Elastic Potential energy
Brook Edgar & Hannah Shuter
Teachers
Explainer Video
Elastic Potential Energy
Elastic Potential Energy is the energy stored in a stretched or compressed object.
Formula:
, so the equation can also be written
Springs Constant, , is a measure of how stiff a spring is. A large means the spring is stiff and hard to stretch or compress. A small means the spring is soft and easy to stretch or compress. For example, the suspension in a car uses springs that are very stiff as they must support hundreds of kilograms and absorb bumps. They have a high value of spring constant.
On the other hand, the spring used in a clicky pen is very soft, it has a low value of , as it only needs to push the click mechanism back into place.
Extension just means a change in length. If the extension was metres, either the object got longer, extending by metres or was compressed, getting smaller by metres. If the equation tells us that a spring was originally metres in length and it was stretched to metres in length, the extension would be metres.
We can see from the equation that the more stiff a spring is (the higher the value of spring constant, ) the more elastic potential energy an object has. We can also see that the more a spring extends, the more elastic potential energy it has.
We can use the equation to calculate the elastic potential energy of a spring with spring constant of that is stretched .
We can simplify this equation by calculating three squared first,
Worked Example:
Calculate the elastic potential energy of a spring with spring constant of that is stretched .
Answer:
To calculate the elastic potential energy, when given the extension and the spring constant we use the equation, and substitute the numbers given into the correct places. As extension (change in length) is measured in metres, . As spring constant is measured in newtons per metre, .
We can simplify this equation by calculating squared first,
Teacher Tip: We simplified the equation in the second-to-last step by calculating to get .
Worked Example:
A spring with a spring constant is stretched by .
How much energy does it store?
Answer:
We know that as the spring is being stretched, the type of energy it stores is elastic potential energy . We also know to use this equation as it is the only energy store we can calculate a value for when given the spring constant -> , and the extension -> stretched . But we know that extension (change in length) must be measured in metres!
Remember, century = years, so ,
Next, we fill in the numbers into the correct places,
We can simplify this equation by calculating squared first,
Rearranging Equations
Sometimes we need to calculate the extension of a stretched object or its spring constant, so we need to rearrange the equation.
Always follow the same steps:
1. Write the equation.
2. Fill the numbers into their correct places using their units.
3. Calculate the final answer, remembering to include the final unit.
For example, let's say we want to calculate the extension of a spring with a spring constant of , that has of elastic potential energy.
We know the only equation that has all of these terms in it, extension, spring constant and energy is, .
We then fill the numbers into their correct places. Spring constant is measured in newtons per metre so the number we use for spring constant is . Energy is measured in joules, so the number we use for energy is , as we are given the energy in kilojoules (remember ).
Now we want to calculate the unknown term, -> extension.
To do this, we need to get the letter , by itself on the RHS of the equation.
First, we should simplify the equation,
We then need to get rid of the '' from the RHS. To get rid of something from an equation, we do its opposite. The opposite of multiplying by is dividing by , and what we do to one side, we must do to the other.
However, we are not done yet; we have only found !
To get , the extension, we need to do the opposite of squareing to get rid of the which is square rooting.
The spring is stretched metres -> .
Worked Example:
A bungee cord has of elastic potential energy when stretched when a man jumps off a cliff. Calculate the spring constant of the bungee cord.
Answer:
The question tells us the extension in metres and the elastic energy in kilojoules , but we know that energy is measured in joules, .
of cash pounds
The only physics equation with all these terms in it, that allows us to calculate the spring constant is . We then fill the numbers into the correct places.
Now we want to calculate the unknown term, the spring constant.
To do this, we need to get the letter , by itself on the RHS of the equation.
First, we should simplify the equation by squaring twenty,
We then need to get rid of the '' from the RHS. To get rid of something from an equation, we do its opposite. The opposite of multiplying by is dividing by , and what we do to one side, we must do to the other.
The spring constant is .
Practice Questions
A spring with spring constant is stretched by .
State the equation used to calculate the elastic potential energy stored in a spring.
Calculate the elastic potential energy stored in the spring.
-> Check out Hannah's video explanation for more help.
Answer:
A student compresses a spring during an investigation. The spring constant is and the spring is compressed by .
Calculate the work done in compressing the spring.
Explain why the elastic potential energy stored is equal to the work done on the spring.
Answer:
The work done stretching or compressing the spring transfers energy to the spring.
All of this energy is stored as elastic potential energy, assuming no energy is dissipated.