Atwood Clarification: Tensions & Masses

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Homework Help Overview

The discussion revolves around an Atwood machine scenario involving two masses, M1 and m2, where M1 is greater than m2 and is positioned lower. Participants are exploring the relationships between tensions in the strings and the masses involved, under the assumption of a frictionless environment with massless strings and pulleys.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants attempt to relate the tensions T1, T2, and T3 to the masses M1 and m2, questioning whether T1 should equal T2. They also explore the implications of acceleration on the center of mass (CM) of the system and the concept of negative tension in the context of T3.

Discussion Status

The conversation is ongoing, with participants providing insights and questioning each other's reasoning. Some guidance has been offered regarding the relationship between tensions in the strings and the assumptions about the system's behavior, particularly concerning the center of mass and the nature of tension in the strings.

Contextual Notes

Participants are navigating the complexities of the Atwood machine setup, including assumptions about massless components and the implications of acceleration on the system's dynamics. There is a noted lack of consensus on certain aspects, such as the behavior of T3 and its relationship to the other tensions.

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Homework Statement


In a system where the atwood is suspended by a massless string with T3 and M1>m2. M1 is lower than m2. Relate Tensions and masses if it is frictionless, pulley and string are massless.


Homework Equations


T1 is tension in string holding M1; T2 is tension in string holding M2.


The Attempt at a Solution


I believe that when there is no acceleration:
T3=M1+m2
T1=M1g
T2=m2g
but shouldn't T1=T2?

when there is acceleration then the system CM does not change, but the CM of M1 and m2 is lowered since M1 falls lower. Or will it stay the same since M1 is already lower than m2?

also, since T3 is being taken into account (which I can't find an example of), will it have a negative tension compared with the other tensions?
 
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Vanessa23 said:

Homework Statement


In a system where the atwood is suspended by a massless string with T3 and M1>m2. M1 is lower than m2. Relate Tensions and masses if it is frictionless, pulley and string are massless.


Homework Equations


T1 is tension in string holding M1; T2 is tension in string holding M2.


The Attempt at a Solution


I believe that when there is no acceleration:
T3=M1+m2
T1=M1g
T2=m2g
but shouldn't T1=T2?
Yes, good observation. So what does that tell you about the system when M1 and m2 are not equal?

when there is acceleration then the system CM does not change,
what makes you say that?
but the CM of M1 and m2 is lowered since M1 falls lower. Or will it stay the same since M1 is already lower than m2?
the CM will lower

also, since T3 is being taken into account (which I can't find an example of), will it have a negative tension compared with the other tensions?
there's no such thing as a negative tension. Once you solve for the string tension around the pulley (where you must note that T1=T2 for strings wrapped around massless frictionless pulleys), you can find T3 with a FBD of the massless, at rest pulley.
 
So if it is true that in this situation T3=M1+m2, then why is it that T3 is less than M1+m2+the mass of the pulley (when it isn't massless)?
and why is T1 greater than T2?
and T3 greater than T1+T2?
 
Last edited:

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