Q&A - PSLE Science
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if we were assuming the simple model of classical friction, then friction does not depend on the contact surface area for 2 materials sliding over each other.
F_friction = u F_normal force
Pressure =Force /Area
PA = F
for a constant Force, i.e the weight of the object, increasing the area means a decrease in pressure.
thus, F does not change, and hence the normal force does not change.
if the normal force does not change, and ‘u’ is the coefficient of friction which is determined empirically, then F_friction does not depend on the area.
however, this is merely a model, simplified per say. in reality, surface areas do play a part in more complicated models. for example, surface areas play a significant role in the nano-scale regions.
but for the sake of a primary school physics question, i believe that friction being independent of surface area would suffice. -
Zack7:
In primary school context, surface area do affect amount of friction produced!!if we were assuming the simple model of classical friction, then friction does not depend on the contact surface area for 2 materials sliding over each other.
F_friction = u F_normal force
Pressure =Force /Area
PA = F
for a constant Force, i.e the weight of the object, increasing the area means a decrease in pressure.
thus, F does not change, and hence the normal force does not change.
if the normal force does not change, and 'u' is the coefficient of friction which is determined empirically, then F_friction does not depend on the area.
however, this is merely a model, simplified per say. in reality, surface areas do play a part in more complicated models. for example, surface areas play a significant role in the nano-scale regions.
but for the sake of a primary school physics question, i believe that friction being independent of surface area would suffice. -
take a look at this video by MIT
http://www.youtube.com/watch?v=Oagnr0cMLIU
it shows that sliding friction is independent of mass and surface area. -
Zack7:
Just some clarifications.take a look at this video by MIT
http://www.youtube.com/watch?v=Oagnr0cMLIU
it shows that sliding friction is independent of mass and surface area.
The video demonstrated that friction coefficient is independent of mass and not that friction is independent of mass. Friction is dependent on mass because :
Frictional Force = friction Coefficient x Normal Force
= friction Coefficient x (mass x g)
= mass x [friction Coefficient x g]
The equation Friction Force = friction coeff x normal force, is an empirical formula. It is not derived from any theory. It is based on the assumption that the \"friction coefficient\" is independent of the \"pressure\" at the surfaces in contact with each other. In reality, the \"friction coefficient\" is not independent of the \"pressure\". When the \"pressure\" is small, the coefficient is usually greater than when the \"pressure\" is smaller.
Therefore, if 2 objects of the same mass and material are resting on the same surface, the object with a bigger surface area in contact will be pressing down with a smaller pressure and the frictional force will be greater. Try this out. Place an aluminium foil flat on a plank. Take another aluminium foil of exactly the same size and fold it as many times as possible to form a small cuboid and place it on the same plank. When the plank is tilted, the first one to move will definitely be the foil that has been folded. -
atutor2001:
Just some clarifications.Zack7:
take a look at this video by MIT
http://www.youtube.com/watch?v=Oagnr0cMLIU
it shows that sliding friction is independent of mass and surface area.
The video demonstrated that friction coefficient is independent of mass and not that friction is independent of mass. Friction is dependent on mass because :
Frictional Force = friction Coefficient x Normal Force
= friction Coefficient x (mass x g)
= mass x [friction Coefficient x g]
The equation Friction Force = friction coeff x normal force, is an empirical formula. It is not derived from any theory. It is based on the assumption that the \"friction coefficient\" is independent of the \"pressure\" at the surfaces in contact with each other. In reality, the \"friction coefficient\" is not independent of the \"pressure\". When the \"pressure\" is small, the coefficient is usually greater than when the \"pressure\" is smaller.
Therefore, if 2 objects of the same mass and material are resting on the same surface, the object with a bigger surface area in contact will be pressing down with a smaller pressure and the frictional force will be greater. Try this out. Place an aluminium foil flat on a plank. Take another aluminium foil of exactly the same size and fold it as many times as possible to form a small cuboid and place it on the same plank. When the plank is tilted, the first one to move will definitely be the foil that has been folded.
Yes friction force depends on mass.
But no, it does not depend on surface area.
The classical modeling of friction involves the assumption that friction force is independent of surface area.
Which means the empirical equation that you use has the above assumption.
In fact from the video, if you notice, when the prof released both of the blocks with different surface areas, both of them dropped at approximately the same angle even though the surface area differed by more than 2times. This tells you that surface area plays a very small part and the assumption of independence is good in this regime.
Of course there are always exceptions, then perhaps there r higher level of theories to describe. But for a primary school syllabus, if we were to follow the standard model of friction, then no, surface area is taken to be independent. -
Zack7:
Maybe it is useful to understand why the empirical formula was developed. Empirical formulas are developed when the actual formula is too complex and no physicist is able to come up with the complete basis for actual relationship between frictional force, mass and type of surface yet. Such formula is only an \"approximation\". It is intended mainly as an aid for engineers to make a good-enough estimate on frictional force - something they need for their daily work. However, engineers do know that in reality, frictional force does depend on the size of the surface areas that are in contact. Therefore, probably the Primary school syllabus is geared to teach our young the real situation and thus teaching the students that frictional force does depend on the surface area that is in contact.
.....But no, it does not depend on surface area.
The classical modeling of friction involves the assumption that friction force is independent of surface area.
Which means the empirical equation that you use has the above assumption.
In fact from the video, if you notice, when the prof released both of the blocks with different surface areas, both of them dropped at approximately the same angle even though the surface area differed by more than 2times. This tells you that surface area plays a very small part and the assumption of independence is good in this regime.
Of course there are always exceptions, then perhaps there r higher level of theories to describe. But for a primary school syllabus, if we were to follow the standard model of friction, then no, surface area is taken to be independent.
ps
This is a link to a table on static and kinetic coefficient
http://blog.mechguru.com/machine-design/typical-coefficient-of-friction-values-for-common-materials/
You can find at the end of the table, the following qualification :
\"....The friction coefficient value changes not only with material but also with the position and orientation of the participation materials.
Hope this can help clear your doubts on whether does frictional force depend on the surface area in contact. -
atutor2001:
let me clear your misunderstanding
Maybe it is useful to understand why the empirical formula was developed. Empirical formulas are developed when the actual formula is too complex and no physicist is able to come up with the complete basis for actual relationship between frictional force, mass and type of surface yet. Such formula is only an \"approximation\". It is intended mainly as an aid for engineers to make a good-enough estimate on frictional force - something they need for their daily work. However, engineers do know that in reality, frictional force does depend on the size of the surface areas that are in contact. Therefore, probably the Primary school syllabus is geared to teach our young the real situation and thus teaching the students that frictional force does depend on the surface area that is in contact.Zack7:
.....But no, it does not depend on surface area.
The classical modeling of friction involves the assumption that friction force is independent of surface area.
Which means the empirical equation that you use has the above assumption.
In fact from the video, if you notice, when the prof released both of the blocks with different surface areas, both of them dropped at approximately the same angle even though the surface area differed by more than 2times. This tells you that surface area plays a very small part and the assumption of independence is good in this regime.
Of course there are always exceptions, then perhaps there r higher level of theories to describe. But for a primary school syllabus, if we were to follow the standard model of friction, then no, surface area is taken to be independent.
ps
This is a link to a table on static and kinetic coefficient
http://blog.mechguru.com/machine-design/typical-coefficient-of-friction-values-for-common-materials/
You can find at the end of the table, the following qualification :
\"....The friction coefficient value changes not only with material but also with the position and orientation of the participation materials.
Hope this can help clear your doubts on whether does frictional force depend on the surface area in contact.
friction force does depend on surface area. that is reality. but in physics, science, we assume independence for the normal day regime
if you are going to say friction force depends on surface area, then can you give an equation that says so? can you give the relationship between surface area vs friciton force?
if you can, then case closed. but i can tell you that is not possible at the current level of knowledge. that is why we can only obtain such 'constants' (coefficients) through experiment.
now why do we assume independence? the fact that surface area plays a very minuscule role in friction gives the green light to assuming independence in the normal day regime.
now let me ask you this question
F= ma
are you going to add in the quantum Schrodinger equation that is the analog to this motion equation?
the obvious answer is no. why? because we assume the quantum effects are minuscule in the classical, or normal day regime.
but hey, reality says it is dependent on quantum effects. this is what you are saying. sure you are right, but is it useful to know that quantum effects affect the classical regime? no. because we know its effects are small... just like in the case of friction, the surface area plays a very small non-linear role. that is why we have assumptions in theories because it works and it simplifies our lives.
and this is why we say classical regimes are mostly independent of quantum effects. -
Zack7:
I have not come across any equation linking frictional force to the contact area. The only link to the contact area is through the coefficient of friction. The coefficient of friction is not a constant. It depends on the pressure of the contact area which is a function of the contact area. Therefore, frictional force is a function of the contact area.
let me clear your misunderstanding
friction force does depend on surface area. that is reality. but in physics, science, we assume independence for the normal day regime
if you are going to say friction force depends on surface area, then can you give an equation that says so? can you give the relationship between surface area vs friciton force?
if you can, then case closed. but i can tell you that is not possible at the current level of knowledge. that is why we can only obtain such 'constants' (coefficients) through experiment.
now why do we assume independence? the fact that surface area plays a very minuscule role in friction gives the green light to assuming independence in the normal day regime.
now let me ask you this question
F= ma
are you going to add in the quantum Schrodinger equation that is the analog to this motion equation?
the obvious answer is no. why? because we assume the quantum effects are minuscule in the classical, or normal day regime.
but hey, reality says it is dependent on quantum effects. this is what you are saying. sure you are right, but is it useful to know that quantum effects affect the classical regime? no. because we know its effects are small... just like in the case of friction, the surface area plays a very small non-linear role. that is why we have assumptions in theories because it works and it simplifies our lives.
and this is why we say classical regimes are mostly independent of quantum effects.
Quantum mechanics has always been my nightmare. However, I also have not come across any academician attempting to find frictional force using quantum mechanics.
I have attached this link on static friction. http://www.utwente.nl/ctw/tr/Research/Publications/PhDTheses/thesis_Deladi.pdf
It is long and dry but I have extracted the main points of interests below:
Due to the difficulties encountered in practice, friction has been explored since ancient times. The first recorded studies on friction are dated in fifteenth century and belong to Leonardo da Vinci (1452-1519). His observations became two hundred of years later two of the well-known laws of sliding (dynamic) friction introduced by Guillaume Amontons (1663-1705), namely:
1. Friction force is directly proportional to the applied load.
2. Friction force is independent of the apparent area of contact.
Leonardo da Vinci introduced also the concept of coefficient of friction (μ) as the ratio of the friction force Ff to normal load N:
μ = Ff/N
More detailed experimental studies on friction were conducted by Charles-Augustin Coulomb (1736-1806) who completed the laws of friction with the third
law:
3. Dynamic friction force is independent of the sliding velocity
These empirical laws have been proved to be valid under certain conditions for many material couples. However, these laws are not valid for all material couples.
For instance, the coefficient of friction between polymers sliding against themselves or against metals or ceramics decreases by increasing the normal load (i.e. contact pressure), which is in contradiction with the first law.
The fact that the 3 laws are not applicable to all material pairs necessitates us to move back to the very basic i.e. frictional force depends on the coefficient of friction. However, this coefficient depends on the contact pressure i.e. the contact area. Therefore, frictional force depends on the contact area. -
atutor2001:
I have not come across any equation linking frictional force to the contact area. The only link to the contact area is through the coefficient of friction. The coefficient of friction is not a constant. It depends on the pressure of the contact area which is a function of the contact area. Therefore, frictional force is a function of the contact area.Zack7:
let me clear your misunderstanding
friction force does depend on surface area. that is reality. but in physics, science, we assume independence for the normal day regime
if you are going to say friction force depends on surface area, then can you give an equation that says so? can you give the relationship between surface area vs friciton force?
if you can, then case closed. but i can tell you that is not possible at the current level of knowledge. that is why we can only obtain such 'constants' (coefficients) through experiment.
now why do we assume independence? the fact that surface area plays a very minuscule role in friction gives the green light to assuming independence in the normal day regime.
now let me ask you this question
F= ma
are you going to add in the quantum Schrodinger equation that is the analog to this motion equation?
the obvious answer is no. why? because we assume the quantum effects are minuscule in the classical, or normal day regime.
but hey, reality says it is dependent on quantum effects. this is what you are saying. sure you are right, but is it useful to know that quantum effects affect the classical regime? no. because we know its effects are small... just like in the case of friction, the surface area plays a very small non-linear role. that is why we have assumptions in theories because it works and it simplifies our lives.
and this is why we say classical regimes are mostly independent of quantum effects.
Quantum mechanics has always been my nightmare. However, I also have not come across any academician attempting to find frictional force using quantum mechanics.
I have attached this link on static friction. http://www.utwente.nl/ctw/tr/Research/Publications/PhDTheses/thesis_Deladi.pdf
It is long and dry but I have extracted the main points of interests below:
Due to the difficulties encountered in practice, friction has been explored since ancient times. The first recorded studies on friction are dated in fifteenth century and belong to Leonardo da Vinci (1452-1519). His observations became two hundred of years later two of the well-known laws of sliding (dynamic) friction introduced by Guillaume Amontons (1663-1705), namely:
1. Friction force is directly proportional to the applied load.
2. Friction force is independent of the apparent area of contact.
Leonardo da Vinci introduced also the concept of coefficient of friction (μ) as the ratio of the friction force Ff to normal load N:
μ = Ff/N
More detailed experimental studies on friction were conducted by Charles-Augustin Coulomb (1736-1806) who completed the laws of friction with the third
law:
3. Dynamic friction force is independent of the sliding velocity
These empirical laws have been proved to be valid under certain conditions for many material couples. However, these laws are not valid for all material couples.
For instance, the coefficient of friction between polymers sliding against themselves or against metals or ceramics decreases by increasing the normal load (i.e. contact pressure), which is in contradiction with the first law.
The fact that the 3 laws are not applicable to all material pairs necessitates us to move back to the very basic i.e. frictional force depends on the coefficient of friction. However, this coefficient depends on the contact pressure i.e. the contact area. Therefore, frictional force depends on the contact area.
no, by your logic, the fact that the 3 laws are not applicable to all material pairs means you cannot even talk about the coefficient of friction.
in fact, since it doesn't apply to all material pairs, this model should be scrapped. -
Zack7:
The words in colour were not my logic. They were extracted from the research paper whereby the link I have attached.atutor2001:
I have not come across any equation linking frictional force to the contact area. The only link to the contact area is through the coefficient of friction. The coefficient of friction is not a constant. It depends on the pressure of the contact area which is a function of the contact area. Therefore, frictional force is a function of the contact area.
Quantum mechanics has always been my nightmare. However, I also have not come across any academician attempting to find frictional force using quantum mechanics.
I have attached this link on static friction. http://www.utwente.nl/ctw/tr/Research/Publications/PhDTheses/thesis_Deladi.pdf
It is long and dry but I have extracted the main points of interests below:
Due to the difficulties encountered in practice, friction has been explored since ancient times. The first recorded studies on friction are dated in fifteenth century and belong to Leonardo da Vinci (1452-1519). His observations became two hundred of years later two of the well-known laws of sliding (dynamic) friction introduced by Guillaume Amontons (1663-1705), namely:
1. Friction force is directly proportional to the applied load.
2. Friction force is independent of the apparent area of contact.
Leonardo da Vinci introduced also the concept of coefficient of friction (μ) as the ratio of the friction force Ff to normal load N:
μ = Ff/N
More detailed experimental studies on friction were conducted by Charles-Augustin Coulomb (1736-1806) who completed the laws of friction with the third
law:
3. Dynamic friction force is independent of the sliding velocity
These empirical laws have been proved to be valid under certain conditions for many material couples. However, these laws are not valid for all material couples.
For instance, the coefficient of friction between polymers sliding against themselves or against metals or ceramics decreases by increasing the normal load (i.e. contact pressure), which is in contradiction with the first law.
The fact that the 3 laws are not applicable to all material pairs necessitates us to move back to the very basic i.e. frictional force depends on the coefficient of friction. However, this coefficient depends on the contact pressure i.e. the contact area. Therefore, frictional force depends on the contact area.
no, by your logic, the fact that the 3 laws are not applicable to all material pairs means you cannot even talk about the coefficient of friction.
in fact, since it doesn't apply to all material pairs, this model should be scrapped.
It is common knowledge that coefficient for friction is relatively independent only for hard material. When it comes to soft material like rubber or even our own hand, applying a constant coefficient of friction is irrelevant. The equation F= coeff x normal is still true but the the coeff will change depending on the conditions and one of them is the contact area.
You don't seem to be really interested in friction.
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