Friction forces and motion resulting from them

[Robittybob1]

 

Yes, eventually the friction cannot supply the force that's required. Then it slides.

 

 

Yes, eventually the friction cannot supply the force that's required. Then it slides.

 

 

Yes, eventually the friction cannot supply the force that's required. Then it slides.

And do you accept that the rate of sliding increases as the object slides gaining energy from the friction acting on it in the tangential direction?

It is tricky, for most would think friction slows things down but not if the surface it is on is moving faster than it is.

[swansont]

And do you accept that the rate of sliding increases as the object slides gaining energy from the friction acting on it in the tangential direction?

It is tricky, for most would think friction slows things down but not if the surface it is on is moving faster than it is.

That's what you should expect, since the radial distance will increase and the speed of the surface will thus increase.

[Robittybob1]

That's what you should expect, since the radial distance will increase and the speed of the surface will thus increase.

What amazes me is that there seems to be two types of friction acting on the object at the same time. In the radial direction there is still some centripetal friction slowing it down (doing negative work) and the tangential friction which is speeding up the object (doing positive work on it) Does it slow down more than it speeds up? Or the other way, round does it speed up more than it slows down?

How would we do the maths of that?

I would say the coefficient of friction would be the same in either direction for a starter.

Edited May 29, 2015 by Robittybob1

[swansont]

What amazes me is that there seems to be two types of friction acting on the object at the same time. In the radial direction there is still some centripetal friction slowing it down (doing negative work) and the tangential friction which is speeding up the object (doing positive work on it) Does it slow down more than it speeds up? Or the other way, round does it speed up more than it slows down?

How would we do the maths of that?

I would say the coefficient of friction would be the same in either direction for a starter.

The coefficient should be the same; it's the same two surfaces. The key here is relative motion. The surface does positive work tangentially because it's moving.

 

 

As to which has the greater change in speed, you would have to analyze the force on the object and solve for speed as a function of time, or as a function of position (i.e you could do this in terms of work done). That might be easiest in the rotating frame, meaning there would be a pseudoforce in the problem.

[Robittybob1]

The coefficient should be the same; it's the same two surfaces. The key here is relative motion. The surface does positive work tangentially because it's moving.

 

 

As to which has the greater change in speed, you would have to analyze the force on the object and solve for speed as a function of time, or as a function of position (i.e you could do this in terms of work done). That might be easiest in the rotating frame, meaning there would be a pseudoforce in the problem.

I can't see any way to take measurements of the situation, so could it be done just from logic? Like we say the object is always on the same surface with the same coefficient of friction and it also always at the same radius at the same time.

The speeds are split into the tangential and radial direction and we can be sure the tangential speed never exceeds the tangential speed of the surface (one limit) and the radial speed starts from zero at the time the centripetal force required is exceeded. Then we'd say there is no more angular acceleration of the turntable once it begins to slip.

The dynamic friction being less than the static friction allows the radial motion to continue but the centripetal force will always be in the radial direction no matter how much the object slips behind the starting radial line.

Each increment in the radial direction puts the object onto a surface that is going proportionally faster tangentially.

We could calculate what centripetal force it would take to hold it at any new position, 1. when it wasn't slipping and 2. at its new velocity gained from the work done on it by the turntable (OK I see that now, that is if the object wasn't on the turntable but being held by a string at that instant at that new velocity).

The object on the surface gains angular momentum due to the tangential friction forces being applied to it.

In that table the coefficient of friction of glass on teflon was 0.1 and the static and dynamical friction were the same values, so we could use a glass object on a smooth plastic surface with a coefficient of friction of 0.1.

 

I could set up an Excel spreadsheet that gives me the values if I moved the object in 1 mm increments, that might give me an initial idea of the relationship between the two speeds.

 

Does anyone know how do the problem with calculus?

[imatfaal]

You can model it - but you might find it easier to film and measure; and the experiment is hard to argue with

[Robittybob1]

The cloth requires less force to move than the table or object on top of it. Once the force of the pulling on the cloth is sufficient to move the cloth (and overcome friction) the cloth will move. However there is still insufficient force to move the table or object. So neither the table or object moves only the cloth.

 

I disagree with you when you say "neither the table or object moves only the cloth". The objects on the table cloth do move, you can see them moving, but the movement is not enough to make them fall off the table.

As Swansont said "The surface does positive work tangentially because it's moving."

So The surface (tablecloth) does positive work (on the plates etc) because its moving.

And as I asked before but this time I will say it differently too:

"And do you accept that the rate of sliding increases as the object slides gaining energy from the friction acting on it in the tangential direction?"

changes to:

"And do you accept that the rate of sliding in the radial direction increases as the object slides gaining energy from the friction acting on it (positive work) in the tangential direction?"

Edited May 30, 2015 by Robittybob1

[swansont]

The objects on the table cloth do move but not enough to fall off the table.

As Swansont said "The surface does positive work tangentially because it's moving."

So The surface (tablecloth) does positive work (on the plates etc) because its moving.

 

But that work is small, and thus doesn't transfer much energy to the objects.

[Robittybob1]

 

But that work is small, and thus doesn't transfer much energy to the objects.

That is true but I was just making the point you can't say "the objects don't move". Even if they only move a little bit, they still move and if there wasn't enough friction between them and the table they would continue and fall onto the floor (Newton's First Law).

 

I edited my previous post late (I forgot to press the "save Changes" button before I went out to do some chores) so I'll repeat it here:

 

And as I asked before but this time I will say it differently too:

"And do you accept that the rate of sliding increases as the object slides gaining energy from the friction acting on it in the tangential direction?"

changes to:

"And do you accept that the rate of sliding in the radial direction increases as the object slides gaining energy from the friction acting on it (positive work) in the tangential direction?"

Edited May 30, 2015 by Robittybob1

[Mordred]

The reason I mentioned coefficient of friction is to help you realize the following scenario.

 

Which will be easier to make that trick work ?

 

A) a tablecloth made of smooth plastic

 

B) a table cloth made of a rough course thread?

 

You have two types of friction with three coefficients of friction.

 

The table material.

The table cloth material

The object on top of the table.

 

Each of the above also has its own mass.

 

Work with the formulas for static and kinetic friction of each object

Work with the amount of force needed to move each object in terms of first static friction, then kinetic friction.

 

Key note if you move the table cloth slow the objects will land on the floor. But if you move the table cloth with enough instantaneous velocity the objects remain on the table.

 

Figure out how the above questions relate to the two rates.

(I recall posting a table of various coefficient of friction per material type listings)

[Robittybob1]

The reason I mentioned coefficient of friction is to help you realize the following scenario.

 

Which will be easier to make that trick work ?

 

A) a tablecloth made of smooth plastic

 

B) a table cloth made of a rough course thread?

 

You have two types of friction with three coefficients of friction.

 

The table material.

The table cloth material

The object on top of the table.

 

Each of the above also has its own mass.

 

Work with the formulas for static and kinetic friction of each object

Work with the amount of force needed to move each object in terms of first static friction, then kinetic friction.

 

Key note if you move the table cloth slow the objects will land on the floor. But if you move the table cloth with enough instantaneous velocity the objects remain on the table.

 

Figure out how the above questions relate to the two rates.

(I recall posting a table of various coefficient of friction per material type listings)

Obviously you don't want coarse fabric (as there would be too much friction) and probably not a plastic table cloth either (for it might crinkle forming a barrier).

Is it true that friction is not proportional to velocity, so if it moves slowly the force of friction will be acting for a longer time?

Good point I think we will have to take time into account in the rotating turntable concept as well?

[Mordred]

Which type of friction? Which is the greater?

 

Lets keep this to linear relationships for the time being. Until you have a clear understanding on the linear relationships of force and friction. We don't need added complexity.

(Answering this should answer why a swift, uniform jerk on the tablecloth is needed and why you get a momentary movement of the plates at the initial point at the beginning of the jerk.)

Side note if you plan on practicing this trick use oil cloth. Have maximum two feet over hang. Use heavier smooth objects. Do not pull towards you but rapidly pull down on the table cloth.(why will this make a difference?) Helps to use a long stick initially wrap the cloth around the stick for a uniform pull.

Edited May 30, 2015 by Mordred

[swansont]

 

And as I asked before but this time I will say it differently too:

"And do you accept that the rate of sliding increases as the object slides gaining energy from the friction acting on it in the tangential direction?"

changes to:

"And do you accept that the rate of sliding in the radial direction increases as the object slides gaining energy from the friction acting on it (positive work) in the tangential direction?"

 

It's not clear to me that the sliding in the tangential direction will increase. The radial slipping should increase. The limiting case is no friction at all, and that gives a constant speed, so any friction at all should result in tangential acceleration, which increases the rate at which the object leaves.

[Robittybob1]

 

It's not clear to me that the sliding in the tangential direction will increase. The radial slipping should increase. The limiting case is no friction at all, and that gives a constant speed, so any friction at all should result in tangential acceleration, which increases the rate at which the object leaves.

I was asking about increased sliding in the radial direction. After tangential acceleration it speeds up so what direction do the combined frictional forces make the object leave at? It leaves at a higher rate but not at tangential speed for it is slipping. Because it isn't going at tangential speed it can't leave via the tangent (of the whole apparatus) but in the no friction hypothetical situation it could be likened to leaving at a tangent to the smaller circle, but then when you think about it how did you get the object travelling in a circle in the first place if there was no friction?

You could start it off on the very edge of the turntable, then when it moved there would be no friction and no surface to accelerate on either.

We can't have absolutely no friction or start it off on the very edge. They are not examples that show what friction does in this case.

Which type of friction? Which is the greater?

 

Lets keep this to linear relationships for the time being. Until you have a clear understanding on the linear relationships of force and friction. We don't need added complexity.

(Answering this should answer why a swift, uniform jerk on the tablecloth is needed and why you get a momentary movement of the plates at the initial point at the beginning of the jerk.)

Side note if you plan on practicing this trick use oil cloth. Have maximum two feet over hang. Use heavier smooth objects. Do not pull towards you but rapidly pull down on the table cloth.(why will this make a difference?) Helps to use a long stick initially wrap the cloth around the stick for a uniform pull.

I went out to dinner and experimented with pulling the tablecloth. I did it in a small way with my glass of beer on a doily. There is no easy way to estimate the force used to pull the cloth or the rate it moves, so it too is a complex problem to put the maths around it.

 

The circular motion is so much easier for we will keep the rotational rate constant once the object moves, so it doesn't matter what this speed is.

The glass keeps on accelerating till the doily was pulled right from under it, then it slides a little further on the tabletop slowing down.

 

... you get a momentary movement of the plates at the initial point at the beginning of the jerk

 

That is wrong.

Edited May 30, 2015 by Robittybob1

[swansont]

I was asking about increased sliding in the radial direction.

 

Reread what I wrote. Particularly the second sentence.

It leaves at a higher rate but not at tangential speed for it is slipping.

 

The friction is not zero, so there is a force that will speed it up. Only in the case of zero friction will the object maintain the same speed. Newton's first law.

Because it isn't going at tangential speed it can't leave via the tangent (of the whole apparatus)

 

It doesn't have a tangential speed? Sorry, no. The circular motion has not completely ceased; it is moving with at least the same tangential speed as when the slipping started. The motion is not radial. It's spiraling, so it has both tangential and radial motion.

 

I suspect that you are switching coordinate systems, and that's a huge problem. If we are to apply Newton's laws and talk of forces, you have to be in a coordinate system that is not accelerating. IOW, you can't analyze this in a rotating frame, i.e. the frame of the spinning wheel, and have anything work.

I went out to dinner and experimented with pulling the tablecloth. I did it in a small way with my glass of beer on a doily. There is no easy way to estimate the force used to pull the cloth or the rate it moves, so it too is a complex problem to put the maths around it.

 

The circular motion is so much easier for we will keep the rotational rate constant once the object moves, so it doesn't matter what this speed is.

The glass keeps on accelerating till the doily was pulled right from under it, then it slides a little further on the tabletop slowing down.

 

That is wrong.

 

Given your allergy to maths and level of understanding of motion in general, I submit that you are not in a position to judge complexity of a problem or wrongness of an analysis.

[Mordred]

Have you thought about the portion where I specified a downward as opposed to lateral pull on the table cloth.

 

Why would the previous method make the trick easier to perform? The answer has something to do with friction. Specifically static friction.

[Robittybob1]

 

Reread what I wrote. Particularly the second sentence.

 

The friction is not zero, so there is a force that will speed it up. Only in the case of zero friction will the object maintain the same speed. Newton's first law.

 

It doesn't have a tangential speed? Sorry, no. The circular motion has not completely ceased; it is moving with at least the same tangential speed as when the slipping started. The motion is not radial. It's spiraling, so it has both tangential and radial motion.

 

I suspect that you are switching coordinate systems, and that's a huge problem. If we are to apply Newton's laws and talk of forces, you have to be in a coordinate system that is not accelerating. IOW, you can't analyze this in a rotating frame, i.e. the frame of the spinning wheel, and have anything work.

 

Given your allergy to maths and level of understanding of motion in general, I submit that you are not in a position to judge complexity of a problem or wrongness of an analysis.

Your second sentence "The radial slipping should increase", now is that the same as saying "the rate of radial slipping should increase"? Does the rate change?

If you agree it is spiraling toward the outer edge, I agree with you for I have no problem saying it is slipping in and travelling in a spiral manner. The object is sitting on a surface which is rotating in a normal circular motion fashion and this is the surface which is providing the friction forces to the sliding object. It is the direction wrt the turntable that I describe as tangential or radial so if it moves in a slight diagonal (small increment of spiral) that diagonal surely could be thought of as partly radial and mostly tangential.

If it moves in a strong spiral where it goes from the center region to the outside in less than a half rotation are you saying we can't look at its instantaneous motion and break that down wrt the surface?

 

Even you seem to say this "The motion is not radial. It's spiraling, so it has both tangential and radial motion", so if there is both tangential and radial motion surely we can measure those component speeds.

 

I could tie a tablecloth to a motorbike and get it to travel at a constant (but variable) speed and whip it out from under a mass.

We could measure the distance the friction moved the object forward easy enough.

I could graph the amount of forward movement against speed.

I'm predicting the slower speeds should drag the object the longer distances.

Edited May 30, 2015 by Robittybob1

[swansont]

Your second sentence "The radial slipping should increase", now is that the same as saying "the rate of radial slipping should increase"? Does the rate change?

The radial component of the speed changes.

 

If you agree it is spiraling toward the outer edge, I agree with you for I have no problem saying it is slipping in and travelling in a spiral manner. The object is sitting on a surface which is rotating in a normal circular motion fashion and this is the surface which is providing the friction forces to the sliding object. It is the direction wrt the turntable that I describe as tangential or radial so if it moves in a slight diagonal (small increment of spiral) that diagonal surely could be thought of as partly radial and mostly tangential.

If it moves in a strong spiral where it goes from the center region to the outside in less than a half rotation are you saying we can't look at its instantaneous motion and break that down wrt the surface?

No. I'm doing exactly that. But the coordinate system is not rotating.

 

Even you seem to say this "The motion is not radial. It's spiraling, so it has both tangential and radial motion", so if there is both tangential and radial motion surely we can measure those component speeds.

Yes, we can.

[Robittybob1]

The radial component of the speed changes.

 

 

No. I'm doing exactly that. But the coordinate system is not rotating.

 

 

Yes, we can.

So far we seem to be understanding one another. I am still having trouble with the sentence "the coordinate system is not rotating".

For in my view the coordinates are rotating the same rate as the system (the turntable) or I might even have to rotate the coordinates the same speed as the object in an attempt to get the maths right.

For aren't we allowing the coordinate system to go backward wrt the turntable so we can look at the radial component?

When you say "the coordinate system is not rotating" in reality if we pointed the "y" coordinate toward magnetic North is "y" always pointing to the North even when we spin the turntable?

 

The opposite of this would be to make the coordinates point to marks on the perimeter of the turntable.

If the object is placed on the turntable while it is stationary the straight line drawn from the centre through the object to the perimeter becomes our "y" axis (this is the starting radial line) but not all radial lines are going to be parallel so why not call "y" the line that always exists from the centre through the COM of the object to the perimeter?

 

OK we are close enough to start working on some figures and formulas.

 

Did you want to hazard a prediction regarding your statement "the radial component of the speed changes"? Will that be an increase in speed or a decrease?

Personally I can't imagine it decreasing unless we were to slow the turntable., but that is against the experimental design for we hope to keep the rotation of the turntable constant once sliding movement occurs (well we will in the analysis for sure. In real life all one can do is stop applying any further force to the perimeter, so in reality there is in fact a little slowing for the whole turntable has a little bit of friction from wind resistance and friction within the central bearing.

One more assumption will be that the speed of rotation of the turntable is not significantly slowed by the work done by friction on the object.

Edited May 30, 2015 by Robittybob1

[swansont]

So far we seem to be understanding one another. I am still having trouble with the sentence "the coordinate system is not rotating".

For in my view the coordinates are rotating the same rate as the system (the turntable) or I might even have to rotate the coordinates the same speed as the object in an attempt to get the maths right.

You can't use Newton's laws if you do that. Do you understand that?

 

Did you want to hazard a prediction regarding your statement "the radial component of the speed changes"? Will that be an increase in speed or a decrease?

We start at zero. I thought "increase" was understood.

[Robittybob1]

You can't use Newton's laws if you do that. Do you understand that?

 

 

We start at zero. I thought "increase" was understood.

Not completely. What will go wrong?

Increasing from zero is a very good answer, I can't argue against that.

Which coordinate system do I have to use?

1. make the coordinates point to marks on the perimeter of the turntable. (noninertial rotating frame).

2.make the coordinates point to due North. (the ground frame or lab frame.)

3 make the coordinates point to the sliding mass.

All of these would have one axis in common.

Edited May 31, 2015 by Robittybob1

[Robittybob1]

Introduction to coefficient of friction:

mu = force of friction over the normal force

[swansont]

In a rotating coordinate system, F=0 does not mean an object at rest stays at rest in that frame. F = mr₀w₀² means it stays at rest. That's provided by friction.

 

If you exceed that, either by increasing w or r, then there is a radial component of an acceleration. So you increase w until it starts to move and the friction decreases (static becomes dynamic). It now accelerates. r increases, so the acceleration increases.

[Robittybob1]

In a rotating coordinate system, F=0 does not mean an object at rest stays at rest in that frame. F = mr₀w₀² means it stays at rest. That's provided by friction.

 

If you exceed that, either by increasing w or r, then there is a radial component of an acceleration. So you increase w until it starts to move and the friction decreases (static becomes dynamic). It now accelerates. r increases, so the acceleration increases.

Plus we've got two frictional forces one slowing it down in the radial direction, and the other speeding the object up in the tangential direction.

I took the table's word it, that on this type of surface the static friction and dynamic friction are the same. It can only accelerate at the larger radius if the force of friction acts on it with a component in the tangential direction.

When F = mr0w02 exceeds the force of friction then it moves, then what? I've got that formulated for a 1 kg mass with a mu of 0.2 on a radius of 0.5 m. Now increase the omega till it slides (I was working with tangential velocity actually) and that happens at 0.991 m/sec.

If there were no more friction forces after that it would take a curved path described by the Coriolis Effect, but there is the thought of how much did the tangential velocity exceed the velocity necessary to get it to slip. That thought was countered by the thought it is not possible to exceed this by varying amounts for the object will just slip when the forces tip the balance.

Does that make sense? Which is the right thought? In the Centrifugal force experiment it felt like you could affect the rate it slips off the turntable, but this was probably due to adding energy by increasing the angular velocity after it begun slipping.

Edited May 31, 2015 by Robittybob1

[swansont]

Plus we've got two frictional forces one slowing it down in the radial direction,

Not in the coordinate system you have chosen.

 

 

and the other speeding the object up in the tangential direction.

Again, not in the coordinate system you have chosen.

 

This is the problem I mentioned earlier. You can't jump between coordinate systems.

 

I took the table's word it, that on this type of surface the static friction and dynamic friction are the same.

I don't know what this means. What table?