Friction and Tension with blocks on an incline

[lhinds7]

Homework Statement
Blocks A, B, and C are placed as in the figure and connected by ropes of negligible mass. Both A and B weigh 24.9N each, and the coefficient of kinetic friction between each block and the surface is 0.39. Block C descends with constant velocity.

a) Find the tension in the rope connecting blocks A and B.

b) What is the weight of block C?

c) If the rope connecting A and B were cut, what would be the acceleration of C?The attempt at a solution
I figured out part (a), 9.71N. I am stuck and have a mental block and can't get the weight of block C to save my life. I used the equation:

T₂=T₁+wsin$$\Theta$$+$$\mu$$N_B

which yielded a result of 34.37N, which I know is incorrect. The answer in the back of the book is 30.8N, but the coefficient of friction and weights are different.

 

[lhinds7]

Can anybody point me in the right direction?

 

[leto78]

The exercise states the the block C has a constant velocity, which means that the force created by block C equals all the other forces.
Remember that Block A only contributes with friction, but block B contributes with friction and its part of its weight.
F_C=F_B+F_A

 

[leto78]

Spoiler

F_A=.39*24.9=9.711
F_B=.39*24.9*cos(36.9)+24.9*sin(36.9)=22,716
F_C=32.427

I don't see any faults in my reasoning but I yield a different result. In any case, you should be aware that the friction of block B is only in terms of the perpendicular force to the ramp and not the entire weight of B. On the other hand, the projection the force of gravity towards downward direction is only a small fraction of the entire weight.

 

[lhinds7]

32.4N is the answer that I finally got too and it is correct. Thanks for the help.