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Are you curious about the forces that make springs stretch, rubber bands snap, and bows shoot arrows? If so, get ready to discover the fascinating world of elastic potential energy! In this article, we'll explore the basics of this powerful force, including what it is, how to calculate it, and the factors that can affect its strength. Whether you're a physics student or simply fascinated by the mechanics of motion, this article will take you on a journey into the incredible power of elastic potential energy. So join us as we stretch our knowledge and explore the incredible world of elastic potential energy!
Elastic Potential Energy Defined
We can define elastic potential energy as:
The energy stored in an object when it is stretched or compressed is referred to as an elastic potential energy
OR
The energy stored in an elastic object because of the work done on it is known as elastic potential energy
This type of energy is caused by the elastic properties of the material, which allow it to deform and then return to its original shape when the force is removed. This type of energy can be stored in objects like springs or rubber bands, which can change their shape when force is applied.
- When an elastic object is stretched or compressed, work is done on it, which transfers energy to its elastic potential store.
- This energy is released when the object returns to its original shape, transferring away from its elastic potential store.
Examples of Elastic Potential Energy From Everyday Life
There are many examples of elastic potential energy from everyday life. Some examples are given below:
Trampoline
When a person jumps on a trampoline, they stretch the springs, storing elastic potential energy. This energy is released when the person lands, propelling them back up into the air.
Bungee Jumping
Bungee jumping involves jumping off a high platform with a bungee cord attached to your body. The bungee cord stretches as you fall, storing elastic potential energy that is released as you bounce back up.
Rubber bands
Rubber bands are a common household item that stores elastic potential energy. When stretched, the rubber band stores energy that is released when it returns to its original shape.
Bow and arrow
When a bowstring is pulled back, the bow stores elastic potential energy. This energy is released when the string is released, propelling the arrow forward.
Car suspension
The suspension system in a car is designed to absorb shocks and bumps in the road. The springs in the suspension system store elastic potential energy as they compress, which is released as the car bounces back up.
How to Calculate Elastic Potential Energy of an Object?
To calculate the amount of elastic potential energy stored in a stretched spring, use the following equation:
In this equation:
represents the elastic potential energy stored in joules (J)- k represents the spring constant in newtons per meter (N/m)
- e represents the extension in meters (m)
It is important to note that this equation is valid only when the spring has not been stretched beyond its limit of proportionality.
Now, we will use the above equation to solve some problems.
Example 1
A spring with a spring constant of 380 N/m has a mass attached to its bottom, causing it to stretch from 15.5 cm to 17.9 cm. Calculate the amount of elastic energy stored in the stretched spring.
Solution
Follow these steps to solve this example.
Step 1: Find out the extension of the spring
Extension = Final length of the spring - Original length
e = 17.9 cm - 15.5 cm
e = 2.4 cm
Step 2 : Write down the known quantities
Spring constant = 380 N/m
Extension = 2.4 cm = 0.024 m
Step 3 : Find out the elastic potential energy using the equation
Plug in the known values in the above equation:
Simplifying this equation, we get:
Step 4: Round the answer to two significant figures
Therefore, the elastic potential energy stored by the stretched spring is 0.84 joules.
Example 2
A spring with a spring constant of 300 N/m is stretched by 0.1 m. What is the elastic potential energy stored in the spring?
Solution
Follow these steps to solve this example.
Step 1 : Write down the known quantities
Spring constant = 300 N/m
Extension = 0.1 m
Step 2 : Find out the elastic potential energy using the equation
Plug in the known values in the above equation:
Simplifying this equation, we get:
Therefore, the elastic potential energy stored by the stretched spring is 1.5 joules.
Example 3
A spring with a spring constant of 200 N/m is compressed by 0.05 m. What is the elastic potential energy stored in the spring?
Solution
Follow these steps to solve this example.
Step 1 : Write down the known quantities
Spring constant = 200 N/m
Extension = 0.05 m
Step 2 : Find out the elastic potential energy using the equation
Plug in the known values in the above equation:
Simplifying this equation, we get:
Therefore, the elastic potential energy stored by the stretched spring is 0.25 joules.
Factors Affecting Elastic Potential Energy of the Spring
The main factors affecting elastic potential energy are:
- Spring constant: The spring constant is the measure of how stiff the spring is. It is denoted by the letter "k" and is measured in newtons per meter (N/m). A higher spring constant means the spring is stiffer, and it can store more elastic potential energy when stretched or compressed.
- Deformation or Extension: The amount of deformation or extension of the spring is a critical factor that affects the elastic potential energy. The greater the extension or deformation of the spring, the more elastic potential energy it can store.
Other factors affecting the elastic potential energy are:
- Material: The material of the spring affects its ability to store elastic potential energy. Some materials, such as steel or titanium, have a higher Young's modulus, which allows them to store more elastic potential energy than other materials like rubber or plastic.
- Temperature: The temperature of the spring affects its elasticity and its ability to store elastic potential energy. A spring at a higher temperature will be less elastic and will have less ability to store elastic potential energy.
- Shape and size: The shape and size of the spring also affect its ability to store elastic potential energy. A longer and thinner spring can store more elastic potential energy than a shorter and thicker spring of the same material and spring constant.
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