4.8 • +11k Ratings
Save
Print
Edit
Have you ever wondered how a pogo stick helps you jump higher? why does the rod rebound and push you higher each time you bounce? The origin of this effect is a spring that is hidden inside the body of the pogo stick. The spring cannot push you higher by itself, you need an external force that compresses the spring. That force comes from your body weight. What's interesting is that your body weight is the force that is responsible for compressing the spring. now after it's compressed another force brings the spring back to its original position. What is this restorative force called? and how do we know how much force is required to compress a spring? Keep reading this article to find out!
We looked at how certain objects will try to obtain their position once they're deformed by an external force. When an external force acts on an object it can be deformed by compression (compressing a spring), bending (bending a plastic ruler), or elongating (elongating a rubber band). But remember, there must always be more than one force acting to modify the shape of a stationary object. Here we're interested in the force that helps bring these objects back to their original shape.
The weight of the person operating the pogo stick compresses the internal spring mechanism which causes kinetic energy associated with your falling motion towards the ground to be converted to elastic potential energy, Wikimedia Commons
An elastic force is a force that brings certain materials back to their original shape after being deformed.
Notice how we said certain materials and not all materials. This is because elastic forces are only produced by materials or shapes that are elastic in nature. Such materials are called elastomers. For example, a stretched rubber band will move back to its original shape once the force that's stretching it is removed. But this is only valid if the band is stretched within a certain limit. Once this limit has been exceeded, the band might break or become deformed permanently. To explain this there are two types of deformation that occur: elastic deformation and inelastic deformation.
Elastic deformation occurs when the object returns back to its original shape after the forces are withdrawn.
An inelastic deformation occurs when the object is permanently deformed and does not return back to its original position.
When an object is deformed (stretched, bent, or squeezed), elastic deformation occurs when the forces are withdrawn and the object returns to its original shape. It is an inelastic deformation if it does not return to its original shape. What's interesting is that for some materials, the elastic force exerted by the elastic object is directly proportional to the external force used to deform it. Now, can we connect this with any of Newton's laws of motion? Yes, Newton's third law states that:
"Every action has an equal and opposite reaction''.
The elastic force is nothing but the equal and opposite reaction to the external deforming force. After being compressed or stretched, the elastic force will be maintained in the body until it returns to its original shape. Stretching, compressing, twisting, and rotating are some of the most common deformations.
When a force's work on an object is independent of the object's path, it is called a conservative force. Instead, the work done by a conservative force is limited to the motion's endpoints. Thus, the elastic force is conservative, since it only depends on the displacement, and is independent of the path taken.
A massless, frictionless, unbreakable, and indefinitely stretchy spring is what we define as an ideal spring. When such springs are contracted, the elastic force pushes the spring back to its original position. When they are stretched, the elastic force pulls the spring back to its original position.
So how do we calculate this elastic force that returns the object back to its original shape? Well, we can use the following equation.
or in words,
is the force expressed in Newtons
.
is the stiffness of the spring or the elastic object, expressed in Newtons per meter
.
is the displacement of the spring, expressed in meters
.
The Spring stiffness or spring constant refers to a spring's capacity to resist an external force; the stiffer the spring, the greater the effort required to compress or stretch it. A spring with stiffness or spring constant of 
would require 
to displace it by 
.
The stiffness is a characteristic of the spring. The stiffness of a spring is also determined by the number of coils on it. The fewer coils in your spring, the stiffer it will be. So, the value of 
is determined not only by the kind of elastic material but also by its size and form.
Now as you can infer from the above formula, the extension of the spring or any elastomer is directly proportional to the force applied. However, this is only true up to a point called the limit of proportionality.
The limit of proportionality is the point beyond which the external force will cause an object to experience permanent deformation.
This relationship and condition is stated by Hooke's law. Hooke's law also known as the law of elasticity states that the deformation is directly proportional to the deforming load or force that applies up until the limit of proportionality.
Now let's understand this process of stretching an elastic object using a graph. The graph records the force applied on the Y-axis and the extension of the material on the X-axis.
The force vs extension curve for a spring shows the linear and non-linear relationship between them, Ranjit Boodoo CC-BY-SA-4.0
The figure above shows the relation between the force applied to two different springs versus the extension of the springs. We can see that the force is directly proportional to the displacement of both springs A and B up to a certain point only. This point is the limit of proportionality; once the force exceeds this limit, the relationship between extension and force becomes nonlinear. In many cases, including in the graph shown above, after the limit of proportionality, the extension increases at a higher rate than before for the same increment in force. Now can you say something about the spring constant for springs A and B just by looking at the graphs? Well, we can see that the graph of A is much steeper than B, this means that for the same magnitude of force, spring B gets deformed more than spring A. Hmm, so what does this mean? Well, refer back to the definition of the spring constant. Now you'll be able to say that spring A has a higher spring constant or stiffness than spring B as it requires a greater force to achieve the same deformation. Now that we have a good understanding of how elastic force works, let's see why this force is produced.
Work needs to be done to compress a spring or bring about any kind of deformation. By the principle of the conservation of energy, this work is then stored in the compressed object as elastic potential energy. When the external force is removed this elastic potential energy is released.
The energy stored in elastic materials as a result of stretching or compression is known as elastic potential energy.
The quantity of elastic potential energy stored in such a device is proportional to its extension; the greater the extension or deformation, the greater the elastic potential energy stored.
Springboards store potential energy when the diver jumps and releases it giving the diver a boost, Wikimedia Commons
Springboards are built of an aluminium aviation alloy that can withstand extremely high loads before breaking, allowing them to store significant amounts of elastic potential energy. Before the diver dives off the end of the board, this initial jump stores elastic potential energy in the board, allowing them to benefit from the energy of two independent jumps when they dive off of the board.
The bow stores the elastic potential energy when it is stretched and releases it when the archer lets go of it, Kurt Kaiser CC-Zero
When the archer pulls back on the string, the bow bends. Because it is composed of elastic material, the bow may flex. The bow's elastic potential energy is increased by bending it. The elastic force will allow the bow to retake its initial shape and push the flesh forward.
The following equation may be used to calculate the amount of elastic potential energy contained in a stretched spring:
,or in words,
is the spring constant expressed in Newtons per meter
.
is the extension of the spring expressed in meters
is the elastic potential energy expressed in Joules
.
To find the extension of the spring, you can measure the length of the spring at rest. Then you measure the length of the spring after applying a force to it. The difference between the first and the second measurement will give you the extension of the spring.
A spring is attached to a wall on its left side, as shown in the figure below. The spring constant 
is equal to 
. A block is then attached to the end of the spring, and a force is applied to the box moving the system to the left. The length of the spring has decreased from
to 
.
The elastic force and elastic energy for a compressed spring, StudySmarter Originals.
Step 1: Calculate the displacement of the spring:
The spring was compressed 
to the right.
Step 2: Calculate the magnitude of the spring force:
We can see that a force of 
was required to deform the spring by a distance of 
Step 3: Calculate the magnitude of the elastic potential energy contained in the compressed spring:
Note that the spring force allows it to recover its original position. In this case, the spring was compressed to the left. So, the elastic force will be directed to the right, allowing the spring to recover its original shape.
applied on the elastic object allowing it to recover its original shape, equals the extension or change in length 
times a constant 
,
.The following equation may be used to calculate the amount of elastic potential energy contained in a stretched spring 
.
, and is independent of the path taken. The elastic force can be calculated using the following equation F = ke, where k is the spring constant and e is the extension caused by an external force.
The elastic force is responsible for the elasticity in materials.
Before the diver dives off the end of the board, this initial jump stores elastic energy in the board, allowing them to benefit from the energy of two independent jumps when they exit the board on the second jump.
Yes, the elastic force is conservative, since it only depends on the displacement of the spring, and is independent of the path taken.
Yes, an elastic force or spring force is the force that brings certain materials back to their original form after deformation.
Be perfectly prepared on time with an individual plan.
Test your knowledge with gamified quizzes.
Create and find flashcards in record time.
Create beautiful notes faster than ever before.
Have all your study materials in one place.
Upload unlimited documents and save them online.
Identify your study strength and weaknesses.
Set individual study goals and earn points reaching them.
Stop procrastinating with our study reminders.
Earn points, unlock badges and level up while studying.
Create flashcards in notes completely automatically.
Create the most beautiful study materials using our templates.
Sign up to highlight and take notes. It’s 100% free.
