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Chapter 12: Q67P (page 352)

A solid copper cube has an edge length of 85.5cm. How much stress must be applied to the cube to reduce the edge length to85.0cm ? The bulk modulus of copper is1.4脳1011N/m2 .

Short Answer

Expert verified

Applied stress is,p=2.4脳109鈥塏/尘2 .

Step by step solution

01

Understanding the given information

The length of the edge of copper is85.5鈥塩尘.

The desired length of copper is85.0鈥塩尘.

The bulk modulus for copper is 1.4x1011鈥塏/尘2.

02

Concept and formula used in the given question

Using the formula for the bulk modulus, you can find the applied stress with the help of the given data.

V=L3p=B螖VV

03

Calculation for the stress that must be applied to the cube to reduce the edge length to  85.0 cm

You know that the cube has volume v and in form length,

V=L3

Now, consider

螖VV=螖L3L3=(L+螖L)3鈭�l3L3=3L2螖LL3=3螖LL

Now, by the formula, pressure is

p=B螖VV=3B螖LL=3(1.4脳1011鈥�N/m2)(85.5鈥�m鈭�85.0鈥�m)85.5鈥�m=2.4脳109鈥塏/尘2

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