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Difference between revisions of "Calculating Energy Stores"

(Created page with "==Key Stage 4== ===Meaning=== '''Calculating energy stores''' can be done using information about properties, motion and fields affecting an [...")
 
 
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==Key Stage 4==
 
==Key Stage 4==
 
===Meaning===
 
===Meaning===
−
'''Calculating energy stores''' can be done using information about [[Property|properties]], motion and [[Field (Physics)|fields]] affecting an [[object]].
+
[[Energy Store|Energy stores]] can be calculated from other known facts about an [[object]].
  
 
===About Calculating Energy Stores===
 
===About Calculating Energy Stores===
 +
: '''Calculating energy stores''' can be done using information about [[Property|properties]], distances, motion and [[Force Field|fields]] affecting an [[object]].
 
The following '''[[Energy Store|energy stores]] can be calculated''' from other quantities:
 
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)''
+
*'' [[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>''
 
*'' [[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>''
 
*'' [[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)''
 
*'' [[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]].'''
 +
 +
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>
 +
|}

Latest revision as of 16:57, 7 April 2019

Key Stage 4

Meaning

Energy stores can be calculated from other known facts about an object.

About Calculating Energy Stores

Calculating energy stores can be done using information about properties, distances, motion and fields affecting an object.

The following energy stores can be calculated from other quantities:

Examples

Calculating the Thermal Energy Store
A 2 kg object made from a material with specific heat capacity 5 J/kg/°C is heated by 10°C. Calculate the Thermal Energy transferred to the object. 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.)

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.)

1. State the known quantities

m = 2 kg

c = 5 J/kg/°C

Δθ = 10°C

1. State the known quantities

m = 5.5 kg

c = 4200 J/kg/°C

θ1 = 27°C

θ2 = 100°C

Find the temperature change.

Δθ = θ2 - θ1 = 100 - 27 = 73°C

1. State the known quantities

m = 0.5 kg

c = 450 J/kg/°C

θ1 = 20°C

θ2 = 80°C

Find the temperature change.

Δθ = θ2 - θ1 = 80 - 20 = 60°C

2. Substitute the numbers into the equation and solve.

\(E_t = m c \Delta \theta\)

\(E_t = 2 \times 5 \times 10\)

\(E_t = 100J\)

2. Substitute the numbers into the equation and solve.

\(E_t = m c \Delta \theta\)

\(E_t = 5.5 \times 4200 \times 73\)

\(E_t = 1686300J\)

\(E_t \approx 1700000J\)

2. Substitute the numbers into the equation and solve.

\(E_t = m c \Delta \theta\)

\(E_t = 0.5 \times 450 \times 60\)

\(E_t = 13500J\)

\(E_t \approx 14000J\)

Calculating the Elastic Potential Energy Store
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. 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.

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.

1. State the known quantities

k = 400N/m

x = 0.5m

1. State the known quantities

k = 45N/m

x = 30m

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

2. Substitute the numbers into the equation and solve.

\(E_e = \frac{1}{2} k x^2\)

\(E_e = \frac{1}{2} \times 400 \times 0.5^2\)

\(E_e = \frac{1}{2} \times 400 \times 0.25\)

\(E_e = 50J\)

2. Substitute the numbers into the equation and solve.

\(E_e = \frac{1}{2} k x^2\)

\(E_e = \frac{1}{2} \times 45 \times 30^2\)

\(E_e = \frac{1}{2} \times 45 \times 900\)

\(E_e = 20250J\)

\(E_e \approx 20,000J\)

2. Substitute the numbers into the equation and solve.

\(E_e = \frac{1}{2} k x^2\)

\(E_e = \frac{1}{2} \times 0.80 \times 9.0^2\)

\(E_e = \frac{1}{2} \times 0.80 \times 81\)

\(E_e = 32.4J\)

\(E_e \approx 32J\)

Calculating the Kinetic Energy Store
A 700kg formula one racing car has a top speed of 100m/s. Calculate the kinetic energy of the car to two significant figures. A cheetah of mass 75kg runs at a speed of 32m/s. Calculate the kinetic energy of the cheetah correct to two significant figures. A 160g cricket ball is hit at 44m/s. Calculate the kinetic energy of the cricket ball correct to two significant figures.
1. State the known quantities

m = 700kg

v = 100m/s

1. State the known quantities

m = 75kg

v = 32m/s

1. State the known quantities

m = 160g

Convert mass into kilograms.

min kilograms = \(\frac{160}{1000}\)

m = 0.16kg

v = 32m/s

2. Substitute the numbers into the equation and solve.

\(E_k = \frac{1}{2} m v^2\)

\(E_k = \frac{1}{2} \times 700 \times 100^2\)

\(E_k = \frac{1}{2} \times 700 \times 10,000\)

\(E_k = 3,500,000J\)

2. Substitute the numbers into the equation and solve.

\(E_k = \frac{1}{2} m v^2\)

\(E_k = \frac{1}{2} \times 75 \times 32^2\)

\(E_k = \frac{1}{2} \times 75 \times 1024\)

\(E_k = 38,400J\)

\(E_k \approx 38000J\)

2. Substitute the numbers into the equation and solve.

\(E_k = \frac{1}{2} m v^2\)

\(E_k = \frac{1}{2} \times m \times v^2\)

\(E_k = \frac{1}{2} \times 0.16 \times 44^2\)

\(E_k = \frac{1}{2} \times 0.16 \times 1936\)

\(E_k = 154.88J\)

\(E_k \approx 150J\)


Calculating the Gravitational Potential Energy Store
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

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.

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.

1. State the known quantities

m = 50kg

g = 9.8N/kg

Δh = 2.0m

1. State the known quantities

m = 12tonne = 12,000kg

g = 9.8N/kg

Δh = 0.80m

1. State the known quantities

m = 320kg

g = 9.8 N/kg

Δh = h2 - h1 = 1450 - 730 = 720m

2. Substitute the numbers into the equation and solve.

\(E_g = m g \Delta h\)

\(E_g = m \times g \times \Delta h\)

\(E_g = 50 \times 9.8 \times 2\)

\(E_g = 980J\)

2. Substitute the numbers into the equation and solve.

\(E_g = m g \Delta h\)

\(E_g = m \times g \times \Delta h\)

\(E_g = 0.80 \times 9.8 \times 12000\)

\(E_g = 94080J\)

\(E_g \approx 94000J\)

2. Substitute the numbers into the equation and solve.

\(E_g = m g \Delta h\)

\(E_g = m \times g \times \Delta h\)

\(E_g = 320 \times 9.8 \times 720\)

\(E_g = 2257920J\)

\(E_g \approx 2300000J\)

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