Question #121378

A mass of 1019Kg is supported by two wires A and B each made of a different material. Before loading the wires are of equal length. After loading they are still of equal length. Find the load carried by each wire.

(WA = 3066N) (WB = 6930N)

Wire

Diameter mm

E Nmm-2

A

1

206,000

B

2

116,000

(WA = 3066N) (WB = 6930N)

Wire

Diameter mm

E Nmm-2

A

1

206,000

B

2

116,000

Expert's answer

**Solution.**

"m=1019kg;\ng=9.81N\/kg;"

"d_A=1mm;"

"d_B=2mm;"

"E_A=206000N\/mm^2;"

"E_B=116000N\/mm^2;"

"F_g=F_A+F_B;"

"F_g=mg;"

"F_g=1019kg\\sdot9.81N\/kg=9996N;"

"\\sigma=\\dfrac{F}{S};" "\\sigma=E\\epsilon \\implies F=ES\\epsilon;"

"S=\\pi \\dfrac{d^2}{4};"

"S_A=3.14\\sdot\\dfrac{(1mm)^2}{4}=0.785mm^2;"

"S_B=3.14\\sdot\\dfrac{(2mm)^2}{4}=3.14mm^2;"

"F_g=E_AS_A\\epsilon+E_BS_B\\epsilon;"

"\\epsilon=\\dfrac{F_g}{E_AS_A+E_bS_B};"

"\\epsilon=\\dfrac{9996N}{206000N\/mm^2\\sdot0.785mm^2+116000N\/mm^2\\sdot3.14mm^2}=0.019;"

"F_A=206000N\/mm^2\\sdot0.785mm^2\\sdot0.019=3072N;"

"F_B=116000N\/mm^2\\sdot3.14mm^2\\sdot0.019=6924N;"

**Answer: **"F_A=3072N;"

"F_B=6924N."

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