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Concept explainers
(a)
The dimension over wires of the American national thread under given scenario.
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Answer to Problem 32A
Dimension over wires of the American national thread =0.9556 inches.
Explanation of Solution
Given information:
The formula to calculate the dimension of over wires as per American national standard is given as-
M=D−(1.5155×P)+(3×W)
Where, M= dimension over wires, D= Major dimension, P= Pitch and W= Wire diameter.
Also, it is given that D=0.8750, P=0.1250, W=0.0900.
Calculation:
As per the problem statement formula to calculate the dimension of over wires as per American national standard is given as-
M=D−(1.5155×P)+(3×W)
Here, we have been given D=0.8750, P=0.1250, W=0.0900. All dimension are in inches.
Putting above values in standard formula, we get-
M=D−(1.5155×P)+(3×W)⇒M=0.8750−(1.5155×0.1250)+(3×0.0900) {Multiplication within parentheses}⇒M=0.8750−0.1894375+0.27⇒M=0.8750+0.27−0.1894375 {Addition}⇒M=1.145−0.1894375 {Subtraction} ⇒M=0.95555625 ⇒M=0.9556 {Rounding off to 4 decimal places}
Hence, dimension over wires of the American national thread =0.9556 inches.
(b)
To calculate the dimension over wires of the American national thread under given scenario.
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Answer to Problem 32A
Dimension over wires of the American national thread =0.2792 inches.
Explanation of Solution
Given information:
The formula to calculate the dimension of over wires as per American national standard is given as-
M=D−(1.5155×P)+(3×W)
Where, M= dimension over wires, D= Major dimension, P= Pitch and W= Wire diameter.
Also, it is given that D=0.2500, P=0.0500, W=0.0350.
Calculation:
As per the problem statement formula to calculate the dimension of over wires as per American national standard is given as-
M=D−(1.5155×P)+(3×W)
Here, we have been given D=0.2500, P=0.0500, W=0.0350. All dimension are in inches.
Putting above values in standard formula, we get-
M=D−(1.5155×P)+(3×W)⇒M=0.2500−(1.5155×0.0500)+(3×0.0350) {Multiplication within parentheses}⇒M=0.2500−0.075775+0.1050 {Re-arranging}⇒M=0.2500+0.1050−0.075775 {Addition}⇒M=0.3550−0.075775 {Subtraction} ⇒M=0.279225 ⇒M=0.2792 {Rounding off to 4 decimal places}
Hence, dimension over wires of the American national thread =0.2792 inches.
(c)
To evaluate the dimension over wires of the American national thread.
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Answer to Problem 32A
Dimension over wires of the American national thread =0.6835 inches.
Explanation of Solution
Given information:
The formula to calculate the dimension of over wires as per American national standard is given as-
M=D−(1.5155×P)+(3×W)
Where, M= dimension over wires, D= Major dimension, P= Pitch and W= Wire diameter.
Also, it is given that D=0.6250, P=0.1000, W=0.0700.
Calculation:
As per the problem statement formula to calculate the dimension of over wires as per American national standard is given as-
M=D−(1.5155×P)+(3×W)
Here, we have been given D=0.6250, P=0.1000, W=0.0700. All dimension are in inches.
Putting above values in standard formula, we get-
M=D−(1.5155×P)+(3×W)⇒M=0.6250−(1.5155×0.1000)+(3×0.0700) {Multiplication within parentheses}⇒M=0.6250−0.15155+0.210 {Re-arranging}⇒M=0.6250+0.210−0.15155 {Addition}⇒M=0.8350−0.15155 {Subtraction} ⇒M=0.68345 ⇒M=0.6835 {Rounding off to 4 decimal places}
Hence, dimension over wires of the American national thread =0.6835 inches.
(d)
To evaluate the dimension over wires of the American national thread.
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Answer to Problem 32A
Dimension over wires of the American national thread =1.7997 inches.
Explanation of Solution
Given information:
The formula to calculate the dimension of over wires as per American national standard is given as-
M=D−(1.5155×P)+(3×W)
Where, M= dimension over wires, D= Major dimension, P= Pitch and W= Wire diameter.
Also, it is given that D=1.3750, P=0.16667, W=0.1500.
Calculation:
As per the problem statement formula to calculate the dimension of over wires as per American national standard is given as-
M=D−(1.5155×P)+(3×W)
Here, we have been given D=1.3750, P=0.16667, W=0.1500. All dimension are in inches.
Putting above values in standard formula, we get-
M=D−(1.5155×P)+(3×W)⇒M=1.3750−(1.5155×0.16667)+(3×0.1500) {Multiplication within parentheses}⇒M=1.3750−0.025259+0.4500 {Re-arranging}⇒M=1.3750+0.4500−0.025259 {Addition}⇒M=1.8250−0.025259 {Subtraction} ⇒M=1.799741 ⇒M=1.7997 {Rounding off to 4 decimal places}
Hence, dimension over wires of the American national thread =1.7997 inches.
(e)
To find the dimension over wires of the American national thread for the given parameters.
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Answer to Problem 32A
Dimension over wires of the American national thread =2.5744 inches.
Explanation of Solution
Given information:
The formula to calculate the dimension of over wires as per American national standard is given as-
M=D−(1.5155×P)+(3×W)
Where, M= dimension over wires, D= Major dimension, P= Pitch and W= Wire diameter.
Also, it is given that D=2.5000, P=0.2500, W=0.1500.
Calculation:
As per the problem statement formula to calculate the dimension of over wires as per American national standard is given as-
M=D−(1.5155×P)+(3×W)
Here, we have been given D=2.5000, P=0.2500, W=0.1500. All dimension are in inches.
Putting above values in standard formula, we get-
M=D−(1.5155×P)+(3×W)⇒M=2.5000−(1.5155×0.2500)+(3×0.1500) {Multiplication within parentheses}⇒M=2.5000−0.375575+0.4500 {Re-arranging}⇒M=2.5000+0.4500−0.375575 {Addition}⇒M=2.9500−0.375575 {Subtraction} ⇒M=2.574425 ⇒M=2.5744 {Rounding off to 4 decimal places}
Hence, dimension over wires of the American national thread =2.5744 inches.
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Chapter 16 Solutions
Mathematics For Machine Technology
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