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→About Calculating Energy Stores
: '''Calculating energy stores''' can be done using information about [[Property|properties]], distances, motion and [[Field (Physics)|fields]] affecting an [[object]].
The following '''[[Energy Store|energy stores]] can be calculated''' from other quantities:
*'' [[Thermal Energy Store|Thermal Energy]] = (Mass ) x (Specific Heat Capacity) x (Change in Temperature)''
*'' [[Elastic Potential Energy Store|Elastic Potential Energy]] = 0.5 x (Spring Constant) x (Extension)<sup>2</sup>''
*'' [[Kinetic Energy Store|Kinetic Energy]] = 0.5 x (Mass) x (Speed)<sup>2</sup>''
*'' [[Gravitational Potential Energy Store|Gravitational Potential Energy]] = (Mass) x (gravitational field strength) x (change in height)''
===Examples===
{| class="wikitable"
|+ Calculating the Thermal Energy Store
|-
| style="height:20px; width:200px; text-align:center;" |A 2 kg [[object]] made from a [[material]] with [[Specific Heat Capacity|specific heat capacity]] 5 J/kg/°C is [[heated]] by 10°C. Calculate the '''Thermal Energy''' transferred to the [[object]].
| style="height:20px; width:200px; text-align:center;" |A sealed metal can containing 5.5 kg of [[water]] is heated over a fire from 27°C to 100°C to sterilise the [[water]]. Calculate the increase in '''thermal energy''' of the [[water]].
The [[Specific Heat Capacity]] of [[water]] is 4200 J/kg/°C.
(Give your answer correct to 2 [[Significant Figures|significant figures]].)
| style="height:20px; width:200px; text-align:center;" |A 0.5kg [[Iron]] baking tray is [[heated]] from 20°C to 80°C in an oven. Calculate the work done by the oven in [[heating]] the tray.
The [[Specific Heat Capacity]] of [[Iron]] is 450 J/kg/°C.
(Give your answer correct to 2 [[Significant Figures|significant figures]].)
|-
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
m = 2 kg
c = 5 J/kg/°C
Δθ = 10°C
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
m = 5.5 kg
c = 4200 J/kg/°C
θ<sub>1</sub> = 27°C
θ<sub>2</sub> = 100°C
'''Find the [[temperature]] change.'''
Δθ = θ<sub>2</sub> - θ<sub>1</sub> = 100 - 27 = 73°C
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
m = 0.5 kg
c = 450 J/kg/°C
θ<sub>1</sub> = 20°C
θ<sub>2</sub> = 80°C
'''Find the [[temperature]] change.'''
Δθ = θ<sub>2</sub> - θ<sub>1</sub> = 80 - 20 = 60°C
|-
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
<math>E_t = m c \Delta \theta</math>
<math>E_t = 2 \times 5 \times 10</math>
<math>E_t = 100J</math>
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
<math>E_t = m c \Delta \theta</math>
<math>E_t = 5.5 \times 4200 \times 73</math>
<math>E_t = 1686300J</math>
<math>E_t \approx 1700000J</math>
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
<math>E_t = m c \Delta \theta</math>
<math>E_t = 0.5 \times 450 \times 60</math>
<math>E_t = 13500J</math>
<math>E_t \approx 14000J</math>
|}
{| class="wikitable"
|+ Calculating the Elastic Potential Energy Store
| 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 (Physics)|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>
|}
{| class="wikitable"
|+ Calculating the Kinetic Energy Store
| style="height:20px; width:200px; text-align:center;" |A 700kg formula one racing car has a top speed of 100m/s. Calculate the '''kinetic energy''' of the [[car]] to two [[Significant Figures|significant figures]].
| style="height:20px; width:200px; text-align:center;" |A cheetah of mass 75kg runs at a speed of 32m/s. Calculate the '''kinetic energy''' of the [[cheetah]] correct to two [[Significant Figures|significant figures]].
| style="height:20px; width:200px; text-align:center;" |A 160g cricket ball is hit at 44m/s. Calculate the '''kinetic energy''' of the cricket ball correct to two [[Significant Figures|significant figures]].
|-
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
m = 700kg
v = 100m/s
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
m = 75kg
v = 32m/s
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
m = 160g
'''Convert [[mass]] into [[kilogram]]s.'''
m<sub>in kilograms</sub> = <math>\frac{160}{1000}</math>
m = 0.16kg
v = 32m/s
|-
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
<math>E_k = \frac{1}{2} m v^2</math>
<math>E_k = \frac{1}{2} \times 700 \times 100^2</math>
<math>E_k = \frac{1}{2} \times 700 \times 10,000</math>
<math>E_k = 3,500,000J</math>
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
<math>E_k = \frac{1}{2} m v^2</math>
<math>E_k = \frac{1}{2} \times 75 \times 32^2</math>
<math>E_k = \frac{1}{2} \times 75 \times 1024</math>
<math>E_k = 38,400J</math>
<math>E_k \approx 38000J</math>
| style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
<math>E_k = \frac{1}{2} m v^2</math>
<math>E_k = \frac{1}{2} \times m \times v^2</math>
<math>E_k = \frac{1}{2} \times 0.16 \times 44^2</math>
<math>E_k = \frac{1}{2} \times 0.16 \times 1936</math>
<math>E_k = 154.88J</math>
<math>E_k \approx 150J</math>
|}
{| class="wikitable"
|+ Calculating the Gravitational Potential Energy Store
| 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>
|}