• Recall and apply the principle of conservation of energy
• Identify different forms of energy and energy transformations
• Calculate kinetic and potential energy in various situations
• Solve problems involving conservation of mechanical energy
• Distinguish between conservative and non-conservative forces
• Analyze energy flow diagrams and Sankey diagrams

• Use appropriate scientific vocabulary related to energy conservation
• Describe energy transformations using precise terminology
• Explain the principle of conservation of energy in both written and oral forms
• Interpret and create energy flow diagrams with correct labeling
• Communicate problem-solving approaches using scientific language

Conservation of Energy

A fundamental principle stating that the total amount of energy in an isolated system remains constant over time.

Translation

Russian: Фундаментальный принцип, утверждающий, что общее количество энергии в изолированной системе остается постоянным во времени.
Kazakh: Оқшауланған жүйедегі энергияның жалпы мөлшері уақыт бойынша тұрақты болып қалатынын мәлімдейтін іргелі принцип.

Kinetic Energy

The energy an object possesses due to its motion, calculated as KE = ½mv².

Translation

Russian: Энергия, которой обладает объект благодаря своему движению, рассчитывается как KE = ½mv².
Kazakh: Заттың қозғалысына байланысты иемденетін энергия, KE = ½mv² формуласымен есептеледі.

Potential Energy

Stored energy in an object due to its position or configuration in a force field.

Translation

Russian: Накопленная энергия в объекте из-за его положения или конфигурации в силовом поле.
Kazakh: Күш өрісіндегі орналасуы немесе конфигурациясына байланысты заттағы жинақталған энергия.

Mechanical Energy

The sum of kinetic and potential energies in a mechanical system.

Translation

Russian: Сумма кинетической и потенциальной энергий в механической системе.
Kazakh: Механикалық жүйедегі кинетикалық және потенциалдық энергиялардың қосындысы.

Energy Dissipation

The process by which energy is lost to the surroundings, often as heat due to friction.

Translation

Russian: Процесс, при котором энергия теряется в окружающую среду, часто в виде тепла из-за трения.
Kazakh: Энергияның қоршаған ортаға, көбінесе үйкеліс салдарынан жылу түрінде жоғалу процесі.

The Principle of Conservation of Energy

The principleқағида/принцип of conservation of energy is one of the most fundamental laws in physics. It states that totalжалпы/общая energy in an isolated system remains constantтұрақты/постоянной. Energy cannot be created or destroyed, but it can be transformedтүрлендірілген/преобразована from one form to another.

Forms of Energy

There are several formsтүрлері/формы of energy that are commonly studiedзерттелген/изучены in mechanics:

• Kinetic Energy (KE): Energy of motionқозғалыс/движение
  Formula: KE = ½mv²
• Gravitational Potential Energy (PE): Energy due to heightбиіктік/высота in a gravitational field
  
  Formula: PE = mgh
• Elastic Potential Energy: Energy storedсақталған/запасенная in compressed or stretched objects

Energy Conservation in Practice

When analyzing mechanicalмеханикалық/механические systems, we often consider the conservation of mechanical energy. In the absenceболмауы/отсутствие of non-conservative forces (like friction), the total mechanical energy remains constant:

E_total = KE + PE = constant

This means that as an object fallsтүседі/падает, its potential energy decreases while its kinetic energy increases by the same amount, keeping the total energy constant.

Energy Dissipation

In real-world situations, some energy is often lostжоғалады/теряется to the surroundings due to friction, air resistance, and other non-conservative forces. This energy is said to be dissipatedшашыранды/рассеяна, usually as heat.

Test Your Understanding

1. Easy: What happens to the total energy in an isolated system according to the conservation of energy principle?
   
   Answer

   The total energy remains constant. Energy cannot be created or destroyed, only transformed from one form to another.
   
2. Medium: A ball is dropped from a height of 10 meters. Explain the energy transformations that occur as it falls.
   
   Answer

   Initially, the ball has maximum gravitational potential energy and zero kinetic energy. As it falls, potential energy decreases while kinetic energy increases. Just before hitting the ground, potential energy is minimum (nearly zero) and kinetic energy is maximum.
   
3. Medium: Why can’t a perpetual motion machine work according to the conservation of energy?
   
   Answer

   A perpetual motion machine would need to create energy to continue running indefinitely without an external energy source. This violates the conservation of energy principle, which states that energy cannot be created or destroyed.
   
4. Critical Thinking: In a real pendulum, the amplitude gradually decreases over time. How does this relate to energy conservation, and what happens to the «lost» energy?
   
   Answer

   Energy is not actually «lost» but transformed into thermal energy due to air resistance and friction at the pivot point. The total energy (mechanical + thermal) is still conserved, but the mechanical energy decreases as it converts to heat, which dissipates to the surroundings. This demonstrates that while total energy is conserved, useful mechanical energy can be degraded into less useful forms.
   

Complete the Sentences

1. The _______ of conservation of energy states that energy cannot be created or destroyed.
2. _______ energy is the energy an object has due to its motion.
3. _______ energy is stored energy due to an object’s position.
4. When energy is lost to the surroundings, it is said to be _______.
5. The sum of kinetic and potential energy is called _______ energy.

Match the Terms

Match each term with its correct definition:

Terms: Kinetic Energy, Potential Energy, Conservation, Dissipation, Mechanical Energy

Definitions:

• A. Energy lost to surroundings
• B. Energy due to motion
• C. Total energy remaining constant
• D. Sum of KE and PE
• E. Stored energy due to position

Related Video Resources:

• Khan Academy: Conservation of Energy
• Crash Course Physics: Work and Energy
• PhET Interactive: Energy Skate Park

Example 1: Falling Object

Example 2: Pendulum Motion

Interactive Simulation: Energy Skate Park

Investigation Questions:

1. Design a track and observe how energy changes as the skater moves. What do you notice about the total energy?
2. Add friction to your track. How does this affect energy conservation?
3. Try different track shapes. Does the track shape affect the maximum speed achieved?
4. What happens to the energy when the skater goes in loops?

Collaborative Learning: Energy Scenarios

Work in pairs or small groups to complete this interactive energy conservation matching activity. Discuss your reasoning with your teammates and explain why certain energy transformations occur in different scenarios.

Group Discussion Questions:

• Compare your answers with other groups. Where do you agree/disagree?
• Create your own energy conservation scenario and challenge another group to solve it.
• Design a simple experiment to demonstrate energy conservation using classroom materials.

Structured Questions — Analysis and Synthesis

1. Analysis (5 marks): A roller coaster car of mass 500 kg starts from rest at the top of a 50 m high hill. If 20% of its mechanical energy is lost to friction by the time it reaches the bottom, calculate:
   • a) The initial potential energy
   • b) The energy lost to friction
   • c) The final kinetic energy
   • d) The final velocity
   Answer

   a) PE_initial = mgh = 500 × 10 × 50 = 250,000 J
   b) Energy lost = 20% of 250,000 = 50,000 J
   c) KE_final = 250,000 — 50,000 = 200,000 J
   d) ½mv² = 200,000, so v = √(400,000/500) = √800 = 28.3 m/s
   
2. Synthesis (6 marks): Design an energy-efficient transportation system for a mountain town. Consider:
   • How would you minimize energy losses?
   • What energy recovery systems could you implement?
   • How would conservation of energy principles guide your design?
   Answer

   Sample answer: Design a cable car system with regenerative braking. When cars descend, their gravitational PE helps lift ascending cars. Use lightweight materials to reduce energy needs. Implement magnetic levitation to reduce friction. Include solar panels to supplement energy needs. The design maximizes energy recovery and minimizes dissipation.
   
3. Critical Analysis (7 marks): A company claims to have invented a machine that can generate 120% of the energy input. Analyze this claim using physics principles and explain why this violates fundamental laws.
   
   Answer

   This violates the conservation of energy law. No machine can output more energy than it inputs without an external energy source. Such a machine would be a perpetual motion machine of the first kind, which is impossible. Any real machine has efficiency less than 100% due to energy dissipation through friction, heat, sound, etc.
   
4. Application (8 marks): Explain how hydroelectric dams demonstrate energy conservation. Trace the energy transformations from rain falling to electricity reaching homes.
   
   Answer

   Rain falls (gravitational PE) → Water accumulates in reservoir (stored PE) → Water flows through turbines (PE converts to KE) → Turbines rotate generators (mechanical energy converts to electrical energy) → Electricity transmitted to homes (electrical energy with some losses as heat in transmission lines). Each step demonstrates energy transformation while total energy is conserved.
   
5. Evaluation (9 marks): Compare and contrast elastic and inelastic collisions in terms of energy conservation. Which type is more common in real life and why?
   
   Answer

   Elastic collisions: Kinetic energy is conserved, total momentum conserved. Objects bounce apart without permanent deformation. Inelastic collisions: Kinetic energy is not conserved (some converts to heat, sound, deformation), but total energy and momentum are conserved. Inelastic collisions are more common in real life because perfect elasticity is rare — most materials undergo some deformation or energy dissipation during collisions.
   

Useful Websites and Links:

• SaveMyExams: Conservation of Energy Notes
• Physics & Math Tutor: Energy Conservation Problems
• Khan Academy: Work and Energy Course
• YouTube — Physics Online: Energy Conservation Playlist
• BBC Bitesize: Energy Resources
• PhET Simulations: Energy Simulations

Self-Assessment Questions:

1. Understanding: Rate your understanding of the conservation of energy principle (1-5 scale):
   
   □ 1 (Need more help) □ 2 (Basic understanding) □ 3 (Good understanding) □ 4 (Very good) □ 5 (Excellent)
2. Application: How confident are you in solving energy conservation problems?
   
   □ Not confident □ Somewhat confident □ Confident □ Very confident
3. Connections: Can you relate today’s lesson to real-world examples?
   
   □ Yes, many examples □ Yes, a few examples □ Not sure □ No
4. Questions: What aspect of energy conservation would you like to explore further?
5. Applications: Give three real-world examples where you can observe energy conservation:

Learning Goals Review:

✓ I can state the principle of conservation of energy
✓ I can identify different forms of energy
✓ I can solve problems using energy conservation
✓ I can explain energy transformations in various systems
✓ I can distinguish between conservative and non-conservative forces

Next Lesson Preview:

In our next lesson, we’ll explore Power and Efficiency, building on today’s energy concepts to understand how quickly energy can be transferred and how efficiently systems can convert energy from one form to another.