Mechanical and civil engineers work with 'stress intensity factors' that have dimensions of mass (time) length The SI units for this factor are more commonly written as Pa√m (Pa is the kg s²√√m' abbreviation for a pascals, the SI unit of pressure). Convert the stress intensity factor of 1.25 Pa√mm to units of Pa√m. Show your work.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Stress Intensity Factors in Engineering**

Mechanical and civil engineers work with 'stress intensity factors' that have dimensions of 

\[
\frac{\text{mass}}{(\text{time})^2 \cdot \text{length}}.
\]

The SI units for this factor are 

\[
\frac{\text{kg}}{\text{s}^2 \cdot \sqrt{\text{m}}}
\]

more commonly written as 

\[
\text{Pa} \sqrt{\text{m}}
\]

(Pa is the abbreviation for pascals, the SI unit of pressure).

**Problem Statement:**

Convert the stress intensity factor of 1.25 

\[
\text{Pa} \sqrt{\text{mm}}
\]

to units of 

\[
\text{Pa} \sqrt{\text{m}}
\]

**Solution:**

To perform the conversion, recognize that 1 mm = 0.001 m, which implies 

\[
\sqrt{\text{mm}} = \sqrt{0.001 \, \text{m}} = 0.03162 \, \text{m}.
\]

Therefore, 1.25 

\[
\text{Pa} \sqrt{\text{mm}}
\]

is equivalent to:

\[
1.25 \times 0.03162 \, \text{Pa} \sqrt{\text{m}} = 0.039525 \, \text{Pa} \sqrt{\text{m}}.
\]

Thus, the stress intensity factor converts to approximately 0.0395 

\[
\text{Pa} \sqrt{\text{m}}.
\]
Transcribed Image Text:**Stress Intensity Factors in Engineering** Mechanical and civil engineers work with 'stress intensity factors' that have dimensions of \[ \frac{\text{mass}}{(\text{time})^2 \cdot \text{length}}. \] The SI units for this factor are \[ \frac{\text{kg}}{\text{s}^2 \cdot \sqrt{\text{m}}} \] more commonly written as \[ \text{Pa} \sqrt{\text{m}} \] (Pa is the abbreviation for pascals, the SI unit of pressure). **Problem Statement:** Convert the stress intensity factor of 1.25 \[ \text{Pa} \sqrt{\text{mm}} \] to units of \[ \text{Pa} \sqrt{\text{m}} \] **Solution:** To perform the conversion, recognize that 1 mm = 0.001 m, which implies \[ \sqrt{\text{mm}} = \sqrt{0.001 \, \text{m}} = 0.03162 \, \text{m}. \] Therefore, 1.25 \[ \text{Pa} \sqrt{\text{mm}} \] is equivalent to: \[ 1.25 \times 0.03162 \, \text{Pa} \sqrt{\text{m}} = 0.039525 \, \text{Pa} \sqrt{\text{m}}. \] Thus, the stress intensity factor converts to approximately 0.0395 \[ \text{Pa} \sqrt{\text{m}}. \]
Expert Solution
Step 1

Sol:-

Given :-kgs2m is represented as PamHere , We have to convert 1.25 Pamm to Pam

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