Question #221483

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.


1
Expert's answer
2021-07-30T16:37:01-0400

Taking mass moment inertia

Mo=Ioα    2002FB(3)=80lb\sum M_o=I_o\alpha \implies200*2-F_B(3)=80lb

andFB=fsNB=fs(4p)and F_B=f_s*N_B=f_s*(4p)

As=p=100lb    FB=80lbA_s=p=100lb\implies F_B=80lb and α=13.33rad1\alpha =13.33rad ^{-1}

fy=0    FB+200=T    280lb\sum f_y=0 \implies F_B+200=T \implies 280lb

Ti=FBetiQ=Ti=80e0.20Q1T_i=F_Be^{t_i*Q}= T_i=80*e^{0.20*Q_1}

T2=80e0.20Q2Q2=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=65.2lb


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