Difference between revisions of "Elastic Potential Energy Store"
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x = The [[Extension (Physics)|extension]] of the [[object]]. | x = The [[Extension (Physics)|extension]] of the [[object]]. | ||
| + | |||
| + | ===Calculating Spring Constant=== | ||
| + | {| 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 (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.''' | ||
| + | |||
| + | <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.''' | ||
| + | |||
| + | <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.''' | ||
| + | |||
| + | <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 = 32.4</math> | ||
| + | |||
| + | <math>E_e \approx 32J</math> | ||
| + | |} | ||
Revision as of 11:13, 31 January 2019
Contents
Key Stage 3
Meaning
The elastic potential energy store is an energy store associated with stretched, squashed and twisted elastic objects.
About Elastic Potential Energy
Examples
 |
 |
 |
| Rubber bands can store elastic potential energy when they are stretched. | A spring stores energy in the elastic potential store when they are stretched, squashed and bent. | A stretched bow stores elastic potential energy. The further it is stretched the more energy it stores. |
Key Stage 4
Meaning
The elastic potential energy store is an energy store associated with stretched, squashed and twisted elastic objects.
About Elastic Potential Energy
- Any object that returns to its original shape after a 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 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 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)2
\(E_e = \frac{1}{2} k x^2\)
Where:
Ee = Elastic Potential Energy stored.
k = The spring constant of the object.
x = The extension of the object.
Calculating Spring Constant
| 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.
\(E_e = \frac{1}{2} k x^2\) \(E_e = \frac{1}{2} \times 0.80 \times 9.0^2\) \(E_e = \frac{1}{2} \times 0.80 \times 81\) \(E_e = 32.4\) \(E_e \approx 32J\) |