If a perfect sphere of a certain material was placed from a moving vehicle on to a perfectly flat surface of the same material, all in a total vacuum, would the spherical object eventually come to a stop or would it roll for ever?

Oh, also, at the moment the sphere first contacts the flat surface, it is spinning at a rate perpendicular to the surface which equals the distance travelled and on a plane perpendicular to the direction the vehicle is traveling.

You forgot to mention gravity.

if the sphere stays on that flat surface it will create heat through friction and the kinetic energy will be transformed to heat thus the ball comes to a stop

feynman talks about the idea of a ball losing energy when it bounces

some of the energy of the ball is lost as it bounces and it makes the particles of the floor vibrate and the particles in the ball vibrate

the vibration is temperature of the ball and floor

feynman talks about the idea of a ball losing energy when it bounces

some of the energy of the ball is lost as it bounces and it makes the particles of the floor vibrate and the particles in the ball vibrate

the vibration is temperature of the ball and floor

Bubblecar said:

You forgot to mention gravity.

The material is perfectly inelastic (ie, the sphere doesn’t bounce). Gravity is zero. The sphere is placed on the surface and rolls along that surface without extraneous forces acting upon it.

wookiemeister said:

if the sphere stays on that flat surface it will create heat through friction and the kinetic energy will be transformed to heat thus the ball comes to a stop

If its a perfect sphere rolling along a perfect plane, why does it create heat through friction?

esselte said:

Bubblecar said:

You forgot to mention gravity.

The material is perfectly inelastic (ie, the sphere doesn’t bounce). Gravity is zero. The sphere is placed on the surface and rolls along that surface without extraneous forces acting upon it.

it wouldn’t matter if the gravity was zero

if its making contact with the surface then fristion is happening which means energy loss from the ball

esselte said:

wookiemeister said:

if the sphere stays on that flat surface it will create heat through friction and the kinetic energy will be transformed to heat thus the ball comes to a stop

If its a perfect sphere rolling along a perfect plane, why does it create heat through friction?

because the word rolling implies that friction is happening

a ball on a surface rolls

a ball in space with no physical contact is simply a ball moving through space – the surface nearby has no bearing on it until it touches it

in all practical terms

if the flat surface was able to impart motion to the ball by the fact it was moving in the other direction that would keep the ball rolling forever but it would take energy from the flat surface

wookiemeister said:

esselte said:

If its a perfect sphere rolling along a perfect plane, why does it create heat through friction?

because the word rolling implies that friction is happening

OK, I think I see what you mean. But if the sphere is both contacting the surface and spinning at a rate initially commensurate to that contact, if this is not described “rolling”, what is it?

esselte said:

wookiemeister said:

esselte said:

If its a perfect sphere rolling along a perfect plane, why does it create heat through friction?

because the word rolling implies that friction is happening

OK, I think I see what you mean. But if the sphere is both contacting the surface and spinning at a rate initially commensurate to that contact, if this is not described “rolling”, what is it?

if the ball is rolling on the surface for whatever reason (no gravity) then contact is still being made.

a ball moving along a surface and has contact with would normally be described as rolling

is the ball advancing along the flat surface?

if the ball is rolling then this means that when the ball touched the flat surface the flat surface was not moving at the same rate as the ball, hence the ball then turned some of its kinetic energy into angular motion, this means that the ball is now moving more slowly than it was before.

wookiemeister said:

if the ball is rolling then this means that when the ball touched the flat surface the flat surface was not moving at the same rate as the ball, hence the ball then turned some of its kinetic energy into angular motion, this means that the ball is now moving more slowly than it was before.

wait a minute you said the ball was spinning beforehand

i stand by my first assessment

if its making contact then friction is happening which means energy loss which means the ball slows down

wookiemeister said:

is the ball advancing along the flat surface?

The ball is advancing, at least at the moment of first contact with the surface, at a rate such that the spin of the ball sees the circumference of the ball rolling along the surface without any outside forces acting to slow that spin. I’m asking f outside forces come in to play following the moment of first contact? And how and why they do, if they do.

In a perfect vacuum they would freeze together

wookiemeister said:

wookiemeister said:

if the ball is rolling then this means that when the ball touched the flat surface the flat surface was not moving at the same rate as the ball, hence the ball then turned some of its kinetic energy into angular motion, this means that the ball is now moving more slowly than it was before.

wait a minute you said the ball was spinning beforehand

Yes. Before contacting the surface the sphere is spinning at a rate and in a plane such that the initial contact with the plane does not see the ball skid or scoot relative to the plane. What happens after the moment of initial contact between a material sphere and a material plane such as I am describing?

esselte said:

wookiemeister said:

is the ball advancing along the flat surface?

The ball is advancing, at least at the moment of first contact with the surface, at a rate such that the spin of the ball sees the circumference of the ball rolling along the surface without any outside forces acting to slow that spin. I’m asking f outside forces come in to play following the moment of first contact? And how and why they do, if they do.

the most relevant force on the ball would be drag. it it was an imaginary flat surface that was perfectly flat then you’d still have drag

19 shillings said:

In a perfect vacuum they would freeze together

Can you elaborate / please explain :)

esselte said:

wookiemeister said:

wookiemeister said:

if the ball is rolling then this means that when the ball touched the flat surface the flat surface was not moving at the same rate as the ball, hence the ball then turned some of its kinetic energy into angular motion, this means that the ball is now moving more slowly than it was before.

wait a minute you said the ball was spinning beforehand

Yes. Before contacting the surface the sphere is spinning at a rate and in a plane such that the initial contact with the plane does not see the ball skid or scoot relative to the plane. What happens after the moment of initial contact between a material sphere and a material plane such as I am describing?

the ball slows becasue friction would still be happening

Both surfaces will deform slightly. This deformation will not be perfectly elastic. So there will be energy loss as the surfaces deform and return to their original position.

the drag could take the form of bonding between the ball and surface

machined surfaces can actually hold themsleves together under the right circumstances

at the point of the perfect ball touching the perfectly flat surface you’d get some kind of attempted bonding at an atomic level i’d reckon

esselte said:

19 shillings said:

In a perfect vacuum they would freeze together

Can you elaborate / please explain :)

——

Perfect vacuum

No external energy, except..

After the initial energy imparted the perfect sphere cools eventually to Kelvin 0

19 shillings said:

esselte said:

19 shillings said:

In a perfect vacuum they would freeze together

Can you elaborate / please explain :)

——

Perfect vacuum

No external energy, except..

After the initial energy imparted the perfect sphere cools eventually to Kelvin 0

the ball is already travelling in a perfect vaccum already so its existing temperature would already be zero?

i think its being suggested that the nature of the ball is not quite the same as everyday matter

wookiemeister said:

19 shillings said:

esselte said:

Can you elaborate / please explain :)

——

Perfect vacuum

No external energy, except..

After the initial energy imparted the perfect sphere cools eventually to Kelvin 0

the ball is already travelling in a perfect vaccum already so its existing temperature would already be zero?

i think its being suggested that the nature of the ball is not quite the same as everyday matter

as in would the ball have friction with the surface

the surface is already at zero as well

19 shillings said:

esselte said:

19 shillings said:

In a perfect vacuum they would freeze together

Can you elaborate / please explain :)

——

Perfect vacuum

No external energy, except..

After the initial energy imparted the perfect sphere cools eventually to Kelvin 0

Why would that cause it to freeze together? There is no water involved.

maybe the ball and the surface would just meld into each other as they would both be some exotic substance at zero kelvin?

morrie said:

19 shillings said:

esselte said:

Can you elaborate / please explain :)

——

Perfect vacuum

No external energy, except..

After the initial energy imparted the perfect sphere cools eventually to Kelvin 0

Why would that cause it to freeze together? There is no water involved.

i think that matter at zero kelvin isn’t like “normal” room temperature matter

its got a different level of existence

morrie said:

19 shillings said:

esselte said:

Can you elaborate / please explain :)

——

Perfect vacuum

No external energy, except..

After the initial energy imparted the perfect sphere cools eventually to Kelvin 0

Why would that cause it to freeze together? There is no water involved.

—

Poetic license ;)

so how does this story end?

wookiemeister said:

so how does this story end?

My suspicion is that it ends with the sphere decelerating to a stop, but I don’t know why it would. This why is what I’m trying to determine.

Morris deformation theory holds some promise, but seems to depend on the direction of travel of the sphere not being absolutely perpendicular to the plane of the surface.

Personally, I’m thinking there might be some differential in the electrostatic forces between the “downwards” moving side of the sphere (relative to the plane surface) and the “upwards” moving side of the sphere.

esselte said:

wookiemeister said:

so how does this story end?

My suspicion is that it ends with the sphere decelerating to a stop, but I don’t know why it would. This why is what I’m trying to determine.

Morris deformation theory holds some promise, but seems to depend on the direction of travel of the sphere not being absolutely perpendicular to the plane of the surface.

Personally, I’m thinking there might be some differential in the electrostatic forces between the “downwards” moving side of the sphere (relative to the plane surface) and the “upwards” moving side of the sphere.

i’m thinking that both ball and surface are operating in a different way than “normal” matter

at zero kelvin somethign strange happens to matter

Absolute zero is the coldest possible temperature. More formally, it is the temperature at which entropy reaches its minimum value. The laws of thermodynamics state that absolute zero cannot be reached using only thermodynamic means. A system at absolute zero still possesses quantum mechanical zero-point energy, the energy of its ground state. The kinetic energy of the ground state cannot be removed. However, in the classical interpretation, it is zero and the thermal energy of matter vanishes.

The zero point of any thermodynamic temperature scale, such as Kelvin or Rankine scale, is set at absolute zero. By international agreement, absolute zero is defined as 0K on the Kelvin scale and as −273.15° on the Celsius scale. This equates to −459.67° on the Fahrenheit scale and 0 R on the Rankine scale. Scientists have achieved temperatures extremely close to absolute zero, where matter exhibits quantum effects such as superconductivity and superfluidity.

i’m not sure you would have or could have a flat surface both would be balls of matter i guess

I’m not really asking about the practicalities Wookie.

This is a thought experiment. My question was prompted by a joke on the TV show Futurama. The robot character Bender has taken up a hobo lifestyle, traveling in the box cars of interstellar trains. Approaching a way station, one f his fellow hobo’s says “Here’s where we get out. We are traveling at near the speed of light, so remember to roll when you hit the ground”.

I imagined how that would go. Robot Bender is anthropomorphic, so rolling isn’t really going to help him in this situation. Indeed, that is the joke.

I’m trying to subtract all the jokey aspects from the scenario… Hobo’s, trains, flailing arms etc to determine what would happen in a practically impossible, theoretically perfect situation.

esselte said:

I’m not really asking about the practicalities Wookie.

This is a thought experiment. My question was prompted by a joke on the TV show Futurama. The robot character Bender has taken up a hobo lifestyle, traveling in the box cars of interstellar trains. Approaching a way station, one f his fellow hobo’s says “Here’s where we get out. We are traveling at near the speed of light, so remember to roll when you hit the ground”.

I imagined how that would go. Robot Bender is anthropomorphic, so rolling isn’t really going to help him in this situation. Indeed, that is the joke.

I’m trying to subtract all the jokey aspects from the scenario… Hobo’s, trains, flailing arms etc to determine what would happen in a practically impossible, theoretically perfect situation.

arghhh i missed futurama! forgot

esselte said:

I’m not really asking about the practicalities Wookie.

This is a thought experiment. My question was prompted by a joke on the TV show Futurama. The robot character Bender has taken up a hobo lifestyle, traveling in the box cars of interstellar trains. Approaching a way station, one f his fellow hobo’s says “Here’s where we get out. We are traveling at near the speed of light, so remember to roll when you hit the ground”.

I imagined how that would go. Robot Bender is anthropomorphic, so rolling isn’t really going to help him in this situation. Indeed, that is the joke.

I’m trying to subtract all the jokey aspects from the scenario… Hobo’s, trains, flailing arms etc to determine what would happen in a practically impossible, theoretically perfect situation.

you you hit anything at light speed you’d probably explode

>Morris deformation theory holds some promise, but seems to depend on the direction of travel of the sphere not being absolutely perpendicular to the plane of the surface.

Both materials would have to have infinite stiffness for that to be the case.

wookiemeister said:

you you hit anything at light speed you’d probably explode

Well, Bender wouldn’t quite impact the ground at light speed as the train is presumably traveling somewhat parallel to the ground… But yes, still huge impact speeds with damaging decelerations which can’t be mitigated by rolling; which as I said before is the basis of the joke.

morrie said:

>Morris deformation theory holds some promise, but seems to depend on the direction of travel of the sphere not being absolutely perpendicular to the plane of the surface.

Both materials would have to have infinite stiffness for that to be the case.

I have already defined them as being a perfect sphere and a perfect plane. Infinite stiffness is a prerequisite of both, isn’t it?

esselte said:

morrie said:

>Morris deformation theory holds some promise, but seems to depend on the direction of travel of the sphere not being absolutely perpendicular to the plane of the surface.

Both materials would have to have infinite stiffness for that to be the case.

I have already defined them as being a perfect sphere and a perfect plane. Infinite stiffness is a prerequisite of both, isn’t it?

Yes, I guess so.

The loss of energy occurs because of the work done by the ball to separate the surface of the ball from the surface of the plane just behind the point of contact, and this is not fully compensated by any energy gain just in front of the point of contact.

The problem with questions like this is they require objects with properties that cannot really exist, such as “perfect smoothness” and “infinite stiffness”, then ask what would really happen.

If the objects are hypothetical objects with these imaginary properties, then the ball would roll for ever.

If they are real objects then there would be transfer of kinetic energy to heat as the ball rolled, so it would slow down and stop.

The loss of energy occurs because of the work done by the ball to separate the surface of the ball from the surface of the plane just behind the point of contact, and this is not fully compensated by any energy gain just in front of the point of contact.

what forces are involved here? van der waals?

Boris said:

The loss of energy occurs because of the work done by the ball to separate the surface of the ball from the surface of the plane just behind the point of contact, and this is not fully compensated by any energy gain just in front of the point of contact.

what forces are involved here? van der waals?

Yes, but I realised that the reason I gave is not the only possibility. If the ball depresses the surface of the plane, then as the ball rolls, work will be done by the ball to depress the plane just in front of the point of contact, and this is not fully compensated by the work done on the ball just behind the point of contact. This is due to the intrinsic inelasticity of the material, but possibly also due to incomplete cancellation of the oscillations set up on either side of the point of contact due to the spatio-temperal separation.

…contact due to the spatio-temperal separation.

i had the sound of a theremin playing in my mind when i read that. uncanny.

;-)

Boris said:

…contact due to the spatio-temperal separation.

i had the sound of a theremin playing in my mind when i read that. uncanny.

;-)

I think that for a hard ball rolling on a hard surface, the oscillations would be main loss of energy and produces the sound of rolling.

KJW said:

Boris said:

…contact due to the spatio-temperal separation.

i had the sound of a theremin playing in my mind when i read that. uncanny.

;-)

I think that for a hard ball rolling on a hard surface, the oscillations would be main loss of energy and produces the sound of rolling.

no atmosphere its a vaccum

there would vibration in the ball though but only if friction occurred – which it would

i was thinking of building a theremin to play whilst i posted here in the evenings

it was the dr who theme in response to the mental image i got to that particular set of word posted by KJW

wookiemeister said:

KJW said:

Boris said:

…contact due to the spatio-temperal separation.

i had the sound of a theremin playing in my mind when i read that. uncanny.

;-)

I think that for a hard ball rolling on a hard surface, the oscillations would be main loss of energy and produces the sound of rolling.

no atmosphere its a vaccum

there would vibration in the ball though but only if friction occurred – which it would

The oscillations are set up in materials of the plane and ball, so no atmosphere is necessary. These oscillations will eventually dissipate as heat if they can’t dissipate as sound. Although the mechanism I gave is a form of friction, friction in the form of resistance to sliding is not necessary.

KJW said:

wookiemeister said:

KJW said:

I think that for a hard ball rolling on a hard surface, the oscillations would be main loss of energy and produces the sound of rolling.

no atmosphere its a vaccum

there would vibration in the ball though but only if friction occurred – which it would

The oscillations are set up in materials of the plane and ball, so no atmosphere is necessary. These oscillations will eventually dissipate as heat if they can’t dissipate as sound. Although the mechanism I gave is a form of friction, friction in the form of resistance to sliding is not necessary.

theres a problem on a philosophical level

“sound” is a purely human/ concious entity related experience

if theres nothing but the ball and the flat surface then no sound occurs because there is no one to hear the vibration in the material

its why the tree falling in a wood question is the wrong question – it doesn’t make a sound because no one is there to hear it

it does make compression waves in the air though but sound is a purely subjective experience based on a concious entity

my understanding of friction is something that happens when two separate surfaces meet

you’d get friction bwteen ball and surface and internal fristion between the atoms of the ball and flat surface

anyway

i just define the energy loss as due to friction

wookiemeister said:

its why the tree falling in a wood question is the wrong question – it doesn’t make a sound because no one is there to hear it

Well that solves that mystery.

Divine Angel said:

wookiemeister said:

its why the tree falling in a wood question is the wrong question – it doesn’t make a sound because no one is there to hear it

Well that solves that mystery.

yeah i just threw that in to spice things up a bit

wookiemeister said:

KJW said:

The oscillations are set up in materials of the plane and ball, so no atmosphere is necessary. These oscillations will eventually dissipate as heat if they can’t dissipate as sound. Although the mechanism I gave is a form of friction, friction in the form of resistance to sliding is not necessary.

theres a problem on a philosophical level

“sound” is a purely human/ concious entity related experience

if theres nothing but the ball and the flat surface then no sound occurs because there is no one to hear the vibration in the material

its why the tree falling in a wood question is the wrong question – it doesn’t make a sound because no one is there to hear it

it does make compression waves in the air though but sound is a purely subjective experience based on a concious entity

my understanding of friction is something that happens when two separate surfaces meet

you’d get friction bwteen ball and surface and internal fristion between the atoms of the ball and flat surface

anyway

i just define the energy loss as due to friction

I don’t think the tree falling in the forest is relevant here. All I was saying was that the sound of rolling that we normally hear for a hard ball rolling on a hard surface is probably due to the mechanism I gave.

It could be argued that all such energy losses are friction, so to say that the energy loss is due to friction is tautologically meaningless, and one should be focussing on the precise mechanism of the energy loss rather than using the catch-all “friction” as an explanation.

wookiemeister said:

you’d get friction bwteen ball and surface and internal fristion between the atoms of the ball and flat surface

My point is that even if there no energy losses at the microscopic level (ie no inelasticity), there is still energy transfer between the ball and plane that will eventually cause the ball to be at rest relative to the plane.

esselte said:

The material is perfectly inelastic (ie, the sphere doesn’t bounce). Gravity is zero. The sphere is placed on the surface and rolls along that surface without extraneous forces acting upon it.

esselte said:

I have already defined them as being a perfect sphere and a perfect plane. Infinite stiffness is a prerequisite of both, isn’t it?

Hmm. So if you throw the sphere at the plane, it won’t bounce because it’s perfectly inelastic, and it won’t deform because it’s infinitely stiff. That sounds like it breaks conservation of momentum.

If the contact between the sphere and plane is perfectly frictionless, what’s the purpose of having the sphere spin?

PM 2Ring said:

If the contact between the sphere and plane is perfectly frictionless, what’s the purpose of having the sphere spin?

I think it’s so that the system is indistinguishable from a ball rolling on a surface without requiring friction to produce the rolling motion (without friction, a ball would simply slide down an inclined plane without rolling)

I suppose I ought to mention that special relativity prohibits perfectly rigid materials, since the speed of sound in such a material would be infinite. Would a material whose speed of sound is almost equal to the speed of light in a vacuum be adequate? :)

KJW said:

PM 2Ring said:

If the contact between the sphere and plane is perfectly frictionless, what’s the purpose of having the sphere spin?

I think it’s so that the system is indistinguishable from a ball rolling on a surface without requiring friction to produce the rolling motion (without friction, a ball would simply slide down an inclined plane without rolling)

Indeed. So if we’re assuming the system is frictionless, the sphere can spin around any axis, or not spin at all, and it won’t make any difference (apart from the energy-momentum stored in the spin of the sphere).

PM 2Ring said:

I suppose I ought to mention that special relativity prohibits perfectly rigid materials, since the speed of sound in such a material would be infinite. Would a material whose speed of sound is almost equal to the speed of light in a vacuum be adequate? :)

I recall Magic Chicken chastising you over a similar point in my “Rotating Rigid Dumbbell” thread long ago. ;-)

Ideal behaviour can be regarded as a limit (in the sense of calculus) of real behaviour.

It should be pointed out that the heat equation also violates special relativity, and from reading Wikipedia, it’s not clear to me that the problem has been fully solved.

KJW said:

wookiemeister said:

KJW said:

The oscillations are set up in materials of the plane and ball, so no atmosphere is necessary. These oscillations will eventually dissipate as heat if they can’t dissipate as sound. Although the mechanism I gave is a form of friction, friction in the form of resistance to sliding is not necessary.

theres a problem on a philosophical level

“sound” is a purely human/ concious entity related experience

if theres nothing but the ball and the flat surface then no sound occurs because there is no one to hear the vibration in the material

its why the tree falling in a wood question is the wrong question – it doesn’t make a sound because no one is there to hear it

it does make compression waves in the air though but sound is a purely subjective experience based on a concious entity

my understanding of friction is something that happens when two separate surfaces meet

you’d get friction bwteen ball and surface and internal fristion between the atoms of the ball and flat surface

anyway

i just define the energy loss as due to friction

I don’t think the tree falling in the forest is relevant here. All I was saying was that the sound of rolling that we normally hear for a hard ball rolling on a hard surface is probably due to the mechanism I gave.

It could be argued that all such energy losses are friction, so to say that the energy loss is due to friction is tautologically meaningless, and one should be focussing on the precise mechanism of the energy loss rather than using the catch-all “friction” as an explanation.

fric·tion

/ˈfrikSHən/
Noun
1.The resistance that one surface or object encounters when moving over another.
2.The action of one surface or object rubbing against another.
3. Physics A force that resists the relative motion or tendency to such motion of two bodies or substances in contact.

Friction is the “evil” of all motion. No matter which direction something moves in, friction pulls it the other way. Move something left, friction pulls right. Move something up, friction pulls down. It appears as if nature has given us friction to stop us from moving anything.

Friction is actually a force that appears whenever two things rub against each other. Although two objects might look smooth, microscopically, they’re very rough and jagged, as this picture shows
http://www.fearofphysics.com/Friction/frintro.html

PM 2Ring said:

I suppose I ought to mention that special relativity prohibits perfectly rigid materials, since the speed of sound in such a material would be infinite. Would a material whose speed of sound is almost equal to the speed of light in a vacuum be adequate? :)

Interesting point.

if that balling is rolling then theres an immediate resistance to that ball continuing to roll

the flat surface will still generate resistance no matter how flat it is as its “flatness is limited to the fact that the atoms its made from aren’t flat – they are normally considered “round” in shape

the act of the ball touching the flat surface will cause atoms in the ball and flat surface to jiggle

wookiemeister said:

Friction is the “evil” of all motion. No matter which direction something moves in, friction pulls it the other way. Move something left, friction pulls right. Move something up, friction pulls down. It appears as if nature has given us friction to stop us from moving anything.

Actually, without friction, we wouldn’t be able to do anything at all.

Speaking of friction…
http://www.youtube.com/watch?v=RwrCUEMl76U

A problem with the initial question is that the assumption of “perfect sphere” presupposes that atoms don’t exist. But atoms do exist, and atoms interact, and that means that energy of interaction is radiated away as sound waves. This loss of energy provides a fixed limit on how low the friction can be.

This loss of energy of a rolling sphere is, not surprisingly, known as “rolling friction”.

mollwollfumble said:

A problem with the initial question is that the assumption of “perfect sphere” presupposes that atoms don’t exist. But atoms do exist, and atoms interact, and that means that energy of interaction is radiated away as sound waves. This loss of energy provides a fixed limit on how low the friction can be.

This loss of energy of a rolling sphere is, not surprisingly, known as “rolling friction”.

don’t use the word friction here – they don’t like it

don’t use the word friction here – they don’t like it

ridicule what you don’t understand.

Boris said:

don’t use the word friction here – they don’t like it

ridicule what you don’t understand.

get your hand off it boris

i thought you would have liked the quote.

Boris said:

i thought you would have liked the quote.

someone didn’t like me using the word friction, i was amazed when someone has come in from left field and started using it regardless

i have read the thread.

There’s a fraction too……umm………..a fraction too many rabbits in China, yeah.

wookiemeister said:

if that balling is rolling then theres an immediate resistance to that ball continuing to roll

the flat surface will still generate resistance no matter how flat it is as its “flatness is limited to the fact that the atoms its made from aren’t flat – they are normally considered “round” in shape

An essential aspect of friction is that it is a non-conservative force. A bumpy surface in itself doesn’t produce friction if the object can follow the terrain of the surface without overall loss of energy (by conservatively interconverting kinetic and potential energy).

Peak Warming Man said:

There’s a fraction too……umm………..a fraction too many rabbits in China, yeah.

So PWM, are you a member of the friction faction fraction or the anti-friction faction fraction?

PM 2Ring said:

I suppose I ought to mention that special relativity prohibits perfectly rigid materials, since the speed of sound in such a material would be infinite. Would a material whose speed of sound is almost equal to the speed of light in a vacuum be adequate? :)

Also the material would require infinite strength since infinite forces would be generated by the impact of any two infinitely rigid bodies.

KJW said:

An essential aspect of friction is that it is a non-conservative force. A bumpy surface in itself doesn’t produce friction if the object can follow the terrain of the surface without overall loss of energy (by conservatively interconverting kinetic and potential energy).

Why is that an essential aspect?

Surely in the limit as the stiffness of the materials increases a bumpy surface could transfer a friction force without any overall loss of energy.

KJW said:

wookiemeister said:

if that balling is rolling then theres an immediate resistance to that ball continuing to roll

the flat surface will still generate resistance no matter how flat it is as its “flatness is limited to the fact that the atoms its made from aren’t flat – they are normally considered “round” in shape

An essential aspect of friction is that it is a non-conservative force. A bumpy surface in itself doesn’t produce friction if the object can follow the terrain of the surface without overall loss of energy (by conservatively interconverting kinetic and potential energy).

as far as i’m aware the scenario isn’t some perfect world the original scene paints the event happening at absolute zero

my take on it now is that the two objects are made from every day materials and made as flat and as spherical as possible its just happening in a vaccum somewhere not near the earth

wookiemeister said:

as far as i’m aware the scenario isn’t some perfect world the original scene paints the event happening at absolute zero

my take on it now is that the two objects are made from every day materials and made as flat and as spherical as possible its just happening in a vaccum somewhere not near the earth

In that case it will eventually come to a stop; no question.

(It couldn’t be at absolute zero in the real world by the way).

As I am sure you understand, you can’t make a perfect sphere or a perfectly flat plane out of baryonic matter (ie ordinary stuff). To answer your question we would need more details on what materials were used.

If you mean “as perfect a sphere and as perfect a flat plane as you can make out of ordinary materials”, then the answer is that it will definitely slow down eventually due to friction.

ok ok

what if the sphere was “the death star” and the flat surface was “the monolith”

i think this would be a more likely scenario

The Rev Dodgson said:

KJW said:

An essential aspect of friction is that it is a non-conservative force. A bumpy surface in itself doesn’t produce friction if the object can follow the terrain of the surface without overall loss of energy (by conservatively interconverting kinetic and potential energy).

Why is that an essential aspect?

Surely in the limit as the stiffness of the materials increases a bumpy surface could transfer a friction force without any overall loss of energy.

After I wrote this, I realised that I had neglected static friction, which need not be a non-conservative force as it produces no energy loss and need not be dissipative in effect. But static friction plays no part in this scenario.

How can a bumpy surface exert a frictional force without any overall loss of energy? dW = F*•d*r. If the force is conservative, then any decrease in kinetic energy of the ball must increase the potential energy. For a cyclic trajectory, friction produces a net loss of kinetic energy, and this by definition is non-conservative.

There can only be static friction between two perfectly rigid bumpy surfaces and this force is conservative. However, any work done in applying this force (causing microscopic displacement) will increase the potential energy which will be converted to kinetic energy when the application of the force is removed. When the applied force is sufficient to overcome the static friction, the work done in overcoming the static friction will remain as some combination of potential energy and kinetic energy, and the dynamic friction will be zero.

PM 2Ring said:

Hmm. So if you throw the sphere at the plane, it won’t bounce because it’s perfectly inelastic, and it won’t deform because it’s infinitely stiff. That sounds like it breaks conservation of momentum.

A perfectly inelastic collision between two perfectly rigid objects is possible, but the kinetic energy of the objects prior to collision must go somewhere. Normally for inelastic collisions, the kinetic energy is converted to heat, but this contradicts the rigidity condition. But if the collision alters the electronic state of the object, and this state relaxes by emission of photons, a chemical transformation, the creation of a magnetic field, etc, then this may satisfy the condition of perfect rigidity. These might not seem realistic and they might not truly satisfy the rigidity condition (or in the case of the emission of photons, perfect inelasticity), but they do show how there could be a perfectly inelastic collision between two perfectly rigid objects without violating any conservation laws.

It should be noted that from a relativistic standpoint, for a perfectly inelasic collision, the rest mass after collision is greater than the sum of the rest masses before collision, and therefore the internal state of the objects must change as a result of the collision.†

† Compton scattering is often described as inelastic, but strictly speaking it is perfectly elastic. The apparent inelasticity of the scattering is actually a frame of reference effect, and there does exist a frame of reference in which the scattering is elastic. Because the elasticity of a collision is an invariant notion, Compton scattering is truly elastic in all frames of reference though it might not appear to be so in a given frame of reference.

>Hmm. So if you throw the sphere at the plane, it won’t bounce because it’s perfectly inelastic, and it won’t deform because it’s infinitely stiff. That sounds like it breaks conservation of momentum

Reminds me a bit of designers who think that granular matter can turn sharp corners.

this ball and flat surface is starting to sound like a perpetual motion machine

KJW said:

† Compton scattering is often described as inelastic, but strictly speaking it is perfectly elastic. The apparent inelasticity of the scattering is actually a frame of reference effect, and there does exist a frame of reference in which the scattering is elastic. Because the elasticity of a collision is an invariant notion, Compton scattering is truly elastic in all frames of reference though it might not appear to be so in a given frame of reference.

However, I should point out that this is from a microscopic point of view for the collision between a photon and an individual charged particle (such as an electron). In the case of Compton scattering from a macroscopic bulk material, the energy imparted to the electrons by the photons eventually get converted to heat and in this sense, the scattering is truly inelastic.

I point this out because what happens at the macroscopic level may differ from what happens at the microscopic level. For example, for the perfectly inelastic collision between two macroscopic objects, the individual collisions at the microscopic level may still be perfectly elastic, but the collision is still described as inelastic because this is what it is from the point of view of the objects themselves rather than their microscopic components. Thus, in the case of Compton scattering, the description as inelastic may not simply be a frame of reference effect, but actually from a macroscopic point of view where it is truly inelastic.

KJW said:

PM 2Ring said:

I suppose I ought to mention that special relativity prohibits perfectly rigid materials, since the speed of sound in such a material would be infinite. Would a material whose speed of sound is almost equal to the speed of light in a vacuum be adequate? :)

I recall Magic Chicken chastising you over a similar point in my “Rotating Rigid Dumbbell” thread long ago. ;-)

He did? I don’t recall that, and unfortunately I didn’t archive that thread.
But I will agree that the notion of rigidity in SR isn’t as simple as my remark that you quoted might imply. OTOH, it appears that the Ehrenfest paradox regarding a spinning rigid disk has an adequate resolution.

KJW said:

Ideal behaviour can be regarded as a limit (in the sense of calculus) of real behaviour.

Certainly.

KJW said:

It should be pointed out that the heat equation also violates special relativity, and from reading Wikipedia, it’s not clear to me that the problem has been fully solved.

Ok. The standard solution to the heat equation makes several unphysical assumptions, not just the zero delay in heat propagation: the Fourier analysis uses perfect sine waves, which would actually have to be of infinite extent to be perfect. Fortunately, these mathematical infinities don’t seem to worry the physicists too much, since the maths leads to usable results. :)

morrie said:

>Hmm. So if you throw the sphere at the plane, it won’t bounce because it’s perfectly inelastic, and it won’t deform because it’s infinitely stiff. That sounds like it breaks conservation of momentum

Reminds me a bit of designers who think that granular matter can turn sharp corners.

But granular matter can turn sharp corners… into dead ends. Or rounded corners. :)

PM 2Ring said:

morrie said:

>Hmm. So if you throw the sphere at the plane, it won’t bounce because it’s perfectly inelastic, and it won’t deform because it’s infinitely stiff. That sounds like it breaks conservation of momentum

Reminds me a bit of designers who think that granular matter can turn sharp corners.

But granular matter can turn sharp corners… into dead ends. Or rounded corners. :)

Yeah, thats what happens. Not rounded corners though, but straight lines.

wookiemeister said:

this ball and flat surface is starting to sound like a perpetual motion machine

Being without energy loss due to friction doesn’t make it a perpetual motion machine. Perpetual motion machines violate the laws of physics by attempting to extract energy from where it is impossible to do so. Either they violate the conservation of energy by neglecting to balance all the energy transactions, or they violate the second law of thermodynamics by attempting to convert useless energy into work.

morrie said:

PM 2Ring said:

morrie said:

>Hmm. So if you throw the sphere at the plane, it won’t bounce because it’s perfectly inelastic, and it won’t deform because it’s infinitely stiff. That sounds like it breaks conservation of momentum

Reminds me a bit of designers who think that granular matter can turn sharp corners.

But granular matter can turn sharp corners… into dead ends. Or rounded corners. :)

Yeah, thats what happens. Not rounded corners though, but straight lines.

Well they must be a bit rounded somewhere, I suppose. But what I see is pretty well straight surfaces.

morrie said:

Yeah, thats what happens. Not rounded corners though, but straight lines.

Ah. I see. That sounds like it could get expensive.

Well it could be a perpetual motion machine of the third kind.
From Wikipedia

A more obscure category is a perpetual motion machine of the third kind, usually (but not always) defined as one that completely eliminates friction and other dissipative forces, to maintain motion forever (due to its mass inertia). Third in this case refers solely to the position in the above classification scheme, not the third law of thermodynamics. Although it is impossible to make such a machine, as dissipation can never be 100% eliminated in a mechanical system, it is nevertheless possible to get very close to this ideal (see examples in the Low Friction section). Such a machine would not serve as a source of energy but would have utility as a perpetual energy storage device.

PM 2Ring said:

morrie said:

Yeah, thats what happens. Not rounded corners though, but straight lines.

Ah. I see. That sounds like it could get expensive.

I didn’t explain well. I meant that where one might expect the material to form a concave surface in a sharp bend, it doesn’t. It forms the third side of a triangle if you can understand what I mean.

morrie said:

I didn’t explain well. I meant that where one might expect the material to form a concave surface in a sharp bend, it doesn’t. It forms the third side of a triangle if you can understand what I mean.

I thinks so. My remarks about rounding were in connection to a sufficiently hard granular material having an abrasive action.

PM 2Ring said:

morrie said:

I didn’t explain well. I meant that where one might expect the material to form a concave surface in a sharp bend, it doesn’t. It forms the third side of a triangle if you can understand what I mean.

I thinks so. My remarks about rounding were in connection to a sufficiently hard granular material having an abrasive action.

I see what you mean. You might expect a concave surface to develop over time. There are lots of mechanisms going on though. Its pretty complex. I see the straight surfaces in the work I do.

PM 2Ring said:

KJW said:

I recall Magic Chicken chastising you over a similar point in my “Rotating Rigid Dumbbell” thread long ago. ;-)

He did? I don’t recall that, and unfortunately I didn’t archive that thread.

The point he made is that it is not enough to simply point out that a stated ideal condition is unphysical, that one needs to examine the problem itself.

I made the point that an ideal condition can be regarded as a limit of physically real conditions so that questions involving an ideal condition can be reasonably answered without making impossible assumptions about the existence of the ideal condition.

KJW said:

I made the point that an ideal condition can be regarded as a limit of physically real conditions so that questions involving an ideal condition can be reasonably answered without making impossible assumptions about the existence of the ideal condition.

A bit like “infinity”, really. :-)

PM 2Ring said:

The standard solution to the heat equation makes several unphysical assumptions, not just the zero delay in heat propagation: the Fourier analysis uses perfect sine waves, which would actually have to be of infinite extent to be perfect.

That the Fourier analysis uses perfect sine waves actually doesn’t matter, and shouldn’t be viewed as an approximation or idealisation. What a Fourier analysis does is to completely decompose a vector in Hilbert space into its components in the frequency basis. Because the heat equation is linear and homogenous, the sum (or integral) of a set of solutions is also a solution. The Fourier analysis thus allows one to construct the solution vector in Hilbert space as a vector sum of basis solution vectors in the frequency basis. Any complete set of basis vectors could have been chosen for the decomposition, and none are more correct than any other, though the frequency basis is often the easiest to deal with.

The flaw with the heat equation is with the equation itself, not with any method of solving it.

PM 2Ring said:

Fortunately, these mathematical infinities don’t seem to worry the physicists too much, since the maths leads to usable results. :)

One example of the effectiveness of mathematics to yield correct results beyond anything that can be considered physically reasonable is the derivation of the Casimir effect, in particular zeta function regularization

PM 2Ring said:

OTOH, it appears that the Ehrenfest paradox regarding a spinning rigid disk has an adequate resolution

I never saw a philosophical problem with the Ehrenfest paradox. Although I have never analysed this particular problem, I have analysed the simpler problem of an accelerating spring, concluding that the relativistic length contraction manifests itself in a physical manner and is not just a consequence of the different frames of reference (as it is for constant velocity). Thus, I see a rigid disk becoming stressed, perhaps to the point of destruction, by being rotated at relativistic speeds.

PM 2Ring said:

But I will agree that the notion of rigidity in SR isn’t as simple as my remark that you quoted might imply. OTOH, it appears that the Ehrenfest paradox regarding a spinning rigid disk has an adequate resolution.

Actually, the notion of spin itself is fairly complicated in relativity. Some may regard spin in three-dimensional space as complicated, but spin in four-dimensional spacetime is taken to a whole new level of complication. For one thing, spin can no longer be treated as a vector. The representation of spin as a pseudovector directed parallel to the spin axis by applying the right-hand rule only applies to three-dimensional space because spin is actually a bivector and its Hodge dual is the pseudovector that is used in physics, but in four-dimensional spacetime, the Hodge dual of a bivector is also a bivector (a pseudobivector). Also, acceleration is a (hyperbolic) rotation in spacetime, so accelerating a spinning object or the composition of two accelerations may produce precessional effects (See Thomas precession). Then, there are the spinors…

>Then, there are the spinors…

At this point perhaps a video might be entertaining.

http://www.youtube.com/watch?v=GgahTJybT5U

KJW said:

The Rev Dodgson said:

KJW said:

An essential aspect of friction is that it is a non-conservative force. A bumpy surface in itself doesn’t produce friction if the object can follow the terrain of the surface without overall loss of energy (by conservatively interconverting kinetic and potential energy).

Why is that an essential aspect?

Surely in the limit as the stiffness of the materials increases a bumpy surface could transfer a friction force without any overall loss of energy.

After I wrote this, I realised that I had neglected static friction, which need not be a non-conservative force as it produces no energy loss and need not be dissipative in effect. But static friction plays no part in this scenario.

How can a bumpy surface exert a frictional force without any overall loss of energy? dW = F*•d*r. If the force is conservative, then any decrease in kinetic energy of the ball must increase the potential energy. For a cyclic trajectory, friction produces a net loss of kinetic energy, and this by definition is non-conservative.

I disagree that static friction plays no part in this scenario. The ball is rotating so that the relative velocity of the ball and the plane is zero at the point of contact. For any real ball and plane there will be some deformation at the point of contact, so some energy transfer and loss of kinetic energy in the ball, but as the rigidity of both objects approaches infinity, and the smoothness of both surfaces approaches perfect, the deformation, and the energy loss, will tend to zero. The “static friction” will also tend to zero, but as we are considering behaviour as properties tend towards hypothetical limits I’d say that static friction does play a part in the scenario.

I don’t see that dynamic friction plays any part in the scenario, although at a sufficiently small scale there is no clear distinction between the two anyway.

take a piece of paper

draw a ball on a line with an arrow of the direction of the ball

write “conforms to no known measure of reality” in the corner

at the bottom of the paper write “therefore ball travels forever”

now take that piece of paper, scrunch it up and throw it in the dustbin

What is the purpose of the recommended ritual?

The Rev Dodgson said:

What is the purpose of the recommended ritual?

that the situation set out is too far removed from reality to have any relevance or known outcome when inconvenient known facts are tidily removed to make sure the ball achieves perpetual motion on a flat surface

wookiemeister said:

The Rev Dodgson said:

What is the purpose of the recommended ritual?

that the situation set out is too far removed from reality to have any relevance or known outcome when inconvenient known facts are tidily removed to make sure the ball achieves perpetual motion on a flat surface

That’s why we are looking at the way the behaviour changes as the properties move towards an unattainable limit.

Did you miss that bit, or choose to ignore it?

The Rev Dodgson said:

wookiemeister said:

The Rev Dodgson said:

What is the purpose of the recommended ritual?

that the situation set out is too far removed from reality to have any relevance or known outcome when inconvenient known facts are tidily removed to make sure the ball achieves perpetual motion on a flat surface

That’s why we are looking at the way the behaviour changes as the properties move towards an unattainable limit.

Did you miss that bit, or choose to ignore it?

thats not what i got from the original post

KJW said:

PM 2Ring said:

KJW said:

I recall Magic Chicken chastising you over a similar point in my “Rotating Rigid Dumbbell” thread long ago. ;-)

He did? I don’t recall that, and unfortunately I didn’t archive that thread.

The point he made is that it is not enough to simply point out that a stated ideal condition is unphysical, that one needs to examine the problem itself.

I made the point that an ideal condition can be regarded as a limit of physically real conditions so that questions involving an ideal condition can be reasonably answered without making impossible assumptions about the existence of the ideal condition.

Fair enough. Idealisations are very useful, both in developing theory and in performing practical calculations.

The Rev Dodgson said:

I disagree that static friction plays no part in this scenario. The ball is rotating so that the relative velocity of the ball and the plane is zero at the point of contact.

Static friction plays no part because:

(a): The motion is rolling motion, not sliding motion, with its differences in the relative motion between the two surfaces (perpendicular vs parallel).
(b): The ball is already in motion so that there is no static friction to the rolling motion.

The point is that there are two distinct types of motion for a ball on a surface: rolling and sliding, and each of these will have there own static and dynamic friction. Since we are talking about rolling, the static and dynamic friction to sliding motion is irrelevant, and thus we are only interested in the static and dynamic friction to rolling motion. But since the ball is already in motion, the static friction to rolling motion is also irrelevant, leaving only the dynamic friction to rolling motion to consider.

The Rev Dodgson said:

at a sufficiently small scale there is no clear distinction between the two anyway.

It seems to me that at the microscopic scale, there is a very clear distinction between static and dynamic friction. Here’s the way I see it:

At a mechanistic level, the total friction for a given type of motion can be decomposed into static and dynamic components:

Let S be the mechanisitic static friction. This component is conservative
Let D(v) be mechanistic dynamic friction. This component is non-conservative.
Let F_s be the phenomenological static friction.
Let F_d(v) be the phenomenological dynamic friction.

Then:

F_s = S + lim_v–›0 D(v)
F_d(v) = D(v)

S is the force required to get the ball out of any potential energy well. However, this not the total static friction actually measured. There are also the dissipative mechanisms that apply even at rest and this is added to the conservative force. But, once the ball is actually in motion, the conservative mechanisms no longer contribute and the friction drops to the purely dissipative component.

Because F_d(v) = D(v), then:

F_s = S + lim_v–›0 F_d(v)

and:

S = F_s – lim_v–›0 F_d(v)

Thus, both S and D(v) can be obtained from the measured quantities F_s and F_d. Note that lim_v–›0 F_d(v) was chosen rather than F_d(0) because F_d(0) is not measurable except as the limit as the speed approaches zero.

The Rev Dodgson said:

For any real ball and plane there will be some deformation at the point of contact, so some energy transfer and loss of kinetic energy in the ball, but as the rigidity of both objects approaches infinity, and the smoothness of both surfaces approaches perfect, the deformation, and the energy loss, will tend to zero.

For a ball that is rolling on a surface, what is happening just behind the region of contact is ostensibly the reverse of what is happening just in front of the region of contact. So, ideally, the work done by the ball at one side of the region of contact should exactly match the work done on the ball at the other side of the region of contact, and the ball will continue to roll indefinitely at constant speed, in which case, there is no friction as all components of the forces and torques that act to change the speed of the ball cancel. Therefore, friction is the consequence of the asymmetry between the two sides of the region of contact, specifically the difference between the work done by the ball and the work done on the ball. This difference can be due to inelastic deformations (including effects related to cold welding, etc), but I’ve also identified a mechanism based on elastic deformations where oscillations induced in the material fail to completely cancel as a result of the separation between the two sides of the region of contact. Note that elastic deformation in itself cannot be a source of friction as this does not produce any difference between the work done by the ball and the work done on the ball. But persistent oscillations set up in the materials does represent an irreversible loss of kinetic energy from the rolling motion of the ball that is a dynamic friction effect.

if you do work

you produce heat

Note that in the above, there is no mention of the smoothness of the surfaces. Provided there is enough energy to provide macroscopic motion of the ball (static friction is overcome), then lack of smoothness alone will not produce friction (dynamic friction). It then gets back to the inelasticity and elastic oscillations I discussed above. Lack of smoothness may have an impact on these, but does not directly produce dynamic friction.

>Note that elastic deformation in itself cannot be a source of friction as this does not produce any difference between the work done by the ball and the work done on the ball.

I find that hard to follow. A real world two dimensional version of this is the motion of an idler against a conveyor belt. In that case, the deformation of the belt is definitely correlated with work done and with effective friction.

morrie said:

>Note that elastic deformation in itself cannot be a source of friction as this does not produce any difference between the work done by the ball and the work done on the ball.

I find that hard to follow. A real world two dimensional version of this is the motion of an idler against a conveyor belt. In that case, the deformation of the belt is definitely correlated with work done and with effective friction.

yeah i think it was when he started using the word “work” that the whole thing unravelled

morrie said:

>Note that elastic deformation in itself cannot be a source of friction as this does not produce any difference between the work done by the ball and the work done on the ball.

I find that hard to follow. A real world two dimensional version of this is the motion of an idler against a conveyor belt. In that case, the deformation of the belt is definitely correlated with work done and with effective friction.

But is it perfectly elastic? In other words, can you recover all the work required to deform the belt by allowing to belt to be restored to its original shape? If not, then that IS a source of friction.

wookiemeister said:

if you do work

you produce heat

Not necessarily. There has to be some mechanism for converting work to heat… it isn’t automatic. Even the second law of thermodynamics doesn’t make this inevitable, although it does place limitations on converting heat into work.

KJW said:

wookiemeister said:

if you do work

you produce heat

Not necessarily. There has to be some mechanism for converting work to heat… it isn’t automatic. Even the second law of thermodynamics doesn’t make this inevitable, although it does place limitations on converting heat into work.

using real world materials you always get loss in the form of heat

if you do work on the atom infront of the ball by depressing it then you make the atom vibrate, when the atom vibrates then it raises the temperature of the atom. of course some of the energy is used to physically move that atom in the right way so it pushes the ball along and away from it (behind the ball) but energy will be used to jiggle the atom/s at the front of the ball.

as i’ve been told anykind of work ultimately means loss of energy one way or the other

you’d have the atoms behind the ball jiggling around too

KJW said:

But is it perfectly elastic? In other words, can you recover all the work required to deform the belt by allowing to belt to be restored to its original shape? If not, then that IS a source of friction.

It occurred to me that there might be some confusion as to the meaning of the word “elastic” that is being applied. I have been using it to mean that the work required to deform an object is completely recovered by the restoration of the shape of the object. I have not been using it to mean that the object simply restores its shape.

Note that in the above, there is no mention of the smoothness of the surfaces
—-

I considered this but I figured that the phrase “perfect sphere” implies perfect smoothness (and hence, a non-baryonic composition).

dv said:

Note that in the above, there is no mention of the smoothness of the surfaces
—-

I considered this but I figured that the phrase “perfect sphere” implies perfect smoothness (and hence, a non-baryonic composition).

The phrase “in the above” refers to what I said in my previous post, not what anyone else said. However, I do think that many people would assume that lack of smoothness would produce dynamic friction, and it is probably counterintuitive that it doesn’t. I think esselte assumed that it did and wanted to remove this source by the assumption of perfect smoothness. It really wasn’t necessary.

KJW said:

morrie said:

>Note that elastic deformation in itself cannot be a source of friction as this does not produce any difference between the work done by the ball and the work done on the ball.

I find that hard to follow. A real world two dimensional version of this is the motion of an idler against a conveyor belt. In that case, the deformation of the belt is definitely correlated with work done and with effective friction.

But is it perfectly elastic? In other words, can you recover all the work required to deform the belt by allowing to belt to be restored to its original shape? If not, then that IS a source of friction.

No. I didn’t realise you were talking about perfectly elastic deformation.

morrie said:

No. I didn’t realise you were talking about perfectly elastic deformation.

I didn’t use the word “perfect” because I thought this was implied. Basically, I was dealing with two mutually exclusive properties: elastic and inelastic. A material will generally be neither perfectly elastic nor perfectly inelastic, but I was focussing on the characteristics of the properties rather than the materials (real or otherwise). Clearly, if a material is perfectly elastic, then all of the work is recovered, and if the material is perfectly inelastic, then none of the work is recovered, and that for a typical material, some of the work will be recovered. If some of the work is recovered, that is a measure of its elasticity, and the work not recovered is a measure of its inelasticity.

wookiemeister said:

using real world materials you always get loss in the form of heat

if you do work on the atom infront of the ball by depressing it then you make the atom vibrate, when the atom vibrates then it raises the temperature of the atom. of course some of the energy is used to physically move that atom in the right way so it pushes the ball along and away from it (behind the ball) but energy will be used to jiggle the atom/s at the front of the ball.

as i’ve been told anykind of work ultimately means loss of energy one way or the other

No one is denying that there will be losses due to the conversion of work to heat. The point I’ve been making is to more closely identify those losses.

Motion of the atoms doesn’t become heat until that motion becomes randomised. The deformations produced by the ball rolling on a hard surface produce motion of the atoms that is quite ordered, and the energy of this motion can be largely recovered as work.

KJW said:

Motion of the atoms doesn’t become heat until that motion becomes randomised. The deformations produced by the ball rolling on a hard surface produce motion of the atoms that is quite ordered, and the energy of this motion can be largely recovered as work.

I think it’s important to note that we are talking about the collective motion of the collection of atoms. It makes no sense to speak about the temperature of individual atoms.

KJW said:

I’ve also identified a mechanism based on elastic deformations where oscillations induced in the material fail to completely cancel as a result of the separation between the two sides of the region of contact.

KJW said:

It occurred to me that there might be some confusion as to the meaning of the word “elastic” that is being applied. I have been using it to mean that the work required to deform an object is completely recovered by the restoration of the shape of the object. I have not been using it to mean that the object simply restores its shape.

It might seem as if these two quotes are contradictory in terms of the use of the word “elastic”, that the loss of energy due to oscillations induced in (perfectly) elastic materials conflicts with the complete recoverability of work from an elastic deformation. However, the energy associated with the oscillations IS completely recoverable as work, just not by the ball.

KJW said:

Note that in the above, there is no mention of the smoothness of the surfaces. Provided there is enough energy to provide macroscopic motion of the ball (static friction is overcome), then lack of smoothness alone will not produce friction (dynamic friction). It then gets back to the inelasticity and elastic oscillations I discussed above. Lack of smoothness may have an impact on these, but does not directly produce dynamic friction.

However, I do think that one should limit one’s attention to surfaces that are realistically smooth, that the deviation from perfect smoothness be insignificant compared to the size of the ball. The point I was making was that perfect smoothness is not a requirement for a dynamically frictionless surface.

KJW said:

The Rev Dodgson said:

For any real ball and plane there will be some deformation at the point of contact, so some energy transfer and loss of kinetic energy in the ball, but as the rigidity of both objects approaches infinity, and the smoothness of both surfaces approaches perfect, the deformation, and the energy loss, will tend to zero.

For a ball that is rolling on a surface, what is happening just behind the region of contact is ostensibly the reverse of what is happening just in front of the region of contact. So, ideally, the work done by the ball at one side of the region of contact should exactly match the work done on the ball at the other side of the region of contact, and the ball will continue to roll indefinitely at constant speed, in which case, there is no friction as all components of the forces and torques that act to change the speed of the ball cancel. Therefore, friction is the consequence of the asymmetry between the two sides of the region of contact, specifically the difference between the work done by the ball and the work done on the ball. This difference can be due to inelastic deformations (including effects related to cold welding, etc), but I’ve also identified a mechanism based on elastic deformations where oscillations induced in the material fail to completely cancel as a result of the separation between the two sides of the region of contact. Note that elastic deformation in itself cannot be a source of friction as this does not produce any difference between the work done by the ball and the work done on the ball. But persistent oscillations set up in the materials does represent an irreversible loss of kinetic energy from the rolling motion of the ball that is a dynamic friction effect.

Two points in response to this:

1) No real materials are perfectly linear elastic, so if there is deformation there will be transfer of kinetic energy to heat. There will also be transfer of kinetic energy in the ball to elastic/kinetic energy in the form of compression waves in the material forming the flat surface, as you describe.

2) Even if the materials were perfectly linear elastic there will still be a conversion of kinetic energy to heat because the ball and the plane only have zero relative velocity at one point (the lowest point of the sphere). If there is any deformation at all there will be a finite contact area, and hence necessarily some sliding with associated friction forces and generation of heat. This is why I said that at a small enough scale there is not a clear distinction between static and dynamic friction.

The Rev Dodgson said:

1) No real materials are perfectly linear elastic, so if there is deformation there will be transfer of kinetic energy to heat.

Agreed, but this was never in question. However, linearity is irrelevant. All that is required is that there exists a potential energy function of the shape. The particular form of this function (such a linear) is irrelevant. If there does exist a potential energy function of the shape, then the object can be deformed in any way whatsoever, and after returning to its original shape, no net work would have been done.

The Rev Dodgson said:

There will also be transfer of kinetic energy in the ball to elastic/kinetic energy in the form of compression waves in the material forming the flat surface, as you describe.

Note that what I described is incomplete cancellation of the compression waves. The locations in front of and behind the region of contact are two sources of the waves and these are largely out of phase.

The Rev Dodgson said:

2) Even if the materials were perfectly linear elastic there will still be a conversion of kinetic energy to heat because the ball and the plane only have zero relative velocity at one point (the lowest point of the sphere). If there is any deformation at all there will be a finite contact area, and hence necessarily some sliding with associated friction forces and generation of heat. This is why I said that at a small enough scale there is not a clear distinction between static and dynamic friction.

In the above, I made no assumption about the size of the contact region (I described it as a region, not point). The assumption of perfect elasticity can be extended to any relative motion parallel to the surfaces as it is reasonable to assume that perfect elasticity in the vertical direction implies perfect elasticity in the horizontal direction (and one can make this an explicit assumption). The above wasn’t specifically about rolling motion and also applies to sliding motion. All losses in perfectly elastic materials are of the form of incomplete cancellation of waves formed at the front and behind the region of contact irrespective of whether the motion is rolling or sliding.

but if you do work then you’ll always have a loss, the ball is heating up the flat surface by rolling across it

wookiemeister said:

but if you do work then you’ll always have a loss, the ball is heating up the flat surface by rolling across it

No one is denying that there will be losses due to the conversion of work to heat. The point I’ve been making is to more closely identify those losses.

KJW said:

wookiemeister said:

but if you do work then you’ll always have a loss, the ball is heating up the flat surface by rolling across it

No one is denying that there will be losses due to the conversion of work to heat. The point I’ve been making is to more closely identify those losses.

ahh ok

i thought this was some kind of intellectual gymnastics to disprove that the ball will roll forever

now i’m ready to look further.

wookiemeister said:

KJW said:

wookiemeister said:

but if you do work then you’ll always have a loss, the ball is heating up the flat surface by rolling across it

No one is denying that there will be losses due to the conversion of work to heat. The point I’ve been making is to more closely identify those losses.

ahh ok

i thought this was some kind of intellectual gymnastics to disprove that the ball will roll forever

now i’m ready to look further.

edit

to PROVE the ball will roll forever

wookiemeister said:

to PROVE the ball will roll forever

Just put a brick under one end of your perfectly flat surface.

the ball and flat surface will change shape

the ball will flatten slightly

the flat surface will bend slightly

atoms in the ball will start vibrating more

atoms on the flat surface will start vibrating too

i suppose if you could measure the speed of the ball you could work out the energy loss this way, the slowing of the ball represents the energy loss i’m not sure if you could split the energy loss caused by the ball and that caused by the flat ball

the longer the ball rolls the more loss will happen for the same amount of time

the ball will get warm and so the surface of the ball will become less uniform

An infinite flat plane is a bit of a difficulty. It would have to be set in a non-universe.

Evening all

Well that is Easter over and done with for another year.

My horse ride this morning was successful and I managed to stay on for the whole ride. Knowing that the body hurts when one falls these days makes you a lot more cautious. I did however manage a short canter :)

Spider Lily said:

Evening all

Well that is Easter over and done with for another year.

My horse ride this morning was successful and I managed to stay on for the whole ride. Knowing that the body hurts when one falls these days makes you a lot more cautious. I did however manage a short canter :)

Sorry…

cleans up and moves to right thread

Spider Lily said:

Evening all

Well that is Easter over and done with for another year.

My horse ride this morning was successful and I managed to stay on for the whole ride. Knowing that the body hurts when one falls these days makes you a lot more cautious. I did however manage a short canter :)

Did you encounter a rolling ball?

esselte said:

Bubblecar said:

You forgot to mention gravity.

The material is perfectly inelastic (ie, the sphere doesn’t bounce). Gravity is zero. The sphere is placed on the surface and rolls along that surface without extraneous forces acting upon it.

If there is no gravity, there is nothing holding them together except vanderwaals forces?

Kingy said:

esselte said:

Bubblecar said:

You forgot to mention gravity.

The material is perfectly inelastic (ie, the sphere doesn’t bounce). Gravity is zero. The sphere is placed on the surface and rolls along that surface without extraneous forces acting upon it.

If there is no gravity, there is nothing holding them together except vanderwaals forces?

i think we might have ditched that

gravity happens

wookiemeister said:

Kingy said:

esselte said:

The material is perfectly inelastic (ie, the sphere doesn’t bounce). Gravity is zero. The sphere is placed on the surface and rolls along that surface without extraneous forces acting upon it.

If there is no gravity, there is nothing holding them together except vanderwaals forces?

i think we might have ditched that

gravity happens

And it is extremely uneven except in small regions.

KJW said:

The locations in front of and behind the region of contact are two sources of the waves and these are largely out of phase.

This is an oversimplification of the situation. In fact, all points in and around the region of contact are sources of oscillation. However, the points inside the region of contact are undergoing a more-or-less forced oscillation, whereas the points away from the region of contact are more freely able to oscillate at their natural frequency. It is reasonable to assume that the dominant frequency components of the forced oscillation will not be close to the resonance frequency of the surface (although the glass harp shows that this assumption is not too hard to invalidate).

First a word or two on gravity. If there was no gravity (or other “force”) keeping the ball and plane in contact then at the first bump the ball would gain a velocity component away from the plane, and would go off into space, where it would act like any other spinning ball travelling through a vacuum.

I will leave KJW to consider what “perfectly flat” means in a situation with gravity and two moving masses.

KJW said:

The Rev Dodgson said:

1) No real materials are perfectly linear elastic, so if there is deformation there will be transfer of kinetic energy to heat.

Agreed, but this was never in question. However, linearity is irrelevant. All that is required is that there exists a potential energy function of the shape. The particular form of this function (such a linear) is irrelevant. If there does exist a potential energy function of the shape, then the object can be deformed in any way whatsoever, and after returning to its original shape, no net work would have been done.

I’m not sure what you mean by a “potential energy function of the shape”, but it is not sufficient for the materials to be perfectly elastic. Rubber (for instance) is almost perfectly elastic but has a very different stress-strain curve under compression and expansion, so it absorbs a lot of energy when it is compressed. A perfectly linear elastic material would necessarily return all its stored elastic energy to kinetic energy, when it returned to zero compression. I suppose non-linear stress-strain curves could also do this, but in real materials the only ones that come close to zero energy loss over a cycle have a near linear stress-strain relationship; hence I used “linear elastic” as shorthand for “no loss of energy over a cycle”.

KJW said:

The Rev Dodgson said:

There will also be transfer of kinetic energy in the ball to elastic/kinetic energy in the form of compression waves in the material forming the flat surface, as you describe.

Note that what I described is incomplete cancellation of the compression waves. The locations in front of and behind the region of contact are two sources of the waves and these are largely out of phase.

I don’t think complete cancellation of the waves is possible even in principle. There will be a wavefront expanding into the body of the material under the infinite plane, with nothing to prevent it from expanding for ever (in a “perfectly linear-elastic” material), so any energy in this wave cannot be returned to the rolling ball.

What might happen if the infinite plane was replaced with a large spherical surface is an interesting question.

KJW said:

The Rev Dodgson said:

2) Even if the materials were perfectly linear elastic there will still be a conversion of kinetic energy to heat because the ball and the plane only have zero relative velocity at one point (the lowest point of the sphere). If there is any deformation at all there will be a finite contact area, and hence necessarily some sliding with associated friction forces and generation of heat. This is why I said that at a small enough scale there is not a clear distinction between static and dynamic friction.

In the above, I made no assumption about the size of the contact region (I described it as a region, not point). The assumption of perfect elasticity can be extended to any relative motion parallel to the surfaces as it is reasonable to assume that perfect elasticity in the vertical direction implies perfect elasticity in the horizontal direction (and one can make this an explicit assumption). The above wasn’t specifically about rolling motion and also applies to sliding motion. All losses in perfectly elastic materials are of the form of incomplete cancellation of waves formed at the front and behind the region of contact irrespective of whether the motion is rolling or sliding.

I don’t agree that “All losses in perfectly elastic materials are of the form of incomplete cancellation of waves formed at the front and behind the region of contact irrespective of whether the motion is rolling or sliding.” (even taking “perfectly elastic” to mean no conversion of elastic energy to heat).

As the front of the contact area moves forwards the surface of the ball will have a different velocity to the plane surface. Since the contact stress will be close to zero the two surfaces will initially slide, so there will be heat generated by the friction. As the contact stresses increase the difference in velocity will be accommodated by elastic deformation, so at that stage the only non-recoverable loss of energy from the ball will be in the expanding compression wave.

That’s assuming infinitely strong materials. For any real materials as local high areas come into contact there will be enormous stresses at the contact point, and some plastic deformation in the ball and/or plane.

The Rev Dodgson said:

I’m not sure what you mean by a “potential energy function of the shape”, but it is not sufficient for the materials to be perfectly elastic. Rubber (for instance) is almost perfectly elastic but has a very different stress-strain curve under compression and expansion, so it absorbs a lot of energy when it is compressed. A perfectly linear elastic material would necessarily return all its stored elastic energy to kinetic energy, when it returned to zero compression. I suppose non-linear stress-strain curves could also do this, but in real materials the only ones that come close to zero energy loss over a cycle have a near linear stress-strain relationship; hence I used “linear elastic” as shorthand for “no loss of energy over a cycle”.

It is true that Hooke’s law is a linear relationship and that deviations from linearity are usually an indication of plastic deformation with its inherent losses. However, I’m looking at this from a mathematical rather than a physical perspective. The shape of an object can be regarded as a location in the space of all configurations of the object, and the “potential energy function of the shape” is a mathematical function over this configuration space. It is a representation of all the positional degrees of freedom of the system, the generalised coordinates in Lagrangian mechanics. If there exists a potential energy function of the generalised coordinates, then the work done in moving the system from one location in the generalised coordinate system to another depends only on the potential energy at the end-points and not on the path, and there will be zero net work in moving the system around any cyclic path. This doesn’t depend on the form of the potential energy function, though the physics will impose constraints on this. In the case of plastic deformation, the potential energy function does not exist, and the total work will be path-dependent, leading to net work for cyclic paths.

The Rev Dodgson said:

I don’t think complete cancellation of the waves is possible even in principle.

I find it quite intriguing the number of apparently non-thermodynamic processes that conspire to maintain the second law of thermodynamics. The most intriguing to me is still the impossibility of focussing a light source to a point that is brighter than the light source itself, a limitation that is purely geometric, but which would violate the second law of thermodynamics if it were possible.

The Rev Dodgson said:

I don’t agree that “All losses in perfectly elastic materials are of the form of incomplete cancellation of waves formed at the front and behind the region of contact irrespective of whether the motion is rolling or sliding.” (even taking “perfectly elastic” to mean no conversion of elastic energy to heat).

As the front of the contact area moves forwards the surface of the ball will have a different velocity to the plane surface. Since the contact stress will be close to zero the two surfaces will initially slide, so there will be heat generated by the friction. As the contact stresses increase the difference in velocity will be accommodated by elastic deformation, so at that stage the only non-recoverable loss of energy from the ball will be in the expanding compression wave.

That’s assuming infinitely strong materials. For any real materials as local high areas come into contact there will be enormous stresses at the contact point, and some plastic deformation in the ball and/or plane.

It seems that we mean different things by “perfectly elastic”. You appear to be limiting this to the purely mechanical macroscopic level, whereas I am regarding this all the way down to the molecular level and even including chemical interaction between the surfaces. Thus to me, “perfectly elestic” implies the absence of friction to sliding motion as the mechanism of sliding friction is an inelastic process at the microscopic level.

It is worth noting that the low coefficient of friction of teflon compared to… well anything else, but particularly diamond, hightlights the principal role of intermolecular forces in friction compared to deformations of the surface.

KJW said:

The Rev Dodgson said:

I don’t agree that “All losses in perfectly elastic materials are of the form of incomplete cancellation of waves formed at the front and behind the region of contact irrespective of whether the motion is rolling or sliding.” (even taking “perfectly elastic” to mean no conversion of elastic energy to heat).

As the front of the contact area moves forwards the surface of the ball will have a different velocity to the plane surface. Since the contact stress will be close to zero the two surfaces will initially slide, so there will be heat generated by the friction. As the contact stresses increase the difference in velocity will be accommodated by elastic deformation, so at that stage the only non-recoverable loss of energy from the ball will be in the expanding compression wave.

That’s assuming infinitely strong materials. For any real materials as local high areas come into contact there will be enormous stresses at the contact point, and some plastic deformation in the ball and/or plane.

OK, well if “perfectly elastic” means identical behaviour under loading and unloading and zero friction, which also implies infinite strength, then I agree, the only loss left is the expanding wave fronts through the material below the plane surface, and perhaps through the ball itself (the waves would be constrained in volume, but they could keep increasing in amplitude, couldn’t they?).

It seems that we mean different things by “perfectly elastic”. You appear to be limiting this to the purely mechanical macroscopic level, whereas I am regarding this all the way down to the molecular level and even including chemical interaction between the surfaces. Thus to me, “perfectly elestic” implies the absence of friction to sliding motion as the mechanism of sliding friction is an inelastic process at the microscopic level.

It is worth noting that the low coefficient of friction of teflon compared to… well anything else, but particularly diamond, hightlights the principal role of intermolecular forces in friction compared to deformations of the surface.

KJW said:

The Rev Dodgson said:

I don’t think complete cancellation of the waves is possible even in principle.

I find it quite intriguing the number of apparently non-thermodynamic processes that conspire to maintain the second law of thermodynamics. The most intriguing to me is still the impossibility of focussing a light source to a point that is brighter than the light source itself, a limitation that is purely geometric, but which would violate the second law of thermodynamics if it were possible.

Agreed.

Also interesting that such a simple question offers so many different potentially valid hypotheses when you look closer.

wookiemeister said:

the ball and flat surface will change shape

the ball will flatten slightly

the flat surface will bend slightly

You seem to be suggesting that all of the work in deforming the ball and surface will be lost as heat. In fact, for the types of materials of interest to us in this thread, most of the work of deformation will be temporarily stored as potential energy and transferred back to ball.

The Rev Dodgson said:

OK, well if “perfectly elastic” means identical behaviour under loading and unloading and zero friction, which also implies infinite strength, then I agree, the only loss left is the expanding wave fronts through the material below the plane surface, and perhaps through the ball itself (the waves would be constrained in volume, but they could keep increasing in amplitude, couldn’t they?).

In the ball, assuming perfect elasticity and isolated from anything else, standing waves would persist.

KJW said:

In the ball, assuming perfect elasticity and isolated from anything else, standing waves would persist.

See the Wikipedia article about spherical harmonics.

Thanks to everyone who contributed here… It was an interesting read.

esselte said:

Thanks to everyone who contributed here… It was an interesting read.

next thread

a perfect square, infinite flat plane and friction

or should that be cube