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Forces; Two blocks connected by a pulley with friction

  1. Feb 25, 2015 #1
    1. The problem statement, all variables and given/known data
    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.

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

    3. 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.
     
  2. jcsd
  3. Feb 25, 2015 #2
    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
     
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