1.7.1 Energy

Learning objectives

1.7.1.1Energy may be stored as kinetic• State: energy may be stored as kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic and internal (thermal)1.7.1.2Energy is transferred between stores• Describe how energy is transferred between stores during events and processes, including examples of transfer by forces (mechanical work done), electrical currents (electrical work done), heating, and by electromagnetic, sound and other waves 1.7.1.3Principle of the conservation of• Know the principle of the conservation of energy and apply this principle to simple examples including the interpretation of simple flow diagrams 1.7.1.4Kinetic energy: Ek = 1/2 mv^2• Recall/use kinetic energy: Ek = 1/2 mv^2 1.7.1.5Recall/use: for the change in• Recall/use: for the change in gravitational potential energy ∆Ep = mg∆h 1.7.1.6Principle of the conservation of• Know the principle of the conservation of energy and apply this principle to complex examples involving multiple stages, including the interpretation of Sankey diagrams

Energy is held in stores associated with objects or systems. The amount in a store changes when energy is transferred.

Energy store	Typical clue
kinetic	a moving object
gravitational potential	an object at height in a gravitational field
chemical	fuels, food and charged batteries
elastic (strain)	a stretched or compressed spring or elastic object
nuclear	atomic nuclei
electrostatic	separated electric charges
internal (thermal)	the particles within a hotter object or surroundings

Name the store and the object that has it: for example, the gravitational potential store of raised water or the elastic store of a compressed spring.

Electricity, heating, light and sound describe transfer pathways, not stores. A battery's store is chemical; an electric current transfers energy from it.

Energy is transferred between stores by mechanical work, electrical work, heating, or waves.

Pathway	What transfers energy	Example
mechanical work	a force acts through a distance	lifting transfers energy to a gravitational potential store
electrical work	charges move through a potential difference	a motor transfers energy electrically from a battery
heating	energy moves because of a temperature difference	a hot plate increases a pan's internal store
electromagnetic waves	light, infrared or other electromagnetic radiation	sunlight transfers energy to a solar cell or warms a surface
sound and other waves	a travelling wave carries energy	a vibrating source transfers energy by sound

Use the structure: energy is transferred from the [initial] store of [object], by [pathway], to the [final] store of [object]. Include more than one destination when energy is dissipated to the surroundings.

As a falling object slows in air, its gravitational potential store decreases; energy is transferred mechanically to its kinetic store and by heating to the internal stores of the object and air.

Do not say energy is 'used up' or simply changes into work. Work is a transfer pathway; energy remains in stores before and after the transfer.

Energy cannot be created or destroyed. In a closed system, the total energy is constant, although energy may move between stores or spread into the surroundings.

$E_{total,before}=E_{total,after}$

Step	Action
1	define the system and identify the initial energy stores
2	identify the transfer pathways and final stores
3	include useful changes and energy dissipated to surroundings
4	equate the total input or initial energy to all outputs or final stores

In a simple flow diagram, every output branch is part of the energy account. The sum of the output energies must equal the input energy.

Dissipated energy has not disappeared: it has spread, usually into internal stores of the surroundings, and is less available for a useful transfer.

A decrease in one named store does not mean total energy decreases. Look for increases in other stores and transfers to the surroundings.

The kinetic energy of a moving object depends on its mass and on the square of its speed.

$E_k=\frac{1}{2}mv^2$

Symbol	Meaning	SI unit
$E_k$	kinetic energy	J
$m$	mass	kg
$v$	speed	m/s

Convert mass to kilograms, square the speed, multiply by the mass, then divide by two. To find speed, rearrange to $v=\sqrt{2E_k/m}$ and take the positive speed.

At constant mass, doubling speed makes kinetic energy four times larger; tripling speed makes it nine times larger. At constant speed, kinetic energy is directly proportional to mass.

Do not forget the square on speed and do not use grams in the SI equation. The equation uses speed, so kinetic energy is not negative.

Changing an object's vertical position in a gravitational field changes its gravitational potential energy.

$\Delta E_p=mg\Delta h$

Symbol	Meaning	SI unit
$\Delta E_p$	change in gravitational potential energy	J
$m$	mass	kg
$g$	gravitational field strength	N/kg
$\Delta h$	vertical height change	m

Choose a reference level, calculate final height minus initial height, then substitute. A rise gives positive $\Delta h$ and an energy gain; a fall gives negative $\Delta h$ and an energy loss.

Use only the vertical height change, not the length of a ramp or the distance travelled along a curved path.

Do not replace mass with weight without adjusting the equation. If weight $W=mg$ is given, then $\Delta E_p=W\Delta h$ .

For a multi-stage process, conserve energy across the whole system and at every stage: each stage's outputs become stores or inputs for later stages.

Step	Action
1	list the initial stores and calculate any known energy values
2	follow each stage in time and record useful transfers and dissipated energy
3	write one energy balance for each stage or one balance for the complete process
4	solve the missing value and check that every output is included

$E_{input}=E_{useful}+E_{dissipated}$

In a Sankey diagram, arrow width represents energy. The main forward arrow usually shows useful output and side branches show other outputs; their widths and energy values must add to the input width and value.

When a scale is given, count the width units perpendicular to the arrow, convert each width to energy, and add all relevant wasted branches. Do not measure arrow length.

Energy transferred against friction or air resistance is not missing: include it as energy dissipated to internal stores of the object and surroundings, and include sound when supported by the event.

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—1.7.2 WorkRead

1.7.1 Energy

Learning objectives

Identify the eight energy stores

Describe pathways of energy transfer

Apply conservation of energy to simple systems

Calculate kinetic energy

Calculate gravitational potential energy change

Track energy through multiple stages and Sankey diagrams

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