential for understanding mechanics, thermodynamics, and many real-world phenomena.
For example, when a ball is dropped from a height, it does not bounce back to its original position. The energy isn't lost but is converted into sound, heat, and motion of air around the ball. This demonstrates how energy continually shifts forms, yet the total energy in a closed system stays the same.
Types of Energy
Energy exists in several forms. Some of the common types are:
- Kinetic Energy (energy of motion)
- Gravitational Potential Energy (energy due to height)
- Elastic Potential Energy (energy stored in stretched objects)
- Thermal Energy (energy due to temperature)
- Sound Energy
- Light Energy
- Electrical Energy
- Chemical Energy
- Nuclear Energy
Law of Conservation of Energy: Explanation and Formula
In a closed system, the sum of all energies before an event equals the sum after the event. This is generally written as:
For instance, if you drop a ball from a height, it has gravitational potential energy at the start. As it falls, some of this energy converts into kinetic energy.
When it hits the ground, some energy turns into sound and heat, while the remainder is kinetic. At each stage, if you sum all the energies, the total remains constant within the system.
| Event Stage | Total Energy Expression | Explanation |
|---|---|---|
| Before Drop | ΣEbefore = Eg | All energy is gravitational potential |
| During Fall | ΣEfalling = Eg + Ek | Energy is partly potential, partly kinetic |
| At Ground Impact | ΣEground = Ek + Esound + Eheat | Energy converted into kinetic, sound & heat |
Worked Example: Ball Dropped From Height
Suppose a 0.5 kg ball is dropped from 10 meters. Find the energy lost as heat and sound if its speed on impact is 13 m/s.
- Gravitational potential energy at the start:
Eg = m g Δh = 0.5 × 9.8 × 10 = 49 J - Kinetic energy just before impact:
Ek = (1/2) × 0.5 × (13)2 = 42.25 J - By conservation:
Eg = Ek + Edissipated
Edissipated = 49 – 42.25 = 6.75 J
So, 6.75 J of energy is lost as sound and heat during the ball’s fall.
Key Formulas in Conservation of Energy
| Type | Formula | Description |
|---|---|---|
| Kinetic Energy | Ek = (1/2)mv2 | Energy due to motion |
| Gravitational Potential Energy (surface) | Eg = m g Δh | Energy due to height above ground |
| Gravitational Potential Energy (general) | Eg = -G m ME/r | For objects far from Earth’s surface |
| Elastic Potential Energy | Es = (1/2)k(Δx)2 | Energy stored in springs |
| Conservation Principle | ΣEbefore = ΣEafter | Total energy remains constant |
Hooke’s Law and Energy in Springs
Hooke’s Law states that the force F needed to stretch or compress a spring is proportional to its displacement Δx: F = –kΔx, where k is the spring constant.
The elastic potential energy stored is: Es = (1/2)k(Δx)2
- Spring compressed by 0.2 m by a 40 N force:
k = F/Δx = 40/0.2 = 200 N/m - Energy stored:
Es = (1/2) × 200 × (0.2)2 = 4 J
Step-by-Step Problem Solving: Conservation of Energy
| Step | Description | Formula To Use |
|---|---|---|
| 1 | Identify all forms of energy in problem | KE, PE, Elastic, etc. |
| 2 | Write total energy before event | ΣEbefore |
| 3 | Write total energy after event | ΣEafter |
| 4 | Apply ΣEbefore = ΣEafter; solve for unknown | Use relevant formulas |
Further Practice & Learning Links
- Detailed: Conservation of Mechanical Energy
- Work, Energy and Power Overview
- Forms of Energy
- Energy Conservation: Principles & Examples
- Potential and Kinetic Energy Concepts
- Elastic Potential Energy
Explore these resources for more examples, in-depth explanations, and practice questions to strengthen your understanding of the law of conservation of energy.
FAQs on Law of Conservation of Energy: Physics Concept Explained
1. What is the law of conservation of energy?
The law of conservation of energy states that energy cannot be created or destroyed; it can only change from one form to another. In any closed system, the total energy remains constant, even as it transforms among different forms such as kinetic, potential, heat, or sound energy.
2. State the law of conservation of energy with example.
The law of conservation of energy means energy only changes form but is never lost.
Example: If a ball is dropped from a height, its potential energy converts into kinetic energy as it falls. When it hits the ground, some energy becomes sound and heat, but the total energy remains the same throughout the process.
3. Law of conservation of energy formula
The law of conservation of energy formula is:
Total Energyinitial = Total Energyfinal
This can be written as:
KE1 + PE1 = KE2 + PE2
where KE is kinetic energy and PE is potential energy.
4. Give a simple definition of law of conservation of energy.
The law of conservation of energy says the total energy in a closed system stays the same. Energy can neither be created nor destroyed, but only changes from one type to another—like from potential energy to kinetic energy or heat.
5. Does the law of conservation of energy always hold?
Yes, the law of conservation of energy always applies in closed systems, meaning total energy is constant.
- In real-world situations, some energy may appear "lost" as heat, sound, or light, but it is just transferred or transformed, not destroyed.
- On very small (quantum) scales or under relativity, energy conservation includes all related forms, such as mass-energy equivalence.
6. What is conservation of mechanical energy?
Conservation of mechanical energy states that the sum of kinetic energy (KE) and potential energy (PE) remains constant in an ideal system with no friction or external forces.
It is mathematically written as: KE + PE = constant.
7. What type of energy is conserved when an object is falling freely?
Mechanical energy is conserved during free fall (if air resistance is neglected). The gravitational potential energy decreases as kinetic energy increases, but their sum remains the same throughout the motion.
8. How is energy transformed in a bouncing ball experiment?
In a bouncing ball experiment:
- Before release, the ball has gravitational potential energy.
- As it falls, this changes to kinetic energy.
- On impact, some energy transfers to sound and heat.
- During the bounce, elastic potential energy is stored and then converted back.
The total energy remains conserved, but is divided among different forms during each stage.
9. What are common forms of energy mentioned in the law of conservation of energy?
Common forms of energy include:
- Kinetic Energy (KE)
- Potential Energy (PE): gravitational and elastic
- Thermal Energy
- Sound Energy
- Light (Radiant) Energy
- Chemical Energy
- Electrical Energy
- Nuclear Energy
All these forms can be transformed into one another according to the law of conservation of energy.
10. What is the significance of the negative sign in Hooke’s law formula?
The negative sign in Hooke’s law (F = -kΔx) indicates that the restoring force exerted by a spring is always in the direction opposite to the displacement.
This ensures the spring returns to its equilibrium position when stretched or compressed, showing elastic restoring force.
11. How to calculate the elastic potential energy stored in a spring?
The elastic potential energy (Es) stored in a spring:
Es = (1/2)k(Δx)2
Where:
- k is the spring constant
- Δx is the displacement from equilibrium
12. What is the difference between conservation of energy and conservation of momentum?
Conservation of energy refers to the total energy (all forms) remaining constant in a system, while conservation of momentum means the total linear momentum stays the same. Energy is measured in joules (J); momentum in kg·m/s. Both are fundamental laws, but apply to different physical quantities and scenarios.
