It's right that I started with one statement and ended up forgetting it, I apologise for that. However, this means that I didn't commit any misconception, right?
I've tried to solve this exercise but I haven't used one of the properties of the system (the displacement of the masses) so I don't know if I'm wrong about my procedure.
First of all, we (obviously) know that
$$
P=P
$$
And since we can express the power of a force in two different ways, we...
Well, since the friction is a reaction force, it has to be ##f=0\,\mathrm{N}##
I guess that technically, when ##T=15\,\mathrm{N}## then ##f=15\,\mathrm{N}## because there's no resulting movement and ##\mu_{s}=0.8## is just the maximum value that it could take.
The thing with this exercise is that I don't think that the question makes sense at all (or, at least, is incomplete).
First of all, we don't know if the mass moves with any of those tensions, therefore I cannot know which coefficient apply. Second of all, even if we suppose that the mass is...
Oh, yeah, I'm so sorry. I've been studying for a long time and rn is 3 am in Spain so my brain didn't translate that correctly, lmao.
Thank you for your patience and taking the time to answer :)
Taking all that in consideration I get the same result:
First I find ##T_{1}## knowing that, at the joint, there's an equilibrium in the ##x## axis in which ##T_{2}## doesn't participate (now with the angles corrected):
$$
\begin{align}
\sum F_{x} & =0 \\
\cos \left(30^\circ\right) ·T_{1}+\cos...
It asks you to find the values of ##T_{1}##, ##T_{2}## and ##m## supposing that the cables have no mass and that ##g=9,81\,\mathrm{\frac{m}{s^{2}}}##. The wording is just as I wrote it in the title.
TL;DR Summary: I don't know if my procedure is correct in this excercise
I've tried to solve this problem but I find my solution unintuitive and I think I might be wrong.
First of all, applying Newton's Laws I calculated the value for ##T_1## like this:
$$
\begin{align}
\sum F_{x} &=0\\...