Can someone please help me to solve the following problem showing all work neatly thank you! 1.Steel tape used in a tape measure has a thickness of 0.0065 in. If the allowablestress is 68 ksi, what is the smallest spool diameter the tape can be wrapped around?[in.]Spool diameter D→Tape thickness t

Answered: 1. Steel tape used in a tape measure…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Can someone please help me to solve the following problem showing all work neatly thank you!

1.
Steel tape used in a tape measure has a thickness of 0.0065 in. If the allowable
stress is 68 ksi, what is the smallest spool diameter the tape can be wrapped around?
[in.]
Spool diameter D
→Tape thickness t

Expert Solution

Step 1: Given Data:

We can use the calculation for the stress in a curved beam to estimate the smallest spool diameter the tape may be wrapped around without going above the permitted stress:

thickness of tape (t)= 0.0065 in
$A l l o w a b l e space s t r e s s open parentheses sigma close parentheses equals 68 space k s i$
Young's Modulus (E)= 29,000 ksi

Formula: $sigma equals fraction numerator E cross times t over denominator r end fraction$

where,

$sigma equals i s space t h e space s t r e s s space left parenthesis 68 space k s i space i n space t h i s space c a s e right parenthesis$
E is the modulus of elasticity (assumed to be 29,000 ksi for steel)
t is the thickness of the steel tape (0.0065 in)
r is the radius of the spool.

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