Why doesn't the released mass m2 on pulley have higher acceleration?

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Discussion Overview

The discussion revolves around the dynamics of a mass (m2) on a frictionless pulley system when it is released. Participants explore the implications of releasing the mass versus it being attached to a string, particularly focusing on the acceleration of m2 and the forces acting on it.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question why m2's acceleration would not be greater when released, as it is no longer subject to the tension force from the string.
  • There is a suggestion that the problem may be asking about the scenario when the two masses are still connected, implying that the acceleration depends on the difference between the two masses.
  • Participants discuss the interpretation of "released" versus "cut," with some arguing that "released" implies letting go of the mass rather than severing the string.
  • One participant proposes that if the string were cut, the initial acceleration of m2 would be influenced by its previous acceleration while attached to the string, suggesting a transition from one state to another.
  • There is a debate on whether the change in acceleration can be measured in milliseconds, with some expressing confusion about the instantaneous nature of the change in forces and acceleration.
  • Another participant emphasizes that if the forces change discontinuously, the acceleration will also change accordingly, but acknowledges that there are limits on how rapidly forces can be altered.
  • Some participants attempt to clarify the dynamics of the system, suggesting that after m2 is released, the tension in the string will affect the system's overall motion.

Areas of Agreement / Disagreement

Participants express differing interpretations of the problem, particularly regarding the definitions of "released" and "cut." There is no consensus on the implications of these terms for the acceleration of m2, and multiple competing views remain regarding the dynamics of the system.

Contextual Notes

Participants note that the problem's wording may lead to different interpretations, particularly concerning the initial conditions of the masses and the role of tension in the system. The discussion includes assumptions about the frictionless nature of the pulley and the ideal conditions of the string.

annamal
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TL;DR
Why doesn't the released mass m2 on pulley have higher acceleration since it is no longer subject to the upward force of tension?
Consider the pulley in the attached image to be frictionless. (a) If m2 is released, what will its acceleration be?

My question is why wouldn't m2's acceleration be greater if released rather than attached to the string because m2 released is no longer subject to the string's upward force tension?
 

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annamal said:
Summary:: Why doesn't the released mass m2 on pulley have higher acceleration since it is no longer subject to the upward force of tension?

Consider the pulley in the attached image to be frictionless. (a) If m2 is released, what will its acceleration be?

My question is why wouldn't m2's acceleration be greater if released rather than attached to the string because m2 released is no longer subject to the string's upward force tension?
Is there an actual full problem statement associated with this image? Of course if you cut the string, M2 will free fall. But are they actually asking about when the 2 masses are still connected to the string? Then the acceleration will depend on the difference between the 2 masses, no?
 
berkeman said:
Is there an actual full problem statement associated with this image? Of course if you cut the string, M2 will free fall. But are they actually asking about when the 2 masses are still connected to the string? Then the acceleration will depend on the difference between the 2 masses, no?
That's how the problem is worded. I think it just means at that instant the mass 2 is released.
 
annamal said:
That's how the problem is worded. I think it just means at that instant the mass 2 is released.
Usually "released" means let go out of your hand. If they were cutting the string, the verb "cut" would likely be used. I suppose you could submit both answers for extra credit to your teacher... :wink:
 
"Consider the pulley in the attached image to be frictionless. (a) If m2 is released, what will its acceleration be?"

If the problem would mean to cut the string, how important the friction in the pulley would be?
As @berkeman stated above, somebody has been holding mass 2, preventing the system from moving under its own forces.

Please, see:
http://hyperphysics.phy-astr.gsu.edu/hbase/atwd.html

:cool:
 
Lnewqban said:
"Consider the pulley in the attached image to be frictionless. (a) If m2 is released, what will its acceleration be?"

If the problem would mean to cut the string, how important the friction in the pulley would be?
As @berkeman stated above, somebody has been holding mass 2, preventing the system from moving under its own forces.

Please, see:
http://hyperphysics.phy-astr.gsu.edu/hbase/atwd.html

:cool:
a) If m2 were cut, initially a2 = a (acceleration of mass on string) - g but then a2 grows to equal -g
Is that correct?
 
annamal said:
a) If m2 were cut, initially a2 = a (acceleration of mass on string) - g but then a2 grows to equal -g
Is that correct?
As I understand this new question, you previously have released mass ##m_2## from your hand. It is accelerating at some rate ##a## while mass ##m_1## is accelerating at the same rate in the opposite direction.

You ask about how the acceleration changes from ##a## to ##-g##.

If you snip the [ideal, inextensible] cord above mass ##m_2## instantly then the acceleration of ##m_2## will change instantly. It will not slowly "grow".
 
annamal said:
a) If m2 were cut, initially a2 = a (acceleration of mass on string) - g but then a2 grows to equal -g
Is that correct?
No. Use ##F=ma##. What forces are on ##m_2## after the string is cut? That's what determines the acceleration.
 
vela said:
No. Use ##F=ma##. What forces are on ##m_2## after the string is cut? That's what determines the acceleration.
but isn't the acceleration of the cut mass going to be influenced by the acceleration the mass is going with the string
 
  • #10
jbriggs444 said:
As I understand this new question, you previously have released mass ##m_2## from your hand. It is accelerating at some rate ##a## while mass ##m_1## is accelerating at the same rate in the opposite direction.

You ask about how the acceleration changes from ##a## to ##-g##.

If you snip the [ideal, inextensible] cord above mass ##m_2## instantly then the acceleration of ##m_2## will change instantly. It will not slowly "grow".
can this instant change be measured in time of milliseconds or even less?
 
  • #11
annamal said:
can this instant change be measured in time of milliseconds or even less?
that confuses me because doesn't it take time to change acceleration?
 
  • #12
annamal said:
a) If m2 were cut, initially a2 = a (acceleration of mass on string) - g but then a2 grows to equal -g
Is that correct?
Sorry, I don't understand.
My previous post only tried to reason about the release of mass 2 (from a repose condition), rather than being allowed to free fall (detached from the string and the effect of mass 1).

If mass 2 is released, tension in the string increases to a maximum value, which reaches mass 1.
After that instant, mass 1-string-mass 2 become a system that moves (or not) at same rate of acceleration.
Such a system is also known as an Atwood machine.

Being frictionless, the pulley only job here is to change the direction of the string and its internal tension.
 
  • #13
annamal said:
that confuses me because doesn't it take time to change acceleration?
If the force changes discontinuously then so does the acceleration.

Edit: Yes, there are always (almost always?) limits on how rapidly forces can be changed. But they can be changed pretty rapidly.
 
  • #14
jbriggs444 said:
If the force changes discontinuously then so does the acceleration.

Edit: Yes, there are always (almost always?) limits on how rapidly forces can be changed. But they can be changed pretty rapidly.
So therefore if the mass is accelerating at a1 attached to the string, if the string were cut, it would first accelerate at a1 - g and then -g. correct?
 
  • #15
annamal said:
So therefore if the mass is accelerating at a1 attached to the string, if the string were cut, it would first accelerate at a1 - g and then -g. correct?
Sorry, egg all over my face. Forgot which thread I am on.
 

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