   Chapter 9, Problem 65P

Chapter
Section
Textbook Problem

The Deformation of Solids65. A 200.-kg load is hung on a wire of length 4.00 m, cross-section area 0.200 × 10−4 m2, and Young’s modulus 8.00 × 1010 N/m2. What is its increase in length?

To determine
The increase in length of a wire.

Explanation
Yong’s modulus is defined as Y=stress/strain=(F/A)/(ΔL/L0) and from which, the increase in length of that wire is calculated as ΔL=(FL0)/(AY) .

Given info: The cross-sectional area of the wire is 0.200×104m2 , Young’s modulus of the wire is 8.00×1010N/m2 , length of the wire is 4.00m , mass of the load is 200kg , and acceleration due to gravity is 9.80m/s2 .

The formula for the increase in length of the wire is,

ΔL=(mg)L0AY

• m is mass of the load.
• g is acceleration due to gravity.
• L0 is length of the wire.
• A is cross-sectional area of the wire.
• Y is Young’s modulus of the wire.

Substitute 200kg for m , 9

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