View source for Elastic Potential Energy Store

==Key Stage 3==
===Meaning===
[[File:RubberBand.png|right|300px|thumb|Rubber bands can store energy in their '''elastic potential store'''.]]
The '''elastic potential energy store''' is an [[Energy Store|energy store]] associated with stretched, squashed and twisted elastic [[object]]s.

===About Elastic Potential Energy===
: The more an [[object]] is stretched the more [[energy]] it has in its '''elastic potential energy store'''.

===Examples===
{| class="wikitable"
|-
|[[File:RubberBand.png|center|200px]]
|[[File:CoilSpring.png|center|200px]]
|[[File:BowandArrow.png|center|200px]]
|-
| style="height:20px; width:200px; text-align:center;" |Rubber bands can store '''elastic potential energy''' when they are stretched.
| style="height:20px; width:200px; text-align:center;" |A spring stores energy in the '''elastic potential store''' when they are stretched, squashed and bent.
| style="height:20px; width:200px; text-align:center;" |A stretched bow stores '''elastic potential energy.''' The further it is stretched the more [[energy]] it stores.
|}

==Key Stage 4==
{{#ev:youtube|https://www.youtube.com/watch?v=Pe4lX_FcqZ4}}
===Meaning===
The '''elastic potential energy store''' is an [[Energy Store|energy store]] associated with stretched, squashed and twisted elastic [[object]]s.

===About Elastic Potential Energy===
: Any [[object]] that returns to its original shape after a [[Deformation|deforming]] [[force]] has been removed is able to store '''elastic potential energy'''.
: '''Elastic potential energy''' is a [[Potential Energy]] store.
: The '''elastic potential energy store''' of an [[object]] is related to two [[property|properties]] of the [[object]]:
*The [[Spring Constant]] of the [[object]]. - The amount of [[force]] needed to stretch or squash it's shape by a given distance. The greater the [[Spring Constant|spring constant]] the greater the '''elastic potential energy''' stored.
*The [[extension]] of the [[object]]. - The distance that the [[object]] has been stretched or squashed. The greater the [[extension]] the greater the '''elastic potential energy''' stored.

===Equation===
''NB: You will be given this equation in the formula sheet.''

'' '''Elastic Potential Energy''' = 0.5 x (Spring Constant) x (Extension)<sup>2</sup>''

<math>E_e = \frac{1}{2} k x^2</math>

Where:

E<sub>e</sub> = '''Elastic Potential Energy''' stored.

k = The [[Spring Constant|spring constant]] of the [[object]].

x = The [[extension]] of the [[object]].

===Calculating Elastic Potential Energy===
{{#ev:youtube|https://www.youtube.com/watch?v=v7uBIR9RWe0}}
{| class="wikitable"
| style="height:20px; width:200px; text-align:center;" |A bow with a spring constant of 400N/m is stretched 0.5m with a force of 200N. Calculate the elastic potential store of the bow.
| style="height:20px; width:200px; text-align:center;" |A bungee cord with a spring constant of 45N/m stretches by 30m. Calculate the elastic potential store of the cord.

Give your answer correct to 2 [[Significant Figures|significant figures]].
| style="height:20px; width:200px; text-align:center;" |A slinky spring of length 0.1m and spring constant 0.80N/m is stretched to a length of 9.1m. Calculate the elastic potential store of the slinky.

Give your answer correct to 2 [[Significant Figures|significant figures]].
|-
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
k = 400N/m

x = 0.5m
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
k = 45N/m

x = 30m
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''

k = 0.8N/m

Original Length = 0.1m

Final Length = 9.1m

'''Find the [[extension]].'''

x = Final Length - Original Length = 9.1 - 0.1 = 9.0m
|-
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''

<math>E_e = \frac{1}{2} k x^2</math>

<math>E_e = \frac{1}{2} \times 400 \times 0.5^2</math>

<math>E_e = \frac{1}{2} \times 400 \times 0.25</math>

<math>E_e = 50J</math>
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''

<math>E_e = \frac{1}{2} k x^2</math>

<math>E_e = \frac{1}{2} \times 45 \times 30^2</math>

<math>E_e = \frac{1}{2} \times 45 \times 900</math>

<math>E_e = 20250J</math>

<math>E_e \approx 20,000J</math>
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''

<math>E_e = \frac{1}{2} k x^2</math>

<math>E_e = \frac{1}{2} \times 0.80 \times 9.0^2</math>

<math>E_e = \frac{1}{2} \times 0.80 \times 81</math>

<math>E_e = 32.4J</math>

<math>E_e \approx 32J</math>
|}


===References===
====AQA====

:[https://www.amazon.co.uk/gp/product/178294558X/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=178294558X&linkCode=as2&tag=nrjc-21&linkId=f0dfb66dafcb0c6e9449e7b1a4ae1ac110 ''Elastic potential energy stores, pages 12, 55, 56, GCSE Physics; The Revision Guide, CGP, AQA '']
:[https://www.amazon.co.uk/gp/product/1782945598/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945598&linkCode=as2&tag=nrjc-21&linkId=ad276ad49df77ab4b40ab4fd0fe09874 ''Elastic potential energy stores, pages 169, 206, 207, GCSE Combined Science; The Revision Guide, CGP, AQA '']
:[https://www.amazon.co.uk/gp/product/1782946403/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782946403&linkCode=as2&tag=nrjc-21&linkId=32a0abb60dff015b15b50e9b1d7b4644 ''Elastic potential energy stores, pages 21, 27, 28, 141, GCSE Combined Science Trilogy; Physics, CGP, AQA '']
:[https://www.amazon.co.uk/gp/product/1782945970/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945970&linkCode=as2&tag=nrjc-21&linkId=a120d24dcc7cc7a58192069a3aafc1d2 ''Elastic potential energy stores, pages 22, 28, 29, 161, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA '']

====Edexcel====

:[https://www.amazon.co.uk/gp/product/1782948163/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782948163&linkCode=as2&tag=nrjc-21&linkId=0fdbfd5dd397d6e24a9dfb250f08587f ''Elastic potential energy stores, pages 61, 325, GCSE Physics, CGP, Edexcel '']
:[https://www.amazon.co.uk/gp/product/1292120193/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1292120193&linkCode=as2&tag=nrjc-21&linkId=572df39392fb4200db8391d98ae6314e ''Elastic potential energy, page 316, GCSE Combined Science, Pearson Edexcel '']
:[https://www.amazon.co.uk/gp/product/1292120223/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1292120223&linkCode=as2&tag=nrjc-21&linkId=068ecf40278c32406a7f1c6e66751417 ''Elastic potential energy, page 34, GCSE Physics, Pearson Edexcel '']

====OCR====
:[https://www.amazon.co.uk/gp/product/1782945695/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945695&linkCode=as2&tag=nrjc-21&linkId=ceafcc80bcad6b6754ee97a0c7ceea53 ''Elastic potential energy stores, pages 171, 202, 206, Gateway GCSE Combined Science; The Revision Guide, CGP, OCR '']
:[https://www.amazon.co.uk/gp/product/1782945687/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945687&linkCode=as2&tag=nrjc-21&linkId=9a598e52189317a20311d7a632747bc9 ''Elastic potential energy stores, pages 37, 82, 86, Gateway GCSE Physics; The Revision Guide, CGP, OCR  '']