A uniform cylinder with a radius of 15cm has been attached to two cords and the

Question

   A uniform cylinder with a radius of 15cm has been attached to two cords and the cords are would around it and hung from the ceiling.  The cylinder is released from rest and the cords unwind as the cylinder descends. (a) What is the acceleration of the cylinder?  (b)  If the mass of the cylinder is 2.6kg, what is the tension in each cord?

Explanation / Answer

The equation of motion are          mg - 2T = ma ==> T = 0.5 m (g - a)    ...........1 We know that          = I =2T r         ==> 2 T r = 0.5 mr2 * a / r         ==> T = m a /4      .....2 From 1 and 2 we have           a = (2/3) *g             = 6.533 m/s2 The tension in the cable is             T = ma/4 = 2.6 * 6.533 / 4 = 4.246 N

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