A Few Questions on Tension, and Some Work

[Nickg140143]

Homework Statement

You can find the questions, and relevant diagrams for each within the attached image

Homework Equations

Force Equations
$$ƩF=ma$$
$$f_k=μ_kN$$
Work Equations
$$W=Fs$$
(in this case, s=h)
$$W_{tot}=\frac{1}{2}mv^2-\frac{1}{2}mv_0^2$$

My Questions (these are also written on the diagrams):
-Looking at the diagram with the black background, have these tensions been identified correctly? If so, how would I try to solve for T2, given I've created all of my force equations?

-looking at the attachment that has two problems, with forces identified, and specific areas of interest highlighted:
-Have I identified my forces correctly?
-In question 1, it says block m2 just "drops" a distance h, since it says nothing about
the velocity being constant, should I assume that there is an acceleration in the
system?
-In question 2, it says that block c descends with a constant velocity, can I say that
block A and block B also move through the system at a constant velocity?
-When finding the work done on each individual body in both questions, I forgot that
none of the tensions are given to me. Would I simply set up force equations in order
find each tension?


It seems I have most of the concepts understood to a certain degree, but their are certain things that tend to trip me up quite a bit, any help regarding these question would be greatly appreciated.

 

[grzz]

re diagram with black background:
If you show your equations, one can help you.

 

[Nickg140143]

re diagram with black background:
If you show your equations, one can help you.

I have something along these lines
forces:
$$ƩF_{Ax}=T_1-f_{sa}=0 → f_s=T_1$$
$$ƩF_{Ay}=N_A-mg=0 → N_A=mg$$
$$ƩF_{Wy}=m_Wg-T_2=0 → m_W=\frac{T_2}{g}$$
friction:
$$f_s=μ_sN_A$$
so,
$$T_1=μ_smg$$

The third equation is the one I'm not too sure about. I've attached a better diagram of the problem, as well as my own work (you'll notice a typo in the third equation, T3 should be T2)

My main concern regarding this problem is how should I use the given angle to help calculate my tension2? That is, assuming I was even able to get tension1 calculated correctly.

 

[grzz]

If the horizontal tension is T1 then the tension at 45 deg CANNOT be also T1.

 

[Nickg140143]

If the horizontal tension is T1 then the tension at 45 deg CANNOT be also T1.

Alright, so I can now say that I have 3 tensions:
tension on Block A
$$T_1=μ_smg$$

Tension on the wall from the rope at angle 45
$$T_2=$$

tension on hanging weight
$$T_3=$$

Well, I'm looking at the rope on the wall, can I say I have a 45-45-90 triangle here, since one angle is 45, the angle the imaginary horizontal line makes with the wall is 90, and the remaining angle is 180=90+45+x, x=45?

I'm not sure where to take it from here.

 

[grzz]

Sorry for my uprupt disappearance last time due a total power failure in our area.

Now have a look at the point where all three tensions meet. This point is in equilibrium.
Hence you can find the horizontal and vertical components of T2 and get an equation connecting T1 and T2 and another connecting T2 and T3.