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Chapter 1: Q28E (page 359)

A nylon rope used by mountaineers elongates 1.10 m under the weight of a 65.0-kg climber. If the rope is 45.0 m in length and 7.0 mm in diameter, what is Young’s modulus for nylon?

Short Answer

Expert verified

6.77×108Pa

Step by step solution

01

Given information

Length: l0=45.0m,

diameter: d = 7.0 mm,

Elongation: ∆l=1.10m,

Climber mass: m = 65 kg .

02

Concept/Formula used

Y=l0F∆l

Where, Y is Young’s modulus, l0 is length of muscle, F is muscle force, A is cross-sectional area and ∆lis elongation.

03

Area of rope

Area=(d24)=((7.0×10-3m)24)=3.85×10-5m2

04

Weight of climber

W=mg=(65kg)(9.81m/s2)=637N

05

Young’s modulus calculation

Y=(45m)(637N)(3.85×10-5m2)(1.10×10-2m)=6.77×108Pa

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