\"A yo-yo shaped device mounted on a horizontal frictionlessaxis is used to lift

Question

"A yo-yo shaped device mounted on a horizontal frictionlessaxis is used to lift a 30kg box as shown in the above figure. The outer radius R of the device is .50m, and the radius, r, of theHub is .20m. When a constant horizontal force Fapp ofmagnitude 140N is applied to a rope wrapped around the outside ofthe device, the box, which is suspended from a rope wrapped aroudthe hub, has an outward acceleration of magnitude .80 m/s^2. What is the rotational inertia of the device about its axis ofrotation?" Thank you

Explanation / Answer

   in the given problem let us assume that T astension on the rope
   from the newtons second law of motion we get
   T - m g = m a
   T = m (g + a)
   since the box has an upward acceleration a thetension is given by
   T = (30 kg) (9.80 + 0.80)
      = ....... N
   the rotation of the device is desribed by
   Fapp R - T r = I
                       =I a / r
   the moment of inertia will be
   I = r (Fapp R - T r) / a
     = ......... kg . m2

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