A crane is required to lift loads of up to $$ 1.0 imes 10^{5} \mathrm{~N} $$. (a) What is the minimum diameter of the steel cable that must be used? (b) If a cable of twice the minimum diameter is used and it is 8.0 m long when no load is present, how much longer is it when supporting a load of $$ 1.0 imes 10^{5} \mathrm{~N} $$ ? (Data for steel: $$ E=2 imes 10^{11} \mathrm{~Pa} $$, proportional limit $$ =2.0 imes $$ $$ 10^{8} \mathrm{~Pa} $$, elastic limit $$ =3.0 imes 10^{8} \mathrm{~Pa} $$, and tensile strength $$ =5.0 imes 10^{8} \mathrm{~Pa} $$.)

Question

A crane is required to lift loads of up to $$ 1.0 	imes 10^{5} \mathrm{~N} $$. (a) What is the minimum diameter of the steel cable that must be used? (b) If a cable of twice the minimum diameter is used and it is 8.0 m long when no load is present, how much longer is it when supporting a load of $$ 1.0 	imes 10^{5} \mathrm{~N} $$ ? (Data for steel: $$ E=2 	imes 10^{11} \mathrm{~Pa} $$, proportional limit $$ =2.0 	imes $$ $$ 10^{8} \mathrm{~Pa} $$, elastic limit $$ =3.0 	imes 10^{8} \mathrm{~Pa} $$, and tensile strength $$ =5.0 	imes 10^{8} \mathrm{~Pa} $$.)

UpStudy AI · Accepted Answer

(a) الحد الأدنى لقطر الكابل هو حوالي $$ 2.52 \mathrm{~cm} $$. (b) الكابل سيكون أطول بمقدار $$ 2.0 \mathrm{~mm} $$ عند دعم الحمولة.

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