10.67 The figure below (Figure 1) illustrates an Atwood\'s machine. A:Let the ma

Question

10.67 The figure below (Figure 1) illustrates an Atwood's machine.

A:Let the masses of blocks A and B be 3.50kg and 2.00kg , respectively, the moment of inertia of the wheel about its axis be 0.300kg?m2, and the radius of the wheel be 0.110m . Find the magnitude of linear acceleration of block A if there is no slipping between the cord and the surface of the wheel.

B:Find the magnitude of linear acceleration of block  B if there is no slipping between the cord and the surface of the wheel.

C:Find the magnitude of angular acceleration of the wheel C if there is no slipping between the cord and the surface of the wheel.

D:Find the tension in left side of the cord if there is no slipping between the cord and the surface of the wheel.

E: Find the tension in right side of the cord if there is no slipping between the cord and the surface of the wheel.

Must Get all parts of the question right for the points

Explanation / Answer

A) From the FBD,

      mag - T = maa -------------(1)

      T - mbg = mba -------------(2)

      Tr = I(a/r)

      Adding (1) and (2)

      (ma - mb)g = (ma + mb)a

      1.5g = 5.5a

       a = 1.5g/5.5 = 2.68m/s2

B) acceleration of block A = 2.68(-j)

    acceleration of block B = 2.68(j)

    Magnitude is 2.68m/s2.

C) Angular acceleration = a/r = 2.68/0.11 = 24.36rad/s2.

D) Since there is no slipping, magnitude of Tension is same throughout the rope

     T = I(a/r)*1/r

        = 0.3(24.36)/0.11 = 66.45N

E) As explained above the tension is same everywhere.

     T = 66.45N
    

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