Movement of a piston

[JustinW]

I had just had a discussion with a friend of mine about whether a piston's motion stops before it changes direction. He argued that since it pivots on a circular motion from the bottom that it didn't. I say that if he was talking about the piston itself, then it did. Since a piston only goes up and down in the sleeve, then it would have to stop in order to go the opposite direction. I just wanted to get some of your thoughts. Does an object have to stop in order to move in the opposite direction? I believe the answer is yes.

[CaptainPanic]

You are right, your friend is wrong.

 

In an ideal case, the piston moves up and down, and the velocity will reach zero both at the top and bottom on every stroke.

 

In reality, every thing is vibrating, and there will be a very tiny sideways motion to - so nothing really ever stops.

[iNow]

I agree with you. Imagine tossing a ball into the air. It will travel upward, slow down, reach it's highest point, stop, and then begin accelerating in the opposite direction. It travels along one vector and then has to stop in order to begin traveling along the opposite vector. It's going up, and (however momentarily) must stop before it can begin going down.

 

In my view, a piston is merely a more precise and mechanically controlled ball being tossed into the air so can be accurately described the same.

 

That's my conjecture, anyway.

 

EDIT: Cross-posted with CaptainPanic

[Xittenn]

Does an object have to stop in order to move in the opposite direction? I believe the answer is yes.

 

Given your statements previous to this comment I think you know the answer is in fact no. Circular motion can provide an indirect path to inverting the direction traveled by a mass. To linearly invert the direction of a mass along one axis in the objects local space, requires the object to--ideally--come to a complete stop before traveling in the other direction. I'm not sure the most appropriate way to phrase that, but I think when the language is used loosely, this is where people start to come up with their own personal meanings.

 

Maybe another way to say this might be:

 

Given a mass traveling with 'velocity', any component of the 'vector' where the direction of travel of the mass is inverted, will see at minimum, a momentary value of zero.

 

This doesn't however assure that the mass will ever attain zero 'speed'.

 

Another example of choice in wording is seen in iNows reply below.

 

It will travel upward, slow down, reach it's highest point, stop, and then begin accelerating in the opposite direction.

 

A ball thrown into the air begins accelerating in the opposite direction the instant the ball leaves the hand of the individual who has thrown it. Which is quite unlike a piston that accelerates down due to a chemical explosion and up again due to a circular acceleration.

 

Forgive my post if it sounds obnoxious, or contains any misinformation! : D

[JustinW]

It's going up, and (however momentarily) must stop before it can begin going down.

That was exactly the argument I posed. I believe he was trying to refer to the piston as it is connected to the crank. I gave the argument that, yes, that part of the connection doesn't stop because it never changes trajectory. Just rotates in a circular motion to lift the piston up and down. So I guess it is just a matter of being specific. It was sort of a pointless conversation out of boredome. But I saw it as I was write and he was wrong.

 

Given your statements previous to this comment I think you know the answer is in fact no. Circular motion can provide an indirect path to inverting the direction traveled by a mass.

But the trajectory of the crank doesn't change in the same way as the trajectory of the piston.

[Xittenn]

In conventional combustion engines, yes the piston achieves zero velocity along its axis of travel. Given that the velocity is in fact zero, the speed is also zero. This is unlike the crank shaft or piston rod which has constant speed but varying velocity. In the case of velocity varying in direction, components of the vector can and do become zero. : D

 

The piston rod is an ugly thing and I retract any mention of it. . . .

Edited January 5, 2012 by Xittenn

[TonyMcC]

The piston is stationary only for an instant. The question is "how long is an instant?" If the instant is infinitely small can the piston be said to have stopped? By a similar argument can you say that the top of a sine wave has a part that is flat and horizontal?

Edited January 6, 2012 by TonyMcC

[JustinW]

Even if the instant is infinitely small it is still an instant.

[TonyMcC]

Even if the instant is infinitely small it is still an instant.

 

And you are happy to say there is an infinitely small flat area on the top of a sine wave?

[Phi for All]

The piston is stationary only for an instant. The question is "how long is an instant?" If the instant is infinitely small can the piston be said to have stopped?

Actually, the question is, "What is 'stopped'?" Does it mean the piston slows to a velocity of 0?

 

By a similar argument can you say that the top of a sine wave has a part that is flat and horizontal?

I don't see that as a similar argument at all.

[TonyMcC]

Actually, the question is, "What is 'stopped'?" Does it mean the piston is moving at a speed of 0?

 

 

I don't see that as a similar argument at all.

 

The relevance to a sine wave is this -if a piston moves vertically in a cylinder then the height of the piston plotted against time is an approximate sine wave. If the connecting rod is very long compared with crank displacement from the centre line then the approximation is very accurate.

Edited January 6, 2012 by TonyMcC

[Xittenn]

The piston is stationary only for an instant. The question is "how long is an instant?" If the instant is infinitely small can the piston be said to have stopped? By a similar argument can you say that the top of a sine wave has a part that is flat and horizontal?

 

 

And you are happy to say there is an infinitely small flat area on the top of a sine wave?

 

My analogy to your statements. First find a train track. Mark an 'instance' on the track. Now drive over it really fast with a really fast train. Does the wheel ever make contact or drive over the mark? According to your statements, this might be questionable because the time spent in contact might be infinitesimally small depending on the size of the mark chosen, and depending on just how one would define an 'instance' and how you might mark that. Some might try to use this sort of statement to say that the train never really made the trip at all, and that the train in fact merely appeared magically at its destination. I don't believe in magic, so I say the damn thing happened.

 

The point here is, either we have a smooth manifold and we pass through all points, however unequally and however briefly, or we have to further explain a set of non-linear behaviours. In operation you will see the piston slow and then reverse its direction. The time spent at this fraction of the operating speed is enough to satisfy your flat sine wave argument for me because I rarely work in absolutes. That said you are obviously having trouble with this sort of mentality. Maybe you would like to attribute this behaviour of passing through a point, without passing through a point, to quantum tunneling? But tunneling is not something that objects of macroscale mass simply do on their own or even at all. So as it stands, if point B lies in the path between points P and Q then we say that an object traveling from point P to point Q passes through point B.

 

We could further analyze the problem to deal with deformation as different points of the piston will be traveling at different speeds at different times. Sure we could analyze a piston as not being a 'rigid body' at all. But it does nearly operate as a pure rigid body, and being that I don't do work in absolutes I have no problem with this. I guess if you wanted to treat the piston as a fluid and apply fluid dynamics, all of our statements may need to be modified. If this was the method chosen to analyze the piston, then one might have to make a statement about the speed of the waves and so on and I think this might get pretty complicated. Can a fluid attain a uniform speed or a net speed as a single body? Sure. . . . . Could we make these statements about a piston? Good question!

 

I really didn't understand your third statement. Also, keep in mind that I post answers for fun. I am not prepared for a battle about the de-factos and may very well crumble when challenged. I'm discussing, not debating.

Edited January 7, 2012 by Xittenn

[Phi for All]

My analogy to your statements. First find a train track. Mark an 'instance' on the track. Now drive over it really fast with a really fast train. Does the wheel ever make contact or drive over the mark? According to your statements, this might be questionable because the time spent in contact might be infinitesimally small depending on the size of the mark chosen, and depending on just how one would define an 'instance' and how you might mark that. Some might try to use this sort of statement to say that the train never really made the trip at all, and that the train in fact merely appeared magically at its destination. I don't believe in magic, so I say the damn thing happened.

This is the way I thought about it too. The sine wave analogy only made sense to me if you look at the piston's movement up and down with respect to its forward motion as part of the engine of a moving car. Maybe I'm still not seeing the action as Tony sees it.

 

To me, the piston, though part of a larger mechanism, is, in this case, just a single solid cylinder moving up the inside of a tube, reaching the top, stopping, then moving down, reaching the bottom, stopping and then repeating that process. Make the tube clear, isolate the piston on high-speed video and that's just what you'd see. No matter how small a time it stops, it can't change direction WITHOUT stopping.

[TonyMcC]

This is the way I thought about it too. The sine wave analogy only made sense to me if you look at the piston's movement up and down with respect to its forward motion as part of the engine of a moving car. Maybe I'm still not seeing the action as Tony sees it.

 

To me, the piston, though part of a larger mechanism, is, in this case, just a single solid cylinder moving up the inside of a tube, reaching the top, stopping, then moving down, reaching the bottom, stopping and then repeating that process. Make the tube clear, isolate the piston on high-speed video and that's just what you'd see. No matter how small a time it stops, it can't change direction WITHOUT stopping.

 

Rather like Xittenn I often post for fun and sometimes a bit tongue in cheek although what I post I have considered first. Note that in this case my post was in the form of questions (not statements). I don't see the sine wave condition as an analogy as even if the the piston was in a stationary vehicle there is no reason why you can't plot its height with respect to time. I have no problem with the concept that an instant occupies zero time and therefore saying the piston remains stationary for zero time at each end of its travel. My experience has mostly been with electrical matters where often you have to calculate an instantaneous value of alternating voltage or current at a particular time. You calculate a definite value at a definite time. - not a range of values, however small, to accommodate a span of time, however small. So my question remains - if the piston "stops" for zero time can you say it stopped? Is there a flat spot, however small, on the top of a sine wave where there is no change in amplitude with respect to time? As I see it there is, but it is infinitely small.

[Xittenn]

If it didn't attain a speed of zero at all, then there would be a change in velocity [math] \Delta \nu [/math] in zero time [math] \Delta t [/math] such that the resultant energy required to perform the work necessary to achieve such an event, would be infinite.

[TonyMcC]

If it didn't attain a speed of zero at all, then there would be a change in velocity [math] \Delta \nu [/math] in zero time [math] \Delta t [/math] such that the resultant energy required to perform the work necessary to achieve such an event, would be infinite.

 

Not really, as it decelerates for the quarter cycle up to the top of its movement and then accelerates for the next quarter cycle as it leaves the top. There isn't a sudden snatched change of direction.

Edited January 7, 2012 by TonyMcC

[Xittenn]

Not really, as it decelerates for the quarter cycle up to the top of its movement and then accelerates for the next quarter cycle as it leaves the top. There isn't a sudden snatched change of direction.

 

I'm sorry I do not understand what you just said.

[Phi for All]

I have no problem with the concept that an instant occupies zero time and therefore saying the piston remains stationary for zero time at each end of its travel.

I have a problem with that. The stop time at top dead center and bottom dead center will vary depending on the rpm rate of the engine, but it will never be 0. Mainly because of your other question:

 

So my question remains - if the piston "stops" for zero time can you say it stopped?

[swansont]

There is a time at which v=0. If v=0 is acceptable as the definition of being stopped, then it is stopped.

[TonyMcC]

I'm sorry I do not understand what you just said.

 

The piston doesn't move up and down the cylinder at uniform speed. Under the influence of the rotating crank it will be at its fastest in the mid point of its travel. On leaving the mid point, whether going up or down, it decelerates as it travels toward it highest (or lowest point) so that the change from going up to going down is a gradual process. However it is a continually changing process so if we are going to say the piston stopped it will be for an infinitely small time.

[Xittenn]

The piston doesn't move up and down the cylinder at uniform speed. Under the influence of the rotating crank it will be at its fastest in the mid point of its travel. On leaving the mid point, whether going up or down, it decelerates as it travels toward it highest (or lowest point) so that the change from going up to going down is a gradual process. However it is a continually changing process so if we are going to say the piston stopped it will be for an infinitely small time.

 

In a system that is in a continuous state of change, no event is incurred over a period of time. They are incurred as instances, and occur at specific times. We might say that at some moment the piston achieves 1 m/s. We then say the piston achieved 1 m/s at time t. We don't say that the piston was traveling at 1 m/s for a time because it is in a state of change, and the velocity achieved is instantaneous and only exists for a moment with no relevant duration. You can magnify the event as much as you wish and analyze the precision to as many decimal places as makes you happy.

 

I'm sorry I missed Swansont there . . .

Edited January 7, 2012 by Xittenn

[TonyMcC]

There is a time at which v=0. If v=0 is acceptable as the definition of being stopped, then it is stopped.

 

As long as you accept that the piston never stops moving, and I accept that for an infinitely small period of time v=0 then there is no argument. There is a paradox in the statement that a body which is in continual motion can be said to have stopped at some point. I guess its a matter of semantics.

Edited January 7, 2012 by TonyMcC

[Xittenn]

As long as you accept that the piston never stops moving, and I accept that for an infinitely small period of time v=0 then there is no argument. There is a paradox in the statement that a body which is in continual motion can be said to have stopped at some point. I guess its a matter of semantics.

 

A body in continuous motion doesn't stop, but the body that you are refering to is not in continuous motion because it does. The only state that this body is continuously in is accelerating.

[TonyMcC]

A body in continuous motion doesn't stop, but the body that you are refering to is not in continuous motion because it does. The only state that this body is continuously in is accelerating.

 

Now you have got me puzzled. If it is accelerating continuously then it is constantly changing its speed (unless it's something like a satellite). At some instant (of zero time) it will pass through a speed of zero. That isn't in dispute. But can you say it "stopped" as it went through the zero speed point of its cycle? Can we say that a body passing through a speed of zero in an infinitely small time can be said to have stopped?

Edited January 7, 2012 by TonyMcC

[Xittenn]

Yes, at time t, otherwise you have a non-linear discontinuous manifold and modifications would have to be made to its treatment.