4.9.3

Conservation of Energy

Test yourself on Conservation of Energy

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Conservation of Energy

One of the fundamental laws of physics is that energy cannot be created or destroyed, only transferred from one form to another.

Law of energy conservation

Law of energy conservation

This law means that if you measured all the energy in the universe, it would be exactly the same whether you took the measurement now, in 10 billion years, or just after the big bang!

Energy in = energy out

Energy in = energy out

For a machine that converts energy from one form to another, the energy in must equal the energy out.
In the case of a kettle:
- Electrical energy in = heat energy to water + sound energy + heat energy wasted

Energy before = energy after

Energy before = energy after

For a collision or an explosion, the total energy before must equal the total energy after.
- In the case of an inelastic collision, some kinetic energy is converted to other forms and lost from the system.

Types of Energy

There are many forms of energy found in physics problems. Two key examples are kinetic energy and gravitational potential energy.

Kinetic energy

Kinetic energy

The equation for the kinetic energy of an object is:
- $E_k = \frac12 m v^2$
It is the energy involved in moving.

Gravitational potential energy

Gravitational potential energy

The equation for the gravitational potential energy of an object is:
- $\Delta E_p = m g \Delta h$
It is the potential energy of an object in a gravitational field.

Common Energy Problems

Energy conservation problems are very common in physics. Use the conservation of energy to solve them.

Projectile

Projectile

A projectile thrown into the air starts off with purely kinetic energy.
The kinetic energy gradually transfers to gravitational potential energy.
At the top of the throw all the energy has become gravitational potential energy.
We can use the equation:
- kinetic energy at bottom = gravitational potential energy at top
- $\frac12 m v^2 = m g \Delta h$

Climbing stairs

Climbing stairs

A machine carries an object up a flight of stairs.
The work done by the machine must equal the gravitational potential energy of the object at the top of the stairs.
We can use the equation:
- work done by machine = gravitational potential energy at top
- $W = m g \Delta h$

Slingshot

Slingshot

Work is done to pull a slingshot back. The object is fired from the slingshot.
Work done is converted to elastic potential energy, which is converted to kinetic energy.
We can use the equation:
- work done = elastic potential energy at start = kinetic energy at finish
- $W = \frac12 k (\Delta L)^2 = \frac12 m v^2$

1

Principles of Science I

1.1

Structure & Bonding

1.1.1Atomic Model 1.1.2Electron Shells, Sub-Shells & Orbitals 1.1.3Ionic Bonding 1.1.4Representing Ionic Bonds 1.1.5Covalent Bonding 1.1.6Representing Covalent Bonds 1.1.7Metallic Bonding 1.1.8Intermolecular Forces 1.1.9Intermolecular Forces 2 1.1.10End of Topic Test - Bonding 1.1.11Relative Masses 1.1.12The Mole 1.1.13Molar Calculations 1.1.14Molar Calculations 2 1.1.15Empirical & Molecular Formulae 1.1.16Balanced Equations 1.1.17Percentage Yield 1.1.18End of Topic Test - Amount of Substance

1.2

Properties of Substances

1.2.1The Periodic Table 1.2.2Ionisation Energy 1.2.3Factors Affecting Ionisation Energies 1.2.4Trends of Ionisation 1.2.5Trends in the Periodic Table 1.2.6Polarity 1.2.7Metals & Non-Metals 1.2.8Alkali Metals 1.2.9Alkaline Earth Metals 1.2.10Reactivity of Alkaline Earth Metals 1.2.11Redox 1.2.12Transition Metals 1.2.13Redox Reactions of Transition Metals

1.3

Cell Structure & Function

1.3.1Introduction to Cells 1.3.2Prokaryotes 1.3.3Organelles of Eukaryotic Cells 1.3.4Organelles of Eukaryotic Cells 2 1.3.5Organelles in Plant Cells 1.3.6Microscopy 1.3.7End of Topic Test - Cell Structure

1.4

Cell Specialisation

1.4.1Cell Specialisation 1.4.2Blood Cells 1.4.3Plant Cells 1.4.4Gametes

1.5

Tissue Structure & Function

1.5.1Human Gas Exchange 1.5.2Blood Vessels 1.5.3Atherosclerosis 1.5.4Skeletal Muscle 1.5.5Slow & Fast Twitch Fibres 1.5.6Neurones 1.5.7Speed of Transmission 1.5.8Action Potentials 1.5.9End of Topic Test - Neurones & Action Potentials 1.5.10Synapses 1.5.11Types of Synapse 1.5.12Medical Application 1.5.13End of Topic Test - Synapses 1.5.14Chemical Brain Imbalances 1.5.15Effect of Drugs on the Brain

1.6

Working with Waves

1.6.1Progressive Waves 1.6.2Wave Speed & Phase Difference 1.6.3Longitudinal & Transverse Waves 1.6.4Stationary Waves 1.6.5Stationary Waves 2 1.6.6Applications of Stationary Waves 1.6.7Interference 1.6.8Diffraction 1.6.9Diffraction Gratings 1.6.10Application of Diffraction Gratings

1.7

Waves in Communication

1.7.1Refraction at a Plane Surface 1.7.2Internal Reflection & Fibre Optics 1.7.3Applications of Total Internal Reflection 1.7.4Properties 1.7.5Gamma, X-Ray & UV Light 1.7.6Visible Light 1.7.7Infrared, Microwave & Radio Waves 1.7.8Intensity 1.7.9Digital & Analogue Signals 1.7.10Communication Channels

2

Practical Scientific Procedures and Techniques

2.1

Titration

2.1.1pH Curves & Titrations 2.1.2pH Curves & Titrations 2 2.1.3Buffer Solutions

2.2

Colorimetry

2.2.1Measuring Rates 2.2.2Beer-Lambert Law

2.3

Chromatography

2.3.1Overview of Chromatography 2.3.2Thin-Layer Chromatography 2.3.3Column Chromatography 2.3.4Gas Chromatography

3

Science Investigation Skills

3.1

Scientific Processes

3.1.1Aims, Hypotheses & Sampling 3.1.2Pilot Studies & Design 3.1.3Ethics 3.1.4Variables & Control 3.1.5Demand Characteristics & Investigator Effects 3.1.6Features of Science 3.1.7Scientific Report 3.1.8Scientific Report 2

3.2

Data Handling & Analysis

3.2.1Types of Data 3.2.2Descriptive Statistics 3.2.3Presentation & Display of Data

3.3

Enzymes in Action

3.3.1Overview of Protein Structure 3.3.2Enzymes 3.3.3Factors Affecting Enzyme Activity 3.3.4Enzyme-Controlled Reactions

3.4

Diffusion

3.5

Plants & Their Environment

3.5.1Factors Affecting Plant Growth 3.5.2Measuring Number & Distribution of Species

3.6

Energy Content in Fuels

3.6.1Fractions 3.6.2Burning Hydrocarbons 3.6.3Combustion 3.6.4Energy 3.6.5Energy at Home 3.6.6Calorimetry

3.7

Electrical Circuits

3.7.1Circuit Diagrams & Components 3.7.2Diodes, LDRs & Thermistors 3.7.3Resistance 3.7.4Electrical Work 3.7.5Ohm's Law 3.7.6Domestic Uses of Electricity 3.7.7Fuses

4

Principles of Science II

4.1

Extracting Elements

4.1.1Atom Economy

4.2

Relating Properties to use of Substances

4.2.1Group 2 Chemistry 4.2.2End of Topic Test - Group 2 4.2.3Electrolysis 4.2.4Electrolysis Examples 4.2.5Extracting Metals 4.2.6Transition Metals 4.2.7Variable Oxidation States 4.2.8Heterogeneous Catalysts 4.2.9Homogeneous Catalysts

4.3

Organic Chemistry

4.3.1Naming Compounds 4.3.2Functional Groups 4.3.3Isomerism 4.3.4Hydrocarbons 4.3.5Structure of Alkanes 4.3.6Boiling Points of Alkanes 4.3.7Alkenes 4.3.8Curly Arrows & Mechanisms 4.3.9Cracking 4.3.10Combustion 4.3.11Free Radical Substitution of Alkanes 4.3.12Electrophilic Addition of Alkenes

4.4

Energy Changes in Industry

4.4.1The Kelvin Scale 4.4.2Enthalpy Changes 4.4.3Calorimetry 4.4.4Bond Enthalpies 4.4.5Hess' Law

4.5

The Circulatory System

4.5.1The Circulatory System 4.5.2Blood Vessels 4.5.3Blood Transfusion & the ABO Rhesus System 4.5.4The Heart 4.5.5The Cardiac Cycle 4.5.6Cardiac Output 4.5.7Coordination of Heart Action 4.5.8Heart Dissection 4.5.9Controlling Heart Rate 4.5.10Electrocardiograms 4.5.11Cardiovascular Disease 4.5.12Investigating Heart Rates

4.6

Ventilation & Gas Exchange

4.6.1Human Gas Exchange 4.6.2Ventilation 4.6.3Measuring Gas Exchange 4.6.4Controlling Ventilation Rate 4.6.5Lung Disease 4.6.6Lung Disease Data

4.7

Urinary System

4.7.1Kidneys & Control of Water Balance 4.7.2Kidneys & Osmoregulation 4.7.3Kidneys & Blood Pressure 4.7.4Urine 4.7.5Kidney Failure & Urinalysis 4.7.6Dialysis 4.7.7Transplants

4.8

Cell Transport

4.8.1Cell Membrane Structure 4.8.2Diffusion 4.8.3Osmosis 4.8.4Active Transport

4.9

Thermal Physics

4.9.1Power & Efficiency 4.9.2Work & Energy 4.9.3Conservation of Energy 4.9.4Pressure 4.9.5First Law of Thermodynamics 4.9.6Second Law of Thermodynamics 4.9.7Heat Engines, Heat Pumps & Refrigerators 4.9.8Non-Flow Processes 4.9.9p-V Diagrams 4.9.10Ideal Gases 4.9.11Ideal Gases 2 4.9.12Thermal Energy Transfer 4.9.13Thermal Energy Transfer Experiments

4.10

Materials

4.10.1Density 4.10.2Stress & Strain 4.10.3Properties of Materials 4.10.4Elasticity 4.10.5Plasticity 4.10.6Energy in Materials 4.10.7Young Modulus

4.11

Fluids

4.11.1Fluid Flow 4.11.2Viscosity 4.11.3Density 4.11.4Continuity Equation 4.11.5Bernoulli's Equation 4.11.6Non-Newtonian Fluids

5

Contemporary Issues in Science

5.1

Contemporary Issues in Science

5.1.1Sustainability 5.1.2Genetic Engineering 5.1.3Uses of Genetic Modification 5.1.4Stem Cell Therapy 5.1.5Cloning 5.1.6Cloning 2 5.1.7Nanotechnology 5.1.8Ecosystems

5.2

Analysing Scientific Information

5.2.1Validity 5.2.2Peer Review

Jump to other topics

1

Principles of Science I

1.1

Structure & Bonding

1.1.1Atomic Model 1.1.2Electron Shells, Sub-Shells & Orbitals 1.1.3Ionic Bonding 1.1.4Representing Ionic Bonds 1.1.5Covalent Bonding 1.1.6Representing Covalent Bonds 1.1.7Metallic Bonding 1.1.8Intermolecular Forces 1.1.9Intermolecular Forces 2 1.1.10End of Topic Test - Bonding 1.1.11Relative Masses 1.1.12The Mole 1.1.13Molar Calculations 1.1.14Molar Calculations 2 1.1.15Empirical & Molecular Formulae 1.1.16Balanced Equations 1.1.17Percentage Yield 1.1.18End of Topic Test - Amount of Substance

1.2

Properties of Substances

1.2.1The Periodic Table 1.2.2Ionisation Energy 1.2.3Factors Affecting Ionisation Energies 1.2.4Trends of Ionisation 1.2.5Trends in the Periodic Table 1.2.6Polarity 1.2.7Metals & Non-Metals 1.2.8Alkali Metals 1.2.9Alkaline Earth Metals 1.2.10Reactivity of Alkaline Earth Metals 1.2.11Redox 1.2.12Transition Metals 1.2.13Redox Reactions of Transition Metals

1.3

Cell Structure & Function

1.3.1Introduction to Cells 1.3.2Prokaryotes 1.3.3Organelles of Eukaryotic Cells 1.3.4Organelles of Eukaryotic Cells 2 1.3.5Organelles in Plant Cells 1.3.6Microscopy 1.3.7End of Topic Test - Cell Structure

1.4

Cell Specialisation

1.4.1Cell Specialisation 1.4.2Blood Cells 1.4.3Plant Cells 1.4.4Gametes

1.5

Tissue Structure & Function

1.5.1Human Gas Exchange 1.5.2Blood Vessels 1.5.3Atherosclerosis 1.5.4Skeletal Muscle 1.5.5Slow & Fast Twitch Fibres 1.5.6Neurones 1.5.7Speed of Transmission 1.5.8Action Potentials 1.5.9End of Topic Test - Neurones & Action Potentials 1.5.10Synapses 1.5.11Types of Synapse 1.5.12Medical Application 1.5.13End of Topic Test - Synapses 1.5.14Chemical Brain Imbalances 1.5.15Effect of Drugs on the Brain

1.6

Working with Waves

1.6.1Progressive Waves 1.6.2Wave Speed & Phase Difference 1.6.3Longitudinal & Transverse Waves 1.6.4Stationary Waves 1.6.5Stationary Waves 2 1.6.6Applications of Stationary Waves 1.6.7Interference 1.6.8Diffraction 1.6.9Diffraction Gratings 1.6.10Application of Diffraction Gratings

1.7

Waves in Communication

1.7.1Refraction at a Plane Surface 1.7.2Internal Reflection & Fibre Optics 1.7.3Applications of Total Internal Reflection 1.7.4Properties 1.7.5Gamma, X-Ray & UV Light 1.7.6Visible Light 1.7.7Infrared, Microwave & Radio Waves 1.7.8Intensity 1.7.9Digital & Analogue Signals 1.7.10Communication Channels

2

Practical Scientific Procedures and Techniques

2.1

Titration

2.1.1pH Curves & Titrations 2.1.2pH Curves & Titrations 2 2.1.3Buffer Solutions

2.2

Colorimetry

2.2.1Measuring Rates 2.2.2Beer-Lambert Law

2.3

Chromatography

2.3.1Overview of Chromatography 2.3.2Thin-Layer Chromatography 2.3.3Column Chromatography 2.3.4Gas Chromatography

3

Science Investigation Skills

3.1

Scientific Processes

3.1.1Aims, Hypotheses & Sampling 3.1.2Pilot Studies & Design 3.1.3Ethics 3.1.4Variables & Control 3.1.5Demand Characteristics & Investigator Effects 3.1.6Features of Science 3.1.7Scientific Report 3.1.8Scientific Report 2

3.2

Data Handling & Analysis

3.2.1Types of Data 3.2.2Descriptive Statistics 3.2.3Presentation & Display of Data

3.3

Enzymes in Action

3.3.1Overview of Protein Structure 3.3.2Enzymes 3.3.3Factors Affecting Enzyme Activity 3.3.4Enzyme-Controlled Reactions

3.4

Diffusion

3.5

Plants & Their Environment

3.5.1Factors Affecting Plant Growth 3.5.2Measuring Number & Distribution of Species

3.6

Energy Content in Fuels

3.6.1Fractions 3.6.2Burning Hydrocarbons 3.6.3Combustion 3.6.4Energy 3.6.5Energy at Home 3.6.6Calorimetry

3.7

Electrical Circuits

3.7.1Circuit Diagrams & Components 3.7.2Diodes, LDRs & Thermistors 3.7.3Resistance 3.7.4Electrical Work 3.7.5Ohm's Law 3.7.6Domestic Uses of Electricity 3.7.7Fuses

4

Principles of Science II

4.1

Extracting Elements

4.1.1Atom Economy

4.2

Relating Properties to use of Substances

4.2.1Group 2 Chemistry 4.2.2End of Topic Test - Group 2 4.2.3Electrolysis 4.2.4Electrolysis Examples 4.2.5Extracting Metals 4.2.6Transition Metals 4.2.7Variable Oxidation States 4.2.8Heterogeneous Catalysts 4.2.9Homogeneous Catalysts

4.3

Organic Chemistry

4.3.1Naming Compounds 4.3.2Functional Groups 4.3.3Isomerism 4.3.4Hydrocarbons 4.3.5Structure of Alkanes 4.3.6Boiling Points of Alkanes 4.3.7Alkenes 4.3.8Curly Arrows & Mechanisms 4.3.9Cracking 4.3.10Combustion 4.3.11Free Radical Substitution of Alkanes 4.3.12Electrophilic Addition of Alkenes

4.4

Energy Changes in Industry

4.4.1The Kelvin Scale 4.4.2Enthalpy Changes 4.4.3Calorimetry 4.4.4Bond Enthalpies 4.4.5Hess' Law

4.5

The Circulatory System

4.5.1The Circulatory System 4.5.2Blood Vessels 4.5.3Blood Transfusion & the ABO Rhesus System 4.5.4The Heart 4.5.5The Cardiac Cycle 4.5.6Cardiac Output 4.5.7Coordination of Heart Action 4.5.8Heart Dissection 4.5.9Controlling Heart Rate 4.5.10Electrocardiograms 4.5.11Cardiovascular Disease 4.5.12Investigating Heart Rates

4.6

Ventilation & Gas Exchange

4.6.1Human Gas Exchange 4.6.2Ventilation 4.6.3Measuring Gas Exchange 4.6.4Controlling Ventilation Rate 4.6.5Lung Disease 4.6.6Lung Disease Data

4.7

Urinary System

4.7.1Kidneys & Control of Water Balance 4.7.2Kidneys & Osmoregulation 4.7.3Kidneys & Blood Pressure 4.7.4Urine 4.7.5Kidney Failure & Urinalysis 4.7.6Dialysis 4.7.7Transplants

4.8

Cell Transport

4.8.1Cell Membrane Structure 4.8.2Diffusion 4.8.3Osmosis 4.8.4Active Transport

4.9

Thermal Physics

4.9.1Power & Efficiency 4.9.2Work & Energy 4.9.3Conservation of Energy 4.9.4Pressure 4.9.5First Law of Thermodynamics 4.9.6Second Law of Thermodynamics 4.9.7Heat Engines, Heat Pumps & Refrigerators 4.9.8Non-Flow Processes 4.9.9p-V Diagrams 4.9.10Ideal Gases 4.9.11Ideal Gases 2 4.9.12Thermal Energy Transfer 4.9.13Thermal Energy Transfer Experiments

4.10

Materials

4.10.1Density 4.10.2Stress & Strain 4.10.3Properties of Materials 4.10.4Elasticity 4.10.5Plasticity 4.10.6Energy in Materials 4.10.7Young Modulus

4.11

Fluids

4.11.1Fluid Flow 4.11.2Viscosity 4.11.3Density 4.11.4Continuity Equation 4.11.5Bernoulli's Equation 4.11.6Non-Newtonian Fluids

5

Contemporary Issues in Science

5.1

Contemporary Issues in Science

5.1.1Sustainability 5.1.2Genetic Engineering 5.1.3Uses of Genetic Modification 5.1.4Stem Cell Therapy 5.1.5Cloning 5.1.6Cloning 2 5.1.7Nanotechnology 5.1.8Ecosystems

5.2

Analysing Scientific Information

5.2.1Validity 5.2.2Peer Review

Practice questions on Conservation of Energy

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1
What is the equation for kinetic energy?Multiple choice
2
When does a projectile have maximum potential energy?Multiple choice

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Work & Energy

Pressure