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Chapter 1: Q11-25E (page 1)

A circular steel wire 2.00 m long must stretch no more than 0.25 cm when a tensile force of 700N is applied to each end of the wire. What minimum diameter is required for the wire?

Short Answer

Expert verified

Minimum diameter is d = 1.9mm

Step by step solution

01

Given information:

Force F = 700N, Elongation ∆I=0.25cm, length l0 = 2m

02

Concept/Formula used:

Y=l0FAΔl

Where, Y is Young’s modulus, I0 is length of muscle, F is muscle force, A is cross-sectional area and ∆lis elongation.

03

Calculation for diameter:

Y=l0FAΔlA=l0FYΔlForsteelT=2.0×1011PaA=2.0m700N2.0×1011Pa0.25×10-2m=2.8×10-6m2A=πr2r=Aπ=2.8×10-6m2π=9.44×10-4md=2r=2×9.44×10-4m=1.9mm

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