Calculate Mass of Cylinder Given Tension & Distance

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Homework Help Overview

The problem involves a solid cylinder with a light string wrapped around it, from which a 300 g mass is suspended. The mass falls a distance of 54 cm in 3.0 seconds, and the objective is to calculate the mass of the cylinder. The original poster expresses uncertainty regarding the necessary equations and the role of the cylinder's radius in the calculations.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the tension in the string and its relation to the mass of the cylinder. There are attempts to derive equations involving torque and angular acceleration, but confusion arises regarding the cancellation of the radius in the calculations. Some participants question the implications of the cylinder's radius on determining the mass.

Discussion Status

The discussion is ongoing, with participants exploring various equations related to forces and torques. There is a recognition of the complexity involved in the problem, and some guidance has been offered regarding the relationships between the variables, though no consensus has been reached.

Contextual Notes

Participants note the absence of the cylinder's radius as a significant constraint in solving the problem. The original poster also mentions that this is a study question, indicating a potential concern about the difficulty of similar questions in future assessments.

doub
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Homework Statement



A light string is wrapped around a solid cylinder and a 300 g mass hangs from the free end of the string, as shown. When released, the mass falls a distance 54 cm in 3.0 s. Calculate the mass of the cylinder?


Homework Equations



not sure


The Attempt at a Solution



I have gotten as far as to determine the Tension on the string of -2.9N. Without known the radius of the cylinder I feel that the mass cannot be determined.

Granted these are study question but if the final is going to be like this...yikes
 
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hi doub! :smile:
doub said:
A light string is wrapped around a solid cylinder and a 300 g mass hangs from the free end of the string, as shown. When released, the mass falls a distance 54 cm in 3.0 s. Calculate the mass of the cylinder?

Without known the radius of the cylinder I feel that the mass cannot be determined.

the motion depends on what i call the rolling mass of the cylinder, I/r2, which is always half the actual mass! :wink:

carry on … you should find that the radius cancels out :smile:
 
The best I can get is

\alpha = (T1 + T2)/I

= (Fr - Tr)/1/2 mr2

= (mra -(ma+mg)r)/ 1/2 mr2

don't see how the radiii cancel each other though
 
doub said:
\alpha = (T1 + T2)/I

= (Fr - Tr)/1/2 mr2

= (mra -(ma+mg)r)/ 1/2 mr2

sorry, i don't understand any of this :redface:

you should have an F = ma equation and a τ = Iα equation
 

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