1. If the weight is descending freely, determine the tension in the cord both before and after a brake force P – 100 lb is applied. Neglect the thickness of brake.
Taking mass moment inertia
∑Mo=Ioα ⟹ 200∗2−FB(3)=80lb\sum M_o=I_o\alpha \implies200*2-F_B(3)=80lb∑Mo=Ioα⟹200∗2−FB(3)=80lb
andFB=fs∗NB=fs∗(4p)and F_B=f_s*N_B=f_s*(4p)andFB=fs∗NB=fs∗(4p)
As=p=100lb ⟹ FB=80lbA_s=p=100lb\implies F_B=80lbAs=p=100lb⟹FB=80lb and α=13.33rad−1\alpha =13.33rad ^{-1}α=13.33rad−1
∑fy=0 ⟹ FB+200=T ⟹ 280lb\sum f_y=0 \implies F_B+200=T \implies 280lb∑fy=0⟹FB+200=T⟹280lb
Ti=FBeti∗Q=Ti=80∗e0.20∗Q1T_i=F_Be^{t_i*Q}= T_i=80*e^{0.20*Q_1}Ti=FBeti∗Q=Ti=80∗e0.20∗Q1
T2=80∗e0.20∗Q2Q2=Tan(71.60)Q1=tan(−450)∴T1=146lb;T2=65.2lbT_2=80*e^{0.20*Q_2}\\ Q_2=Tan(71.6^0)\\ Q_1=tan(-45^0)\\ \therefore T_1=146lb ; T_2=65.2lbT2=80∗e0.20∗Q2Q2=Tan(71.60)Q1=tan(−450)∴T1=146lb;T2=65.2lb
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