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Chapter 4: Q37P (page 167)

Suppose that we hang a heavy ball with a mass of 10 kg (about 22 lb ) from a steel wire 3m long that is 3 mm in diameter. Steel is very stiff, and Young鈥檚 modulus for steel is unusually large, 2脳1011N/m2.Calculate the stretch螖尝 of the steel wire. This calculation shows why in many cases it is a very good approximation to pretend that the wire doesn鈥檛 stretch at all (鈥渋deal non extensible wire鈥�).

Short Answer

Expert verified

螖尝of steel wire is=2.079脳10鈭�4m鈮�0.2mm, Stretch is very negligible.

Step by step solution

01

Given data

Mass = 10kg

Diameter = 3mm

Length = 3m

02

Step 2:Solution

Young鈥檚 modulus,

Y=F/A螖尝/L鈬�螖尝L=FAY鈬�螖尝=FLAY

From equation,

F=mg=10脳9.8=98NL=3m

A =cross-sectional area =蟺谤2

=蟺脳(1.5脳10鈭�3)2=7.068脳10鈭�6m2

Y=2脳1011N/m2螖尝=98脳37.068脳10鈭�6脳2脳1011=2.079脳10鈭�4m鈮�0.2mm

Stretch is very negligible.

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