Uniform Pully with a single block, do not understand where mass relates?

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Discussion Overview

The discussion revolves around understanding the relationship between the mass of a block and the equations governing a uniform cylindrical pulley system with a single block. Participants explore the dynamics involved, including tension, acceleration, and the equations necessary to solve for unknowns in the system.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about how the mass of the block relates to the equations used in pulley problems, noting a lack of information in their textbook and notes.
  • Another participant attempts to solve for acceleration using the equation ma = mg - T, but finds that it does not yield a correct solution.
  • There is a clarification about the setup involving a massless rope and a block hanging from the pulley, with an emphasis on needing to find the acceleration of the block.
  • Participants discuss the need for a second equation to solve for both tension and acceleration, indicating that the tension is typically unknown.
  • One participant mentions the need for the rotational equivalent of Newton's 2nd law, specifically Net Torque = Iα, as a potential missing equation for the cylinder.

Areas of Agreement / Disagreement

Participants generally agree that two equations are necessary to solve for the unknowns in the system, but there is no consensus on the specific equations or methods to use, as confusion and uncertainty remain regarding the relationship between the mass of the block and the other variables.

Contextual Notes

Participants note the absence of specific equations in their resources, which may limit their ability to fully understand the problem. There is also mention of multiple unknowns (tension and acceleration) complicating the solution process.

StingerManB
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OK, my largest issue with dealing with uniform cylindrical pulleys and a single block (object) is understanding where mass of the block relates in any of the equations.

Specifically, I was doing some problems earlier with no issues at all. Then I came across one asking about the mass of the block hanging from the pulley. The book and my notes do not speak of this.
Known:
mass of the pulley
radius,
Tension,

This seems like a pretty straight-forward topic, yet I cannot seem to locate much on it.
Can anyone please explain the topic?
Thank you in advance, I have already found much help from these forums, and without them would probably not pass calculus based physics!
 
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I tried solving for acceleration then using:

ma = mg - T, rearranged as T = m(g-a) but this did not give me a correct solution either. hmmmmm.
 
StingerManB said:
OK, my largest issue with dealing with uniform cylindrical pulleys and a single block (object) is understanding where mass of the block relates in any of the equations.

Specifically, I was doing some problems earlier with no issues at all. Then I came across one asking about the mass of the block hanging from the pulley. The book and my notes do not speak of this.
Are you talking about a cylinder that has a massless rope wrapped around it from which a block is hanging? And you're supposed to find the acceleration of the block?
Known:
mass of the pulley
radius,
Tension,
Generally the tension is not known, but you can figure it out.

StingerManB said:
I tried solving for acceleration then using:

ma = mg - T, rearranged as T = m(g-a) but this did not give me a correct solution either.
That looks like a reasonable equation for the block. Note that you have two unknowns, tension and acceleration. You need a second equation--one for the cylinder--to solve for the acceleration.
 
Ok, thank you. I will look for some info on this. I am not too familiar with the equations of a pulley.
To clarify the problem, I am looking for the mass of a block hanging from a single pulley.
From the problem I am given the mass of the pulley, the radius of the pulley, and the tension in the cable.
Do you know, specifically, which equation I am missing for the cylinder?
Thank you again for the help. I need to know this subject in and out...
 
StingerManB said:
To clarify the problem, I am looking for the mass of a block hanging from a single pulley.
From the problem I am given the mass of the pulley, the radius of the pulley, and the tension in the cable.
OK. Instead of the tension being unknown, the mass is unknown. You still have two unknowns and need two equations.
Do you know, specifically, which equation I am missing for the cylinder?
Yes, the rotational equivalent of Newton's 2nd law: Net Torque = Iα
 
you have PM.
 

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