Question

15. Three blocks of mass M, 2M and 3M are shown. The middle block (2M) sits on a frictionless table tipped at an angle o with the horizontal as shown. The other two blocks are connected to it by massless unstretchable strings that run over frictionless pulleys. At time t O the system is released from rest. Find: a) The magnitude of the acceleration of the blocks. b) The tensions Ti and T2 in the strings as indicated. T 2M T M ЗМ

Answer 1

( 6 ) 1, LM на! Ө ТИ mg 3м img For block of mass , = Ma 2 - " # 1, Mat M + 11 Fx block of mass 2M, T, T 2 на simv -Т, Т. : т. + мя імя - 2м 4 T, 12 ча!і» 2 ча (ох %: 11 осk оf m«53 3м, - - 3 м а 31 - т = 3MG Met тр = 2 * from equation мі (*), оr - in 0 - 2 Ч + Ng T, + 2Nasih- 12" sing sine ama toimepako на + ме + На : 3 - 1 24ine 11) 23 + a sing см MA - 13 30 - 3 ма 12 м 2 (in), Puke value if Ti a

it sino) g a The acceleration of the blocks in magnitude given by 3 ( 1+ sinog a -- from equation (1), we get 3 mg 3M x 3 (it sinog 3 mg Mg (1 + sine) Mg 12 - sino) from Mat equation sith , we get I mg MX 13 ( 1t sine) g + mg ng [ I sinot 1/3 mg (at sing) 11 +
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