(a)
Interpretation:
The maximum force applied on an aluminum rod needs to be determined.
Concept Introduction:
Expression for stress (S) is given as follows:
Here, Force is F, the cross-sectional area is A.
The expression for Young's Modulus (E) is as follows:
Here, e is the strain.
Length of the rod (L) is expressed as follows:
Strain in the rod is expressed as (e):
Answer to Problem 14.15P
The maximum force applied is 271 N.
Explanation of Solution
Here,
l =10 mm
L= 10 + 0.002
L= 10.002 m
Strain,
e = 0.0002 m
To calculate the area of the rod,
Selecting the value of Young's modulus as 69×109 N/m2 from the table of physical properties of common alloys,
Substitute 69×109 N/m2for E, 0.1963 ×10-4 m2 for A and 0.0002 for e in below equations,
The maximum force applied is 271 N.
(b)
Interpretation:
The maximum force applications on magnesium rod needs to be determined.
Concept Introduction:
Expression for stress (S) is given as follows:
Here, Force is F, the cross-sectional area is A.
The expression for Young's Modulus (E) is as follows:
Here, e is the strain.
Length of the rod (L) is expressed as follows:
Strain in the rod is expressed as (e):
Answer to Problem 14.15P
The maximum force applied is 176 N.
Explanation of Solution
Here,
l =10 mm
L= 10 + 0.002
L= 10.002 m
Strain,
e = 0.0002 m
To calculate the area of the rod,
Selecting the value of Young's modulus as 45×106N/m 2.
Substituting the required values in the below equation,
The maximum force applied in the bar is 176 N.
(c)
Interpretation:
The maximum force applied on beryllium rod needs to be determined.
Concept Introduction:
Expression for stress (S) is given as follows:
Here Force is F, the cross-sectional area is A.
The expression for Young's Modulus (E) is
Where e is the Strain.
Length of the rod (L) is expressed as:
Strain in the rod is expressed as (e):
Answer to Problem 14.15P
The maximum force applied on beryllium is 1138 N.
Explanation of Solution
Here,
l =10 mm
L= 10 + 0.002
L= 10.002 m
Strain,
e = 0.0002 m
To calculate the area of the rod:
From the table of common metals, select the Young's modulus of beryllium as 287×109 N/m2
Substitute the required values in the below equation,
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Chapter 14 Solutions
Essentials Of Materials Science And Engineering, Si Edition
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