Question #124893

A fisherman uses a fishing rod to pull a fish of weight 6.5 kg out of a river. The fish is then suspended vertically on the end of a fishing line of uniform circular cross section. The line has a breaking stress of 65 MPa.

Calculate:

(a)

The minimum diameter of the fishing line required if the line does not break.

(b)

The extension per metre of this line under these conditions.

Calculate:

(a)

The minimum diameter of the fishing line required if the line does not break.

(b)

The extension per metre of this line under these conditions.

Expert's answer

(a)

"\\sigma=\\frac{F}{S}=\\frac{4F}{\\pi d^2}\\to d=\\sqrt{\\frac{4F}{\\pi\\sigma}}=\\sqrt{\\frac{4\\cdot 6.5\\cdot9.81}{3.14\\cdot 65\\cdot10^6}}=0.0011m"

(b)

"\\sigma=E\\frac{\\Delta l}{l}" if "l=1 m" then "\\Delta l=\\frac{\\sigma}{E}"

Assume that "E=1.4\\cdot10^9Pa"

So, we get

"\\Delta l=\\frac{\\sigma}{E}=\\frac{65\\cdot10^6}{1.4\\cdot10^9}=0.046 m"

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