The energy an item has stored in it due to its location is referred to as Potential Energy. When we think about potential energy, the first image that comes to mind is usually an item high in the air that is just starting to fall. Because of its height, it has potential energy stored in it.
As it descends, this energy is converted into kinetic energy. There are, however, certain other circumstances in which an item can have potential energy. An elastic substance is one such example. Here, we will discuss the elastic potential energy formula in this article. Let us study the idea!
What is Potential Energy?
As a function of its position, an object can store energy. When a demolition machine's heavy ball is held in an elevated position, it stores energy. This stored positional energy is referred to as potential energy. Similarly, as a result of its posture, a drawn bow may store energy.
There is no energy stored in the bow while it is in its normal position (i.e., not pulled). However, when its position is changed from its typical equilibrium state, the bow can store energy due to its location. This stored positional energy is referred to as potential energy. Potential energy is the stored energy of an object's location.
Potential energy is the energy a body has due to its position relative to a reference point, often considered to be zero.
Potential energy is classified into two types:
Gravitational Potential Energy: When a body is elevated to a particular height above the ground, the energy it contains is known as gravitational potential energy.
Elastic Potential Energy: Elastic potential energy is the second form of energy. Elastic potential energy may be stretched or squeezed in both directions. For elastic potential energy to operate, the object must be elasticated.
Let's discuss the Elastic Potential Energy in detail as:
Elastic Potential Energy
This is the energy stored in an item as a result of its shape distortion. Elastic potential energy may be found in any item that can be distorted and then returned to its original shape. Rubber bands, sponges, bungee ropes, and other similar items are examples.
Elastic potential energy is the energy that is accumulated as a result of the use of force for the deformation of an elastic element. The energy builds up until the force is to be resolved, and the object will return to its original form, and complete the tasks in the process. Deformation can be compression, stretching, or twisting of an object.
Elastic potential energy is the potential energy stored by stretching or compressing an elastic object by an external force such as the stretching of a spring or an elastic rubber cord.
Have you ever jumped on a trampoline or watched someone else do it? If you pay close attention, you'll notice that the more the trampoline stretches down when someone jumps, the higher they get launched into the air. This is a great example of elastic potential energy in action. Take a look at the image below.
Elastic Potential Energy in springs
Out of the three springs, which one do you think has the most potential energy? It's the third one because it's stretched the most (twice as much), while the others are stretched less (0 and 1 time). Since it's stretched the most, the third spring has the highest amount of elastic potential energy. You can also think of it like this: the work done to stretch the spring is being turned into energy.
According to Hooke's Law, we know that for elastic materials, the force exerted by a spring is directly proportional to how much it is stretched or compressed, as shown in the following equation.
F = kx
where,
F is applied load x is the displacement (stretch or compression) k is the spring constant
When the system is at its equilibrium position (where no force is applied), the potential energy in the spring is zero. To find the potential energy stored in the spring when it's stretched or compressed by a certain amount, you can use the following formula.
U = 1/2 kx2
where U is the elastic potential energy of the system
Spring Potential Energy
Spring potential energy is the energy stored in the spring when it is stretched or compressed from its equilibrium (rest) position. This energy results from the work done to either stretch or compress the spring, and it depends on how far the spring is displaced and the stiffness (spring constant) of the spring.
When considering elastic potential energy, one of the most typical items to consider is a spring. Springs can be distorted in two ways, both of which result in a restoration to equilibrium. They may be stretched as well as compressed. To get the formula for the elastic potential energy of a spring, we must first examine Hooke's law.
There is no energy stored in the bow while it is in its normal position (i.e., not pulled). However, when its position is changed from its typical equilibrium state, the bow can store energy due to its location. This stored positional energy is referred to as potential energy. Potential energy is the stored energy of an object's location.
The displacement of the spring is denoted by x, while the spring constant is denoted by k. This constant is the measure of a spring's stiffness, and it is unique to each spring. The spring constant is affected by factors such as the material of the spring and the thickness of the coiled wire, among others.
The Hooke’s law, states that the strain of the material is proportional to the applied stress within the elastic limit of that material.
Mathematically,
F = –kx
Where F is the force, x is the extension length and k is the spring constant in N/m.
The formula with the negative (-) sign is commonly used to describe Hooke's law as a restoring force, but the positive version is also acceptable. The displacement of the spring is denoted by x, while the spring constant is denoted by k. This constant is the measure of a spring's stiffness, and it is unique to each spring.
The spring constant is affected by factors such as the material of the spring and the thickness of the coiled wire, among others.
When elastic objects stretch, atoms and molecules degenerate until the stress is applied and when the pressure is removed they return to their original state. So According to Hooke’s law, the force applied to stretch the spring is directly proportional to the amount of stretch.
Formula for Elastic Potential Energy
We can say that Elastic potential energy is equal to the work done to stretch the spring which depends on the spring constant k and the distance stretched.
Elastic potential energy
From the above diagram, we can say that the force required to stretch the spring is directly proportional to its displacement.
The force required to stretch the spring is directly proportional to its displacement. It is given as
P.E. = Magnitude of Force × Displacement or P.E. = 1/2 × kx2
Here, -ve sign indicates the opposite direction.
Solved Examples of Elastic Potential Energy
Question 1: Geek pulls a spring with a spring constant k=100 N/m stretching it from its rest length of 0.10 m to 0.20 m, What is the elastic potential energy stored in the spring?
Solution:
The Potential Energy stored in the spring is PE=(1/2)\:k\:d^2 J
displacement d= 0.20 m - 0.10 m
d = 0.10 m k = 100 N/m
Lets substitute all the values in formula.
P.E = (1/2)\:k\:d^2 J
= (1/2)\:(100)\:(0.10)^2 J = 0.50 J
Question 2: The vertical spring is linked to a load of mass 10 kg which is compressed by 10m. Determine the force constant of the spring.
Solution:
Mass m = 10kg
Displacement d = 10 m
F = ma = (10 kg) * 9.8 m/s^2 = 98 N
Force in the stretched spring is
F = kd Then k = F / d = 98 / 10 = 9.8 N/m
k = 9.8 N/m
Question 3: How is potential energy calculated?
Solution:
It is the product of the Force applied on the object and the displacement of the object
P.E = F .d
F -> Force d -> displacement
Question 4: A Boy pulls a spring with a spring constant k=200 N/m stretching by 0.10m, What is the elastic potential energy stored in the spring?
Solution:
The Potential Energy stored in the spring is PE=(1/2)\:k\:d^2 J
