Difference between revisions of "Kinetic Energy Store"
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v = The [[speed]] or [[velocity]] of the [[object]]. | v = The [[speed]] or [[velocity]] of the [[object]]. | ||
| − | ===Calculating Kinetic Energy=== | + | ===Calculating Velocity from Kinetic Energy=== |
| + | {| class="wikitable" | ||
| + | | style="height:20px; width:200px; text-align:center;" |A 75kg person has a '''kinetic energy''' of 96J while while walking. Calculate their [[speed]]. | ||
| + | | style="height:20px; width:200px; text-align:center;" |Question | ||
| + | | style="height:20px; width:200px; text-align:center;" |Question | ||
| + | |- | ||
| + | | style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities''' | ||
| + | E<sub>k</sub> = 96J | ||
| + | |||
| + | m = 75kg | ||
| + | | style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities''' | ||
| + | | style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities''' | ||
| + | |- | ||
| + | | style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].''' | ||
| + | |||
| + | <math>E_k = \frac{1}{2} m v^2</math> | ||
| + | |||
| + | <math>96 = \frac{1}{2} \times 75 \times v^2</math> | ||
| + | |||
| + | <math>96 = 37.5v^2</math> | ||
| + | |||
| + | | style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].''' | ||
| + | | style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].''' | ||
| + | |- | ||
| + | | style="height:20px; width:200px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].''' | ||
| + | |||
| + | <math>v^2 = \frac{96}{37.5}</math> | ||
| + | |||
| + | <math>v = \sqrt{\frac{96}{37.5}}</math> | ||
| + | |||
| + | <math>v = 1.6m/s</math> | ||
| + | |||
| + | | style="height:20px; width:200px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].''' | ||
| + | | style="height:20px; width:200px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].''' | ||
| + | |} | ||
Revision as of 12:48, 31 January 2019
Contents
Key Stage 3
Meaning
The kinetic energy store is the energy store associated with moving objects.
About The Kinetic Energy Store
- The faster an object moves the more energy it has in its kinetic store.
- If two objects are moving at the same speed the one with more mass has more energy in the kinetic store.
Equation
 |
| The equation for kinetic energy written in words. |
 |
| The equation for kinetic energy written in symbols. |
Calculating Kinetic Energy
| 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 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.
\(E_k = \frac{1}{2} m v^2\) \(E_k = \frac{1}{2} \times m \times v^2\) \(E_k = \frac{1}{2} \times 0.16 \times 44^2\) \(E_k = \frac{1}{2} \times 0.16 \times 1936\) \(E_k = 154.88J\) \(E_k \approx 150J\) |
Key Stage 4
Meaning
The kinetic energy store is the energy store associated with moving objects.
About Kinetic Energy
- Any moving object stores kinetic energy.
- The kinetic energy store of an object is related to two properties of the object:
- The mass of the object - The greater the mass the greater the kinetic energy stored.
- The speed or velocity of the object - The greater the speed the greater the kinetic energy stored.
Equation
NB: You must memorise this equation!
Kinetic Energy = 0.5 x (Mass) x (Speed)2
\(E_k = \frac{1}{2} m v^2\)
Where:
Ek = Kinetic Energy stored.
v = The speed or velocity of the object.
Calculating Velocity from Kinetic Energy
| A 75kg person has a kinetic energy of 96J while while walking. Calculate their speed. | Question | Question |
| 1. State the known quantities
Ek = 96J m = 75kg |
1. State the known quantities | 1. State the known quantities |
| 2. Substitute the numbers and evaluate.
\(E_k = \frac{1}{2} m v^2\) \(96 = \frac{1}{2} \times 75 \times v^2\) \(96 = 37.5v^2\) |
2. Substitute the numbers and evaluate. | 2. Substitute the numbers and evaluate. |
| 3. Rearrange the equation and solve.
\(v^2 = \frac{96}{37.5}\) \(v = \sqrt{\frac{96}{37.5}}\) \(v = 1.6m/s\) |
3. Rearrange the equation and solve. | 3. Rearrange the equation and solve. |