GCSE Physics - Elasticity, spring constant, and Hooke's Law #44

Summary

This video explores the concept of elasticity, focusing on elastic and inelastic deformations, and introduces Hooke's Law. It explains how force applied to an object, like a spring, can cause it to stretch or compress, with the spring constant (k) determining the force needed for a unit extension. The video illustrates the direct proportionality between force and extension, represented by the equation f = ke, where f is force and e is extension. It also discusses the elastic limit beyond which Hooke's Law no longer applies, leading to inelastic deformation.

Takeaways

• 🔍 The video discusses different types of elasticity and introduces the concept of spring constant and Hooke's Law.
• 📚 Elasticity is the property of an object to change shape under force and return to its original shape when the force is removed.
• 🔄 Inelastic deformation occurs when an object does not return to its original shape after the force is removed, like plastic that retains its shape.
• 📏 Extension is the increase in length of a spring when it is stretched, which can be measured by adding mass to the spring.
• 💡 The natural length of a spring is slightly shorter than its total length due to the force of its own weight.
• ⚖️ The spring constant (k) is a measure of how stiff a material is, indicating the force required to stretch the spring by one meter.
• 📈 Hooke's Law is represented by the equation f = ke, where f is the force applied, k is the spring constant, and e is the extension.
• 📊 A graph of force against extension typically shows a straight line passing through the origin, indicating a direct proportionality between force and extension.
• 🚫 There is a limit to Hooke's Law, known as the elastic limit or the limit of proportionality, beyond which the material may undergo inelastic deformation.
• 🔧 The video uses a spring as an example to illustrate the concepts, but the principles apply to other objects that can be compressed, stretched, or bent.
• 🔄 The video emphasizes that two forces are always acting on an object to maintain equilibrium, such as the force of the floor when an object is pressed against it.

Q & A

What is the main topic of the video?

The main topic of the video is to explain the different types of elasticity, discuss the spring constant and Hooke's Law, and analyze force-extension graphs.

What happens when you apply a force to an object?

When you apply a force to an object, it can cause the object to compress, stretch, or bend, which is a change in shape known as deformation.

What are the two types of deformation mentioned in the script?

The two types of deformation mentioned are elastic deformation, where the object returns to its original shape after the forces are removed, and inelastic or plastic deformation, where the object remains deformed.

Why do we need to apply more than one force to stay still?

We need to apply more than one force to stay still because if only one force is applied, the object will move as we pull or push it. This is due to the principle of balanced forces, where an equal and opposite force is required to maintain equilibrium.

What is the term used to describe the increasing length of a spring when it's stretched?

The term used to describe the increasing length of a spring when it's stretched is 'extension'.

How does the spring's natural length change when a force is applied?

The spring's natural length will decrease slightly when a force is applied due to the weight of the spring itself and any additional mass, causing some initial extension.

What is the relationship between force and extension in a spring, and how is it represented mathematically?

The relationship between force and extension in a spring is directly proportional, which is represented mathematically as F = k * e, where F is the force, k is the spring constant, and e is the extension.

What is the unit of measurement for the spring constant, and what does it represent?

The unit of measurement for the spring constant is newtons per meter (N/m). It represents the amount of force required to stretch or compress the spring by one meter.

What is Hooke's Law, and how does it relate to the graph of force against extension?

Hooke's Law states that the force needed to stretch or compress a spring is directly proportional to the displacement. It is represented graphically as a straight line passing through the origin, indicating a direct proportionality between force and extension.

What are the elastic limits or limits of proportionality, and what happens when they are exceeded?

The elastic limits or limits of proportionality are the points beyond which Hooke's Law no longer applies. When these limits are exceeded, the object may not return to its original shape after the force is removed, indicating inelastic deformation.

What does the video conclude about the relationship between force and deformation?

The video concludes that while there is a direct proportional relationship between force and deformation as described by Hooke's Law, there is a limit to this relationship. Beyond the elastic limits, the deformation becomes inelastic and the object may not return to its original shape.

Outlines

00:00

🔍 Understanding Elasticity and Hooke's Law

This paragraph introduces the concept of elasticity, explaining the difference between elastic and inelastic deformation. It discusses how objects like springs, balls, or phones can deform and the importance of balanced forces in maintaining an object's position. The paragraph also defines 'extension' as the increase in length of a spring when stretched and introduces the spring constant 'k', which quantifies the force needed to extend a spring by a unit length. Hooke's Law, represented by the equation f = ke, is explained as the direct proportionality between force and extension, indicating that a stiffer spring has a higher spring constant.

05:01

📊 Hooke's Law Limitations and Elastic Limits

The second paragraph delves into the limitations of Hooke's Law, noting that there is a threshold beyond which the linear relationship between force and extension no longer holds, known as the elastic limit or the limit of proportionality. Beyond this point, deformation becomes inelastic, and the object may not return to its original shape after the force is removed. The paragraph concludes by summarizing the video's content and expressing hope for its usefulness to the viewer.

Keywords

💡Elasticity

Elasticity refers to the property of a material to return to its original shape and size after being stretched or compressed. In the video, it is the fundamental concept that explains how objects like springs react when a force is applied to them. The script mentions that elasticity is observed when an object 'springs back' to its original state after the force is removed, which is a key aspect of the video's theme on deformation and material behavior.

💡Spring Constant

The spring constant, denoted by 'k', is a measure of the stiffness of a spring. It indicates the amount of force needed to stretch or compress a spring by a unit length. The video script explains that a higher spring constant means the material is stiffer and requires more force to cause deformation, as seen in the force-extension relationship described by Hooke's Law.

💡Hooke's Law

Hooke's Law is the principle that the force needed to extend or compress a spring by some distance is proportional to that distance, mathematically expressed as F = kx, where F is the force applied, k is the spring constant, and x is the extension. The video emphasizes this law as it describes the linear relationship between force and extension, which is a direct proportionality that holds until the elastic limit is reached.

💡Force Extension Graphs

Force extension graphs are visual representations that show the relationship between the force applied to a spring and the resulting extension. The video script describes how these graphs are used to illustrate Hooke's Law, where a straight line through the origin indicates a direct proportionality between force and extension, demonstrating the elastic behavior of the material.

💡Deformation

Deformation in the video script refers to the change in shape of an object when a force is applied. The script differentiates between two types of deformation: elastic, where the object returns to its original shape after the force is removed, and inelastic, where the object remains deformed. Deformation is central to the video's discussion on material properties and responses to force.

💡Elastic Deformation

Elastic deformation is a type of deformation where an object returns to its original shape after the deforming force is removed. The video script uses the example of an elastic band to illustrate this concept, emphasizing that elastic deformation is reversible and is a key feature of materials that obey Hooke's Law within their elastic limits.

💡Inelastic Deformation

Inelastic deformation, also known as plastic deformation, is when an object does not return to its original shape after the force is removed and retains some degree of the deformation. The video script contrasts this with elastic deformation, noting that inelastic deformation occurs when an object is deformed beyond its elastic limit, resulting in a permanent change in shape.

💡Extension

Extension is the increase in length of a spring when it is stretched. The video script explains how to measure extension by adding mass to the bottom of a spring and observing the change in length. Extension is a critical concept in the video as it directly relates to the force applied and is used to demonstrate Hooke's Law.

💡Natural Length

The natural length of a spring, as mentioned in the video script, is the length of the spring when it is at rest and not under any external force. The script notes that the spring's own weight can cause a slight extension, making the natural length slightly shorter than when the spring is uncompressed. This concept is important for understanding the baseline from which extensions are measured.

💡Elastic Limits

Elastic limits, also referred to as the limits of proportionality in the video script, is the point beyond which Hooke's Law no longer applies, and the material will not return to its original shape after deformation. The script explains that once the force applied exceeds these limits, the deformation becomes inelastic, marking a critical threshold in material behavior.

Highlights

The video explores different types of elasticity and explains the concepts of spring constant and Hooke's law.

Force extension graphs are examined to illustrate the effects of applying force to an object, such as a spring, ball, or phone.

Elasticity is demonstrated through objects that return to their original shape after deformation, unlike inelastic objects which retain their deformed state.

The necessity of applying more than one force to maintain an object's position is explained, including the role of the floor's force when an object is squished against it.

Deformation is categorized into elastic and inelastic types, with elastic deformation allowing objects to spring back to their original shape.

Extension is defined as the increase in length of a spring when stretched, influenced by its own weight and additional mass.

The natural length of a spring is slightly shorter than its total length due to its own weight-induced extension.

The spring constant (k) is introduced as a measure of how much force is needed to stretch a spring by one meter.

Hooke's law is described as the direct proportionality relationship between force (f) and extension (e), expressed as f = ke.

The spring constant is measured in newtons per meter, indicating the stiffness of the material.

A graph plotting force against extension is used to demonstrate the linear relationship and Hooke's law.

The elastic limit or limit of proportionality is identified as the point where Hooke's law no longer applies and the object may undergo inelastic deformation.

The video emphasizes that all deformations shown are elastic, meaning the object will return to its original shape once the force is removed.

The video concludes by summarizing the concepts discussed and expressing hope that the information was useful to viewers.

Transcripts

in today's video we're going to look at

the different types of elasticity

explain the terms at spring constant and

hooked law

and finally look at some force extension

graphs

when you apply a force to an object

you could cause it to compress

to stretch

or to bend

this is easiest to see with a spring

but the same concept applies to other

objects too

like a ball or a phone

these objects are just less elastic

so it's harder to notice any kind of

change in shape

whatever the object is though we always

have to apply more than one force if we

wanted to stay still

otherwise the object will just move as

we pull or push it

even if you squish something against the

floor

and so you only apply one force

the floor itself is applying a force

upwards

so there are still two forces acting on

the object

now when an object changes shape we say

that it's been deformed

but importantly there are two different

types of deformation that you need to

know

elastic

and inelastic

if an object returns back to its

original shape after the forces have

been removed

then we call it elastic deformation

because it's able to spring back like an

elastic band

however if the object doesn't quite

return just normal shape

and stays deformed in some way

then we call it inelastic deformation

or sometimes plastic deformation

because it keeps its shape like plastic

the next concept we need to look at is

extension

which is the increasing length of a

spring when it's stretched

for example if we hang a spring from a

solid support

then we can measure how the spring's

length changes as we add downwards force

to the bottom of the spring

now even before we've had any chance to

add force ourselves

the spring's own mass will be exerting a

force downwards in the form of weight

and this means that the natural length

will be a bit shorter than the spring

itself because there will already be

some extension

this extra length is generally pretty

small though so we tend to ignore it and

think of the entire length as the

natural length

if we then add a mass to the bottom of

the spring

the weight of that mass will pull on the

spring and so increase its length

which we can then measure as the

extension

one thing to point out here is that the

solid support will also be exerting an

equal but opposite force upwards

and this is why the spring doesn't fall

down when we add any mass

it's being perfectly balanced by the

support

as we increase the force on the spring

for example we add more mass

the extension increases proportionally

which we can write as f

is proportional to e

because f is the force and e is a symbol

for extension

although you might sometimes see it

represented as an x instead

exactly how much the spring extends

though for a given force

depends on the particular object's

spring constant

which is denoted by letter k

and if we add this into our force

extension equation that we wrote in the

bottom left

we get f equals ke

with k being measured in newtons per

meter

and extension in meters

the spring constant tells us how many

newtons it would take to stretch the

particular object

like this spring by one meter

so the higher the spring constant the

stiffer the material

because it requires more force to

stretch it

we can show this relationship by

plotting a graph of force against

extension

as the force increases so does the

extension

and because it's a straight line

that passes through the origin

we can tell that force and extension are

directly proportional

we call this relationship hooke's law

and importantly all of this deformation

will be elastic deformation

meaning that once the force is removed

the object will return to its original

shape

there is a limit to this relationship

though

at some point our line will start to

curve

and we call this point the elastic

limits

or the limits of proportionality

after this point hooke's law no longer

applies and the object won't necessarily

go back to its original shape

meaning that it would have been

inelastically deformed

anyway that's everything for this video

so hope you found it useful

and we'll see you soon