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Chapter 14: Q. 32 (page 385)

A 70 kg mountain climber dangling in a crevasse stretches a 50-m-long, 1.0-cm-diameter rope by 8.0 cm. What is Young鈥檚 modulus for the rope?

Short Answer

Expert verified

Young's modulus of the rope is5.5脳109N/m2.

Step by step solution

01

Given information

The mass of the climber is m=70kg

鈭�L=8cm=0.08m

The length of the rope is L=50m

The radius of the rope is r=1.0cm2=0.5cm=0.005m

02

Tensile stress

The tensile stress is given by FA.

role="math" localid="1650295387964" FA=mg蟺谤2=70脳9.8蟺0.0052=8.73脳106N/m2

03

Strain

The strain is given by 鈭�LL.

鈭�LL=0.0850=0.0016

04

Young's modulus of the rope 

The Young's modulus of the rope is given by Y=FA鈭�LL.

Substitute the obtained values

localid="1650296015704" Y=8.73脳1060.0016=5.5脳109N/m2

Therefore, Young's modulus of the rope is localid="1650296024948" 5.46脳109N/m2.

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