I also attempted to solve part C. From the FBD's of each block I got:
##T_B-m_2g=m_2a## and ##m_1g-T_A=m_1a##
using the relationships provided, I was able to obtain the answer:
##a=g\frac{m_1-m_2e^{\mu_k\pi}} {m_1+m_2e^{\mu_k\pi}}##
@haruspex @kuruman I realized I had a couple of mathematical errors as well as an error in conceptualizing the problem. Here's my reattempt at it:
##T_1=T_A=m_1g## and ##T_2=T_B=m_2g## and ##T_B=T_Ae^{-\mu_s\theta}## so ##T_A=T_Be^{\mu_s\theta}##
Thus:
##m_1g=m_2ge^{\mu_s\pi}##...
Okay, I understand that now. So to attempt this again I know that:
##T_1=T_A## and ##T_2=T_B##. I also know that ##T_B=T_Ae^{-\mu_s\theta}##
##m_1## at the point where it begins to slide would mean that ##T_1## and ##T_2## are equal correct?
So would that mean:
##m_1g=m_2ge^{-\mu_s\pi}##
and...
On question B, I've attempted a solution that I have posted. However, I don't think it's correct. Am I allowed to treat this rope that wraps around the rod as a "negative" force and simply attach it to the other side of the equation such that ## m_1g=m_2g+\mu_sN##?
What is the Free Body Diagram on the last block and what is the only Force acting on it? What must be the value of the Force acting on it such that it moves at 10 ## m/s^2##?
I accidentally deleted my initial post so here's the repost:
Ask these questions to yourself:
1) How are the force ##F## and the tension ##T_1## related? (Hint: Consider the relation between ##F## and ##T_2## and then ## T_2## and ##T_1##)
2) Of the two masses involved with ##T_1## which of them...
So going from here then: ##T(r)=m_1\omega^2(\frac{r^2}{2l} -l)##
Then considering the Tension caused by the ball ##T_b=-m_2\omega^2l##
We can combine the two tensions and get the actual T(r) to be ##T(r)=m_1\omega^2(\frac{r^2}{2l} -l) - m_2\omega^2l##
Am I conceptualizing this right? Or...
Got it. This is where I learned the constraint condition method. Perhaps you can use it to answer your question! https://ocw.mit.edu/courses/8-01sc-classical-mechanics-fall-2016/pages/week-4-drag-forces-constraints-and-continuous-systems/12-2-pulley-problem-part-ii-constraint-condition/