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

[StingerManB]

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!

 

[StingerManB]

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.

 

[Doc Al]

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.

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.

 

[StingerManB]

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...

 

[Doc Al]

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

 

[StingerManB]

you have PM.