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Elastic Forces

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Elastic Forces

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!

Elastic force meaning

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.

Elastic Forces The image shows how a pogo stick works StudySmarterThe 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Elastic deformation occurs when the object returns back to its original shape after the forces are withdrawn.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.

Elastic force formula

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.

Elastic Forces The image shows the linear and non-linear relationship between force and extension StudySmarterThe 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.

Elastic energy meaning

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.

Elastic Forces The image shows how a springboard works StudySmarter springboard 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.

Elastic Forces The image shows how a stretched bow fires an arrow StudySmarterThe 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.

Elastic energy formula

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.

Elastic spring force example

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 fromto .

Elastic Forces The force and energy for a compressed spring StudySmarterThe 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.

Elastic Forces - Key takeaways

  • After being stretched or compressed, the force that permits some materials to recover to their previous form is known as elastic force or spring force.
  • After being compressed or stretched, the elastic force will be maintained in the body until it returns to its original shape.
  • A massless, frictionless, unbreakable, and indefinitely stretchy spring is considered as an ideal spring.
  • The energy held in elastic materials as a result of stretching or compressing is known as elastic potential energy.
  • The greater the stretch, the more energy is stored in the string.
  • The magnitude of the applied force 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 .

  • The elastic force is conservative since it only depends on the extension , and is independent of the path taken.

Frequently Asked Questions about Elastic Forces

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.

Final Elastic Forces Quiz

Question

What are Elastic Forces?

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Answer

An elastic force is a force that brings certain materials back to their original form after deformation.

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Question

The type of deformation which occurs when an object is permanently deformed is called …

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Answer

Inelastic deformation.

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Elastic force is path dependent.

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True

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Elastic force is a conservative force.

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True

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Elastic force is responsible for …

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deforming an object.

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The spring constant of a spring depends on ...

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Number of turns.

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The extension of a spring is directly proportional to the force until ...

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it exceeds the limit of proportionality.

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What is the limit of proportionality?

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The limit of proportionality is the point on the force extension curve beyond which an object will experience permanent deformation.

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What is elastic energy?

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Answer

The energy stored in elastic materials as a result of stretching or compressing is known as elastic potential energy.

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Question

If a force acts on an elastic object stretching the object, what kind of energy is stored within the object?


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Gravitational potential energy.

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What is the minimum number of forces required to deform a stationary object?

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There must always be more than one force acting to modify the shape of a stationary object.

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Question

How is the extension of an elastic object related to the force applied for an object which obeys Hooke's law?

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Directly proportional.

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Question

Which of the following items can store elastic potential energy?


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Answer

Rubber band.

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