Chapter 15, Problem 32A

To determine

(a)

The dimension over wires of the American national thread under given scenario.

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-

  $M=D-(1.5155\times P)+(3\times W)$

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-

  $M=D-(1.5155\times P)+(3\times W)$

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-

  $\begin{array}{l}M=D-(1.5155\times P)+(3\times W)\\ \Rightarrow M=0.8750-(1.5155\times 0.1250)+(3\times 0.0900)\text{ {Multiplication within parentheses}}\\ \Rightarrow M=0.8750-0.1894375+0.27\\ \Rightarrow M=0.8750+0.27-0.1894375\text{ {Addition}}\\ \Rightarrow M=1.145-0.1894375\text{ {Subtraction} }\\ \Rightarrow M=0.95555625\\ \Rightarrow M=0.9556\text{ {Rounding off to 4 decimal places}}\end{array}$

Hence, dimension over wires of the American national thread $=0.9556$ inches.

To determine

(b)

To calculate the dimension over wires of the American national thread under given scenario.

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-

  $M=D-(1.5155\times P)+(3\times W)$

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-

  $M=D-(1.5155\times P)+(3\times W)$

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-

  $\begin{array}{l}M=D-(1.5155\times P)+(3\times W)\\ \Rightarrow M=0.2500-(1.5155\times 0.0500)+(3\times 0.0350)\text{ {Multiplication within parentheses}}\\ \Rightarrow M=0.2500-0.075775+0.1050\text{ {Re-arranging}}\\ \Rightarrow M=0.2500+0.1050-0.075775\text{ {Addition}}\\ \Rightarrow M=0.3550-0.075775\text{ {Subtraction} }\\ \Rightarrow M=0.279225\\ \Rightarrow M=0.2792\text{ {Rounding off to 4 decimal places}}\end{array}$

Hence, dimension over wires of the American national thread $=0.2792$ inches.

To determine

(c)

To evaluate the dimension over wires of the American national thread.

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-

  $M=D-(1.5155\times P)+(3\times W)$

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-

  $M=D-(1.5155\times P)+(3\times W)$

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-

  $\begin{array}{l}M=D-(1.5155\times P)+(3\times W)\\ \Rightarrow M=0.6250-(1.5155\times 0.1000)+(3\times 0.0700)\text{ {Multiplication within parentheses}}\\ \Rightarrow M=0.6250-0.15155+0.210\text{ {Re-arranging}}\\ \Rightarrow M=0.6250+0.210-0.15155\text{ {Addition}}\\ \Rightarrow M=0.8350-0.15155\text{ {Subtraction} }\\ \Rightarrow M=0.68345\\ \Rightarrow M=0.6835\text{ {Rounding off to 4 decimal places}}\end{array}$

Hence, dimension over wires of the American national thread $=0.6835$ inches.

To determine

(d)

To evaluate the dimension over wires of the American national thread.

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-

  $M=D-(1.5155\times P)+(3\times W)$

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-

  $M=D-(1.5155\times P)+(3\times W)$

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-

  $\begin{array}{l}M=D-(1.5155\times P)+(3\times W)\\ \Rightarrow M=1.3750-(1.5155\times 0.16667)+(3\times 0.1500)\text{ {Multiplication within parentheses}}\\ \Rightarrow M=1.3750-0.025259+0.4500\text{ {Re-arranging}}\\ \Rightarrow M=1.3750+0.4500-0.025259\text{ {Addition}}\\ \Rightarrow M=1.8250-0.025259\text{ {Subtraction} }\\ \Rightarrow M=1.799741\\ \Rightarrow M=1.7997\text{ {Rounding off to 4 decimal places}}\end{array}$

Hence, dimension over wires of the American national thread $=1.7997$ inches.

To determine

(e)

To find the dimension over wires of the American national thread for the given parameters.

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-

  $M=D-(1.5155\times P)+(3\times W)$

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-

  $M=D-(1.5155\times P)+(3\times W)$

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-

  $\begin{array}{l}M=D-(1.5155\times P)+(3\times W)\\ \Rightarrow M=2.5000-(1.5155\times 0.2500)+(3\times 0.1500)\text{ {Multiplication within parentheses}}\\ \Rightarrow M=2.5000-0.375575+0.4500\text{ {Re-arranging}}\\ \Rightarrow M=2.5000+0.4500-0.375575\text{ {Addition}}\\ \Rightarrow M=2.9500-0.375575\text{ {Subtraction} }\\ \Rightarrow M=2.574425\\ \Rightarrow M=2.5744\text{ {Rounding off to 4 decimal places}}\end{array}$

Hence, dimension over wires of the American national thread $=2.5744$ inches.