10The figure below shows an Atwood\'s Machine with a pulley of non-negligible ma

Question

10The figure below shows an Atwood's Machine with a pulley of non-negligible mass. Block 1 has mass m2.00 kg, block 2 has mass m 1.00 kg. and the pulley, which is mounted on a horizontal axle with negligible friction is a solid disk with radius R-5.00 cm (la-. ½ mouF) when released from rest, block 1 falls with an acceleration 2.00 m/s' downward without the cord slipping on the pulley a) (6 pts) Using Free Body Diagram for block 1, find the tension T T2 T1 m2 21 b) (6 pts) Using Free Body Diagram for block 2, find the tension T? Units c) (6 pts) Find the magnitude of the net torque on the pulley? Units Answer

Explanation / Answer

1)    T1 = m1(g - a)

               =   2 (9.8 - 2)

               = 15.6 N

2)     T2 = m2( a + g)

               =   1 * ( 2 + 9.8 )

                = 11.8 N

3)    magnitude of net torque = (T1 - T2) * R

                                               = (15.6 - 11.8) * 0.05

                                              = 0.19 N.m

4)        angular acceleration = 2/0.05

                                             = 40 rad/sec2

5)    moment of inertia = 0.5 * M * (0.05)2

   =>    0.19 =   0.5 * M * (0.05)2 * 40

=>   M =   3.8 kg

=> moment of inertia of pulley =   0.5 * 3.8 * (0.05)2

                                                                = 4.75 * 10-3   kg-m2

6)   mass of pulley =    3.8 kg

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