Is this correct? Does we can say the body stops?

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Discussion Overview

The discussion revolves around whether it is correct to say that an object stops when it moves up an inclined plane, reaches a momentary halt, and then moves back down. Participants explore the implications of stopping in terms of velocity, sampling rates in experiments, and theoretical considerations of motion.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants argue that there is a moment when the object effectively stops, allowing for a change in direction.
  • Others contend that theoretically, the object does not stop because it can always find a small time interval where its position changes, implying that velocity is never exactly zero.
  • One participant highlights the importance of sampling rates in experiments, suggesting that a higher sampling rate increases the likelihood of detecting a momentary stop.
  • Another viewpoint suggests that the concept of stopping may require a finite interval of unchanged position, which complicates the definition of stopping.
  • Some participants reference theoretical problems, such as the bird between two trains, to illustrate points about motion and stopping.
  • There is a discussion about the interpretation of derivatives and whether velocity can be treated as a fraction, with differing opinions on this matter.
  • One participant proposes that the terms "stops" and "zero velocity" may be conflated, suggesting a need for clarity in definitions.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether it is correct to say the object stops. Multiple competing views remain regarding the definitions and implications of stopping in motion.

Contextual Notes

Some arguments hinge on the interpretation of velocity and the conditions under which an object is considered to stop. The discussion also touches on the implications of sampling rates in experimental contexts and the theoretical nature of certain examples provided.

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Suppose that an object is moving up an inclined plane, then stops and after moves down. Is correct to say that the objects stops, or we can only say that it inverts its motion without stopping?
 
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There is a moment where it effectively stops. Otherwise, how could it invert its way of motion?
 
It stops, but this raises the importance of sampling rates in experiments. If you are only sampling the speed of the object every 10 seconds, odds are you will not see it stopped. But if you sample the speed every femto second you have increased the odds incredably that you will see it stop. The balance comes in how much data can you retain and as sampling rates go up, cost goes up.

CraigD, AMInstP
www.cymek.com
 
Theoretically it doesn't stop. Because something stops only when its velocity is 0. The velocity is dS/dt. For the object, you can always find a small dt (not zero) so that dS is not zero.
 
haiha, you just failed the math exam :wink:
 
haiha said:
Theoretically it doesn't stop. Because something stops only when its velocity is 0. The velocity is dS/dt. For the object, you can always find a small dt (not zero) so that dS is not zero.

Huh?? How can the velocity of an object get from v to -v without passing through zero?
 
cesiumfrog said:
haiha, you just failed the math exam :wink:

With dt not zero, I can always find for you a dS >0 (or<0), that's my argument
 
cristo said:
Huh?? How can the velocity of an object get from v to -v without passing through zero?

You make me remember the problem of a bird flying between two trains approaching each other. Theoretically, it wil never stop.
This case i also marked as theoretical.
 
haiha said:
You make me remember the problem of a bird flying between two trains approaching each other. Theoretically, it wil never stop.
This case i also marked as theoretical.
If your theory predicts the bird will never stop, your theory needs to be revised.
 
  • #10
Imagine the bird has no thickness (a mathematical point), and it always flies faster than the trains. It will never stop. But it ocsillates at increasing frequency.
 
  • #11
The bird "stops" when it's crushed between the colliding trains. That's what enables you to calculate the distance it covered.
 
  • #12
I know that the answer seems obvious; of course it stops. In reality, though, isn't it more likely that the ball or whatever would describe a very small circular path at the apex rather than simply reverse and come straight down? I realize that it could be restricted with rails or a groove or something, but that wasn't specified in the OP.
 
  • #13
haiha, dS/dt is not a fraction.
 
  • #14
Danger said:
I know that the answer seems obvious; of course it stops. In reality, though, isn't it more likely that the ball or whatever would describe a very small circular path at the apex rather than simply reverse and come straight down? I realize that it could be restricted with rails or a groove or something, but that wasn't specified in the OP.

Oh yeah? Well I just redefined this as a 1D problem...it's a circle rolling up an inclined "line". :smile: :-p
 
  • #15
cesiumfrog said:
haiha, you just failed the math exam :wink:

Ouch. The truth hurts sometimes...yes a review of basic calculus is definitely in order.
 
  • #16
cepheid said:
Ouch. The truth hurts sometimes...yes a review of basic calculus is definitely in order.

Never mind, it's a good thing. I've been doing it.
 
  • #17
nealh149 said:
haiha, dS/dt is not a fraction.

Yes, it is.
 
  • #18
KingNothing said:
Yes, it is.

:rolleyes: no it isn't
 
  • #19
Alright, you two... behind the bike racks after school... :rolleyes:
 
  • #20
:mad:What does a fraction have anything to do with the question?

In order for the ball to change direction, the line in the v vs t graph has to go throught eh x-axis. An interesting topic would be to argue how long this 'stop' is.
 
  • #21
prasannapakkiam said:
:mad:What does a fraction have anything to do with the question?

This discussion regarding fractions came about due to this post:

haiha said:
Theoretically it doesn't stop. Because something stops only when its velocity is 0. The velocity is dS/dt. For the object, you can always find a small dt (not zero) so that dS is not zero.

ds/dt is a derivative, but is treated above as if it is a fraction. This is incorrect.
 
  • #22
com'on... Rolle's theorem says, the bird does stop. Unless the velocity function is not continuous, which in normal real life, doesn't really happen.
 
  • #23
Yes, we can say that the body stops

If the body is in motion, then we can sat that the velocity of the body is positive. And at rest or when the body stops the velocity is zero, even though the body stops only for a moment at a particular instance the velocity is zero. After the rest the velocity increases with a negative sign but the motion does not invert, only the direction of the motion.And the it accelarates in the downward motion.
 
  • #24
I still keep the idea that when we say something stops, there must be a piece of time in which the body's position is unchanged, in this case, we can not find that piece of time. The velocity can be zero at certain point of time, but that does not mean it stops. It is something like a car which has problem in the carburetor that it can not goes smoothly, but it doesn't stop.
Another example is the cycloid movement. A point on the rim of a ring is on the move all the time when the ring is rolling on a surface. When it contacts with the surface, its velocity is zero for a moment. But we can not say it stops even then.
 
  • #25
haiha said:
Theoretically it doesn't stop. Because something stops only when its velocity is 0. The velocity is dS/dt. For the object, you can always find a small dt (not zero) so that dS is not zero.

By your reasoning, it will also never have a velocity of 1, or 2, or 1.1, or 54, or whatever you choose!
 
  • #26
moose said:
By your reasoning, it will also never have a velocity of 1, or 2, or 1.1, or 54, or whatever you choose!

I think we may mix the words stops and zero velocity.
 
  • #27
haiha said:
I think we may mix the words stops and zero velocity.
That might explain the problems here. In the context of the initial post, "stop" means have a velocity = 0. Just for an instant, of course--not for some finite interval.
 

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