3. o/2 points| Previous Answers FRKestenCP1 9.P.044 My Notes The elastic limit o

Question

3. o/2 points| Previous Answers FRKestenCP1 9.P.044 My Notes The elastic limit of an alloy is 0.6 x 109 N/m2. What is the minimum radius of a 4-m-long wire made from the alloy if a single strand is designed to support a commercial sign that has a weight of 8000 N and hangs from a fixed point? To stay within safety codes, the wire cannot stretch more than 4 cm 20.6 The elastic limit of an alloy is 0.6 × 109 N/m2. A 4-m-long wire made out of this alloy is designed to hang a sign that weighs 8000 N. The maximum distance the wire can stretch is 4 cm. Assuming that the wire has a circular cross-section, we can calculate the minimum radius of the wire from the weight of the sign, the elastic limit, and the length of the wire. Supporting Materials Pcast eBook

Explanation / Answer

given wight of the board, W =8000 N
length of wire, l = 4m
maximum strech, dl = 0.04 m
hence
strain = dl/l = 0.04/4 = 0.01
elastic limit, E = 0.6*10^9 N/m^2
hence
E = W/pi*r^2
0.6*10^9 = 8000/pi*r^2
r = 2.060129 mm = 0.2060129 cm is the minimum radius of the wire that has to be used

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