Rotational Dynamics Help Needed

[lee_chick]

I'm sure there is something ridiculously simple I'm missing here but this questions has been driving me crazy and now I'm sure I couldn't see the answer if it stared me right in the face.

Homework Statement

A massless string is wrapped around a solid cylinder. A block of mass m=2.0kg hangs from the string. When released the block falls a distance of 82 cm in 2.0s. Starting with a freebody diagram calculate the mass of the cylinder.

*I can't use conservation of energy to solve this as the next question indicates that I am to solve the question again using conservation of mechanical energy.

Homework Equations

y = y₀ + v₀t + 1/2at²
F=ma
torsion = rF
Net Torsion = Moment of Inertia x rotational acceleration

The Attempt at a Solution

r = ? **This is the part that has me stumped - all of the formulae I know need a radius.
m = 2.0kg
y = 0.82m
t = 2.0s
v₀ = 0m/s
m_c = ?

Step One: Determine the force of inertia of the cylinder:

y = y₀ + v₀t + 1/2at²
a=(2y)/(t²)
a = (2 x 0.82m) / (2.0s²)
a = 0.41 m/s²
F_a = ma = 0.41m/s² x 2.0kg = 0.82N
F_g = mg = 9.81m/s² x 2.0kg = 19.62N
F_I = F_g - F_a = 19.62N - 0.82N = 18.8N


This is as far as I can get before I start running into brick walls. I've played with several different formulae but I always run into a point where I need the radius of the cylinder (which I don't have). Am I missing something really obvious here?

 

[Redbelly98]

Try solving it anyway, just leave the radius as "R" without plugging in a number for it. See what you can come up with that way.

p.s. Welcome to PF.

 

[baba89]

Dear student,

It seems like you are on the right track with your calculations. However, you are correct in that you need the radius of the cylinder to continue. It is possible that the question is asking you to solve for the mass of the cylinder using conservation of mechanical energy, which would involve finding the moment of inertia of the cylinder. In order to do this, you would need to know the radius of the cylinder.

If the question specifically states that you are not allowed to use conservation of energy, then it is possible that there is not enough information given to solve for the mass of the cylinder. In that case, I would recommend double checking the problem and seeing if there are any other clues or given information that could help you solve for the radius of the cylinder.

I would also suggest checking with your teacher or classmates for any clarification or hints on how to approach this problem. Sometimes, a fresh perspective can help solve a difficult problem. Keep up the good work and don't give up! There is always a solution to every problem, even if it may seem elusive at first. Good luck!