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===Meaning===
[[File:RockStack.png|right|300px|thumb|The [[rock]] at the top of this stack has a large amount of [[energy]] in the '''gravitational potential energy store'''.]]
The '''gravitational potential energy store''' is the [[Energy Store|energy stored]] in an [[object]] that is in a [[Gravitional Gravitational Field|gravitional gravitational field]].
===About The Gravitational Potential Energy Store===
===Equation===
{| class="wikitable"
|-
|[[File:GravitationalPotentialEnergyEquation.png|center|500px]]
|-
| style="height:20px; width:500px; text-align:center;" |The equation for '''gravitational potential energy''' written in words.
|}
{| class="wikitable"
|-
|[[File:GravitationalPotentialEnergySymbolEquation.png|center|400px]]
|-
| style="height:20px; width:400px; text-align:center;" |The equation for '''gravitational potential energy''' written in symbols.
|}
===Calculating Gravitational Potential Energy===
{| class="wikitable"
| style="height:20px; width:200px; text-align:center;" |A weight lifter lifts a 50kg [[mass]] a distance of 2.0m from the ground. Calculate the increase in '''gravitational potential energy''' of the [[mass]].
g on Earth is 9.8N/kg
| style="height:20px; width:200px; text-align:center;" |A pulley is used to lift a 12 tonne [[mass]] 0.80m above the ground. Calculate the change in energy in the '''gravitational potential store'''.
g on Earth is 9.8N/kg
Give your answer correct to two [[Significant Figures|significant figures]].
| style="height:20px; width:200px; text-align:center;" |During a rock slide a 320kg boulder falls from a [[height]] of 1450m to a [[height]] of 730m above sea level. Calculate the change in '''gravitational potential energy'''.
g on Earth is 9.8N/kg
Give your answer correct to two [[Significant Figures|significant figures]].
|-
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
m = 50kg
g = 9.8N/kg
Δh = 2.0m
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
m = 12tonne = 12,000kg
g = 9.8N/kg
Δh = 0.80m
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
m = 320kg
g = 9.8 N/kg
Δh = h<sub>2</sub> - h<sub>1</sub> = 1450 - 730 = 720m
|-
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
<math>E_g = m g \Delta h</math>
<math>E_g = m \times g \times \Delta h</math>
<math>E_g = 50 \times 9.8 \times 2</math>
<math>E_g = 980J</math>
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
<math>E_g = m g \Delta h</math>
<math>E_g = m \times g \times \Delta h</math>
<math>E_g = 0.80 \times 9.8 \times 12000</math>
<math>E_g = 94080J</math>
<math>E_g \approx 94000J</math>
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
<math>E_g = m g \Delta h</math>
<math>E_g = m \times g \times \Delta h</math>
<math>E_g = 320 \times 9.8 \times 720</math>
<math>E_g = 2257920J</math>
<math>E_g \approx 2300000J</math>
|}
==Key Stage 4==
{{#ev:youtube|https://www.youtube.com/watch?v=-ozi0XAwusY}}
===Meaning===
The '''gravitational potential energy store''' is the [[Energy Store|energy stored]] in an [[object]] that is in a [[Gravitational Field|gravitational field]].
===About Gravitational Potential Energy===
: '''Gravitational Potential Energy''' is a [[Potential Energy|potential energy]] due to the position of a [[mass]] in a [[Gravitational Field|gravitational field]].
: The '''gravitational potential energy store''' of an [[object]] is related to three important factors:
*The [[mass]] - The greater the [[mass]] of an [[object]] the greater the '''gravitational potential energy'''.
*The [[Gravitational Field Strength|gravitational field strength]] - The greater the [[Gravitational Field Strength|gravitational field strength]] the greater the '''gravitational potential energy'''.
*The [[height]] of the [[object]] - The greater the [[height]] of an [[object]] in a [[Gravitational Field|gravitational field]] the greater the '''gravitational potential energy'''.
===Equation===
''NB: You must memorise this equation!''
'' '''Gravitational Potential Energy''' = (Mass) x (gravitational field strength) x (change in height)''
<math>E_g = m g \Delta h</math>
Where:
E<sub>g</sub> = '''Gravitational Potential Energy''' stored.
m = The [[mass]] of the [[object]].
g = The [[Gravitational Field Strength|gravitational field strength]].
Δh = The change in [[height]] of the [[object]].
===Calculating Change in Height from Gravitational Potential Energy===
{| class="wikitable"
| style="height:20px; width:200px; text-align:center;" |An [[object]] of [[mass]] 5.0kg is lifted increasing its '''gravitational potential energy''' by 245J. Calculate the change in [[height]] of the [[object]].
[[Gravitational Field Strength]] on [[Earth]] is 9.8N/kg.
| style="height:20px; width:200px; text-align:center;" |A 3.6kg cat jumps [[vertical]]ly with an initial [[Kinetic Energy Store|kinetic energy]] of 70J. Calculate the maximum [[height]] that the cat will be able to reach in this jump correct to two [[Significant Figures|significant figures]].
[[Gravitational Field Strength]] on [[Earth]] is 9.8N/kg.
| style="height:20px; width:200px; text-align:center;" |A vacationing astronaut takes a bow and arrow to [[The Moon]]. The bow has an initial [[Elastic Potential Energy Store|elastic potential energy store]] of 400J before releasing the arrow [[vertical]]ly. Given the [[mass]] of the arrow is 120g; calculate the maximum [[height]] that the arrow will reach before returning to the ground correct to two [[Significant Figures|significant figures]].
[[Gravitational Field Strength]] on [[Earth]] is 1.6N/kg.
|-
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
m = 5.0kg
g = 9.8N/kg
E<sub>g</sub> = 245J
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
m = 3.6kg
g = 9.8N/kg
E<sub>g</sub> = 70J (Since the law of [[Conservation of Energy]] states that [[energy]] is [[Energy Transfer|transferred]] from one [[Energy Store|store]] into another.)
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
m = 120g = 0.12kg
g = 1.6N/kg
E<sub>g</sub> = 400J (Since the law of [[Conservation of Energy]] states that [[energy]] is [[Energy Transfer|transferred]] from one [[Energy Store|store]] into another.)
|-
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>E_g = m g \Delta h</math>
<math>245 = 5 \times 9.8 \times h</math>
<math>245 = 49h</math>
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>E_g = m g \Delta h</math>
<math>70 = 3.6 \times 9.8 \times h</math>
<math>70 = 35.28h</math>
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>E_g = m g \Delta h</math>
<math>400 = 0.12 \times 1.6 \times h</math>
<math>400 = 0.192h</math>
|-
| style="height:20px; width:200px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>h = \frac{245}{49}</math>
<math>h = 5m</math>
| style="height:20px; width:200px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>h = \frac{70}{35.28}</math>
<math>h = 1.984127m</math>
<math>h \approx 2.0m</math>
| style="height:20px; width:200px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>h = \frac{400}{0.192}</math>
<math>h = 2083.3m</math>
<math>h \approx 2100m</math>
(The astronaut then dies because the arrow comes straight back down on them.)
|}
===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=f0dfb66dafcb0c6e9449e7b1a4ae1ac235 ''Gravitational potential energy stores, pages 11, 12, 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=ad276ad49df77ab4b40ab4fd0fe09968 ''Gravitational potential energy stores, pages 168, 169, 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 ''Gravitational potential energy stores, pages 21, 26, 27, 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 ''Gravitational potential energy stores, pages 22, 27, 28, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA '']
====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 ''Gravitational potential energy stores, pages 167, 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 ''Gravitational potential energy stores, pages 34, 82, 86, Gateway GCSE Physics; The Revision Guide, CGP, OCR '']
:[https://www.amazon.co.uk/gp/product/0198359837/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=0198359837&linkCode=as2&tag=nrjc-21&linkId=3c4229e8b023b2b60768e7ea2307cc6f ''Gravitational potential energy, pages 83, 192, 197-199, Gateway GCSE Physics, Oxford, OCR '']