Forces; Two blocks connected by a pulley with friction

[TheClara]

Homework Statement

A massless rope is attached to Block A, which as mass m_A and rests on a horizontal surface with coefficient of kinetic friction u_k. The rope passes over a frictionless, massless pulley and Block B is attached to the other end. When the blocks are released, Block A moves to the right with an acceleration of magnitude a, Block B moves downward with an acceleration of the same magnitude a. At the location of the experiment, the acceleration of a freely-falling object has magnitude g.

Find the mass of Block B. Your answer should involve no quantities other than m_A, u_k, a, and g.

Homework Equations

F_net = ma
F_f = u_k * n
n = mg (on a level surfaces with angle = 180 degrees)

The Attempt at a Solution

First, I drew free body diagrams for both Block A and Block B.

Block A has 4 forces acting on it: force of gravity (which points directly down), normal force (which points opposite of gravity), force of tension (which points directly right) and force of friction (which points directly left).

Block B has 2 forces acting on it: force of gravity (which points directly down) and force of tension (which points directly up).

I then used Newton's second law to make 3 equations (and listed some other relevant things under them)

Block A:
F_netx = Tension - friction = m_A * a
friction = uk*n = u_k * m_A*g

Fnety = normal - weight of block A = 0
normal = m_A*g

Block B:
F_nety = weight of Block B - tension = m_b * a

I took the first equation and made Tension equal to the weight of Block B. I know this is my first mistake but I don't understand why. Doesn't the tension that Block A experience = the tension that Block B experiences? if that is true, then the mass of Block B would = the tension of Block A.

 

[Chestermiller]

Look at the equation you wrote for Block B and tell me whether that is consistent with what you said in the last paragraph about the tension in the rope being equal to the weight of block B.

Chet