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Chapter 14: Q. 12 (page 383)

A 2000 N force stretches a wire by 1 mm. A second wire of the same material is twice as long and has twice the diameter. How much force is needed to stretch it by 1 mm? Explain

Short Answer

Expert verified

The force required to stretched the second wire by 1mmis4000N.

Step by step solution

01

Given information

Force on wire is F=2000N

The length of the second wire is role="math" localid="1650289361551" L2=2L1

The diameter of the second wire is role="math" localid="1650289386744" d2=2d1

鈭�L=1mm

02

Area of the second wire

As the diameter of the second wire is d2=2d1, the radius of the second wire is r2=2r1.

The area of the second wire is

role="math" localid="1650289304101" A2=蟺谤22=蟺2r12=4蟺谤12=4A

03

Force required to stretched the second wire by 1 mm

Linear stretch and compression is given by FA=Y鈭�LL.

The force required to stretch the second wire with the length of role="math" localid="1650288979993" 鈭�L=1mmis

role="math" localid="1650289601869" F2=A2Y鈭�LL2=4A1Y鈭�L2L1=2A1Y鈭�LL1=2F1=22000=4000N

Therefore, the force to stretch the second wire with the length of1mmis4000N.

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