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Chapter 1: Q11-28E (page 1)

A nylon rope used by mountaineers elongates 1.10m 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

6.77x108Pa

Step by step solution

01

Given information

LengthI0=45.0m,diameterd=7.0mm,Elongation∆I=1.10m,Climbermassm=65kg

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 Δlis elongation.

03

Area of rope

A=πd24=π7.0×10-3m24=3.85×10-5m2

04

Weight of climber

W=mg=65kg9.81m/s2=637N

05

Young’s modulus calculation

Y=45m637N3.85××10-5m21.1o×10-2m=6.77×108Pa

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