The blocks 1 and 2 in the arrangement have equal mass m. The strings AB and BC are light having tension T1 and T2 respectively . The system is in equilibrium with a constant horizontal force mg acting on C, then prove that tanϴ1 = 1/2 , tanϴ2 = 1 , T1 =√5 mg and T2 =√2 mg

Block 2:Fx=0mg-T2sinθ2=0  mg=T2sinθ2  ...... (1)Fy=0mg-T2cosθ2=0  mg=T2cosθ2 ...... (2)(1) / (2):1=tanθ2tanθ2=1θ2=45oHence,T2=mgsin45o    =2mgBlock 1:Fx=0T1sinθ1-T2sinθ2=0  T1sinθ1=T2sinθ2T1sinθ1=2mgsin45o T1sinθ1=mg...... (3)Fy=0mg+T2cosθ2=T1cosθ1T1cosθ1=mg+2mgcos45oT1cosθ1=2mg  ...... (4)(3) / (4):tanθ1=12θ1=26.57oHence,T1=mgsin26.57o    =5mg

  • 137
What are you looking for?