GCSE Physics - Elasticity, spring constant, and Hooke's Law #44
Summary
TLDRThis 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
🔍 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.
📊 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.
Mindmap
Keywords
💡Elasticity
💡Spring Constant
💡Hooke's Law
💡Force Extension Graphs
💡Deformation
💡Elastic Deformation
💡Inelastic Deformation
💡Extension
💡Natural Length
💡Elastic Limits
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
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