Chapter 67, Problem 8A

To determine

(a)

The find the height $\left(H\right)$ of gage block with use of sine bar.

Answer to Problem 8A

  $H=3.258"$.

Explanation of Solution

Given information:

Length of the gage block $\left(L\right)$$=5”$ ; Sine bar angle $(\theta )$$={40}^{\circ }40\text{'}$

Concept Used:

As it's known that A sine bar is generally used with slip gauge blocks. The sine bar forms the hypotenuse of a right triangle, while the slip gauge blocks from the opposite side. The height of the slip gauge block is found by multiplying the sine of the desired angle by the length of the sine bar: $H=L*sin\left(\theta \right).$

Calculation:

As it's known that calculating the height with use of $H=L*sin\left(\theta \right).$ and use of conversion data in degree $\{1^{\circ }(\mathrm{deg})=60\text{'}(\min )\}$

  $\begin{array}{l}H=L\times sin\left(\theta \right)\\ \Rightarrow H=5"\times sin\left({40}^{\circ }40\text{'}\right)\\ \Rightarrow H=5"\times sin\left({40.667}^{\circ }\right)\\ \Rightarrow H=3.258"\end{array}$

Hence, the height $\left(H\right)$ of gage block is $H=3.258"$

To determine

(b)

The find the height $\left(H\right)$ of gage block with use of sine bar.

Answer to Problem 8A

  $H=0.609"$.

Explanation of Solution

Given information:

Length of the gage block $\left(L\right)$$=5”$ ; Sine bar angle $(\theta )$$=7^{\circ }$

Concept Used:

As it's known that A sine bar is generally used with slip gauge blocks. The sine bar forms the hypotenuse of a right triangle, while the slip gauge blocks from the opposite side. The height of the slip gauge block is found by multiplying the sine of the desired angle by the length of the sine bar: $H=L*sin\left(\theta \right).$

Calculation:

As it's known that calculating the height with use of $H=L*sin\left(\theta \right).$ and use of conversion data in degree $\{1^{\circ }(\mathrm{deg})=60\text{'}(\min )\}$

  $\begin{array}{l}H=L\times sin\left(\theta \right)\\ \Rightarrow H=5"\times sin\left(7^{\circ }\right)\\ \Rightarrow H=5"\times sin\left(7^{\circ }\right)\\ \Rightarrow H=0.609"\end{array}$

Hence, the height $\left(H\right)$ of gage block is $H=0.609"$

To determine

(c)

The find the height $\left(H\right)$ of gage block with use of sine bar.

Answer to Problem 8A

  $H=1.054"$.

Explanation of Solution

Given information:

Length of the gage block $\left(L\right)$$=5”$ ; Sine bar angle $(\theta )$$={12}^{\circ }10\text{'}$

Concept Used:

As it's known that A sine bar is generally used with slip gauge blocks. The sine bar forms the hypotenuse of a right triangle, while the slip gauge blocks from the opposite side. The height of the slip gauge block is found by multiplying the sine of the desired angle by the length of the sine bar: $H=L*sin\left(\theta \right).$

Calculation:

As it's known that calculating the height with use of $H=L*sin\left(\theta \right).$ and use of conversion data in degree $\{1^{\circ }(\mathrm{deg})=60\text{'}(\min )\}$

  $\begin{array}{l}H=L\times sin\left(\theta \right)\\ \Rightarrow H=5"\times sin\left({12}^{\circ }10\text{'}\right)\\ \Rightarrow H=5"\times sin\left({12.167}^{\circ }\right)\\ \Rightarrow H=1.054"\end{array}$

Hence, the height $\left(H\right)$ of gage block is $H=1.054"$

To determine

(d)

The find the height $\left(H\right)$ of gage block with use of sine bar.

Answer to Problem 8A

  $H=0.044"$.

Explanation of Solution

Given information:

Length of the gage block $\left(L\right)$$=5”$ ; Sine bar angle $(\theta )$$=0^{\circ }30\text{'}$

Concept Used:

As it's known that A sine bar is generally used with slip gauge blocks. The sine bar forms the hypotenuse of a right triangle, while the slip gauge blocks from the opposite side. The height of the slip gauge block is found by multiplying the sine of the desired angle by the length of the sine bar: $H=L*sin\left(\theta \right).$

Calculation:

As it's known that calculating the height with use of $H=L*sin\left(\theta \right).$ and use of conversion data in degree $\{1^{\circ }(\mathrm{deg})=60\text{'}(\min )\}$

  $\begin{array}{l}H=L\times sin\left(\theta \right)\\ \Rightarrow H=5"\times sin\left(0^{\circ }30\text{'}\right)\\ \Rightarrow H=5"\times sin\left({0.5}^{\circ }\right)\\ \Rightarrow H=0.044"\end{array}$

Hence, the height $\left(H\right)$ of gage block is $H=0.044"$

To determine

(e)

The find the height $\left(H\right)$ of gage block with use of sine bar.

Answer to Problem 8A

  $H=1.869"$.

Explanation of Solution

Given information:

Length of the gage block $\left(L\right)$$=5”$ ; Sine bar angle $(\theta )$$={21}^{\circ }57\text{'}$

Concept Used:

As it's known that A sine bar is generally used with slip gauge blocks. The sine bar forms the hypotenuse of a right triangle, while the slip gauge blocks from the opposite side. The height of the slip gauge block is found by multiplying the sine of the desired angle by the length of the sine bar: $H=L*sin\left(\theta \right).$

Calculation:

As it's known that calculating the height with use of $H=L*sin\left(\theta \right).$ and use of conversion data in degree $\{1^{\circ }(\mathrm{deg})=60\text{'}(\min )\}$

  $\begin{array}{l}H=L\times sin\left(\theta \right)\\ \Rightarrow H=5"\times sin\left({21}^{\circ }57\text{'}\right)\\ \Rightarrow H=5"\times sin\left({21.95}^{\circ }\right)\\ \Rightarrow H=1.869"\end{array}$

Hence, the height $\left(H\right)$ of gage block is $H=1.869"$

To determine

(f)

The find the height $\left(H\right)$ of gage block with use of sine bar.

Answer to Problem 8A

  $H=1.150"$.

Explanation of Solution

Given information:

Length of the gage block $\left(L\right)$$=5”$ ; Sine bar angle $(\theta )$$={13}^{\circ }18\text{'}$

Concept Used:

As it's known that A sine bar is generally used with slip gauge blocks. The sine bar forms the hypotenuse of a right triangle, while the slip gauge blocks from the opposite side. The height of the slip gauge block is found by multiplying the sine of the desired angle by the length of the sine bar: $H=L*sin\left(\theta \right).$

Calculation:

As it's known that calculating the height with use of $H=L*sin\left(\theta \right).$ and use of conversion data in degree $\{1^{\circ }(\mathrm{deg})=60\text{'}(\min )\}$

  $\begin{array}{l}H=L\times sin\left(\theta \right)\\ \Rightarrow H=5"\times sin\left({13}^{\circ }18\text{'}\right)\\ \Rightarrow H=5"\times sin\left({13.3}^{\circ }\right)\\ \Rightarrow H=1.150"\end{array}$

Hence, the height $\left(H\right)$ of gage block is $H=1.150"$

To determine

(g)

The find the height $\left(H\right)$ of gage block with use of sine bar.

Answer to Problem 8A

  $H=3.160"$.

Explanation of Solution

Given information:

Length of the gage block $\left(L\right)$$=5”$ ; Sine bar angle $(\theta )$$={39}^{\circ }12\text{'}$

Concept Used:

As it's known that A sine bar is generally used with slip gauge blocks. The sine bar forms the hypotenuse of a right triangle, while the slip gauge blocks from the opposite side. The height of the slip gauge block is found by multiplying the sine of the desired angle by the length of the sine bar: $H=L*sin\left(\theta \right).$

Calculation:

As it's known that calculating the height with use of $H=L*sin\left(\theta \right).$ and use of conversion data in degree $\{1^{\circ }(\mathrm{deg})=60\text{'}(\min )\}$

  $\begin{array}{l}H=L\times sin\left(\theta \right)\\ \Rightarrow H=5"\times sin\left({39}^{\circ }12\text{'}\right)\\ \Rightarrow H=5"\times sin\left({39.2}^{\circ }\right)\\ \Rightarrow H=3.160"\end{array}$

Hence, the height $\left(H\right)$ of gage block is $H=3.160"$

To determine

(h)

The find the height $\left(H\right)$ of gage block with use of sine bar.

Answer to Problem 8A

  $H=3.525"$.

Explanation of Solution

Given information:

Length of the gage block $\left(L\right)$$=5”$ ; Sine bar angle $(\theta )$$={44}^{\circ }50\text{'}$

Concept Used:

As it's known that A sine bar is generally used with slip gauge blocks. The sine bar forms the hypotenuse of a right triangle, while the slip gauge blocks from the opposite side. The height of the slip gauge block is found by multiplying the sine of the desired angle by the length of the sine bar: $H=L*sin\left(\theta \right).$

Calculation:

As it's known that calculating the height with use of $H=L*sin\left(\theta \right).$ and use of conversion data in degree $\{1^{\circ }(\mathrm{deg})=60\text{'}(\min )\}$

  $\begin{array}{l}H=L\times sin\left(\theta \right)\\ \Rightarrow H=5"\times sin\left({44}^{\circ }50\text{'}\right)\\ \Rightarrow H=5"\times sin\left({44.833}^{\circ }\right)\\ \Rightarrow H=3.525"\end{array}$

Hence, the height $\left(H\right)$ of gage block is $H=3.525"$

To determine

(i)

The find the height $\left(H\right)$ of gage block with use of sine bar.

Answer to Problem 8A

  $H=0.720"$.

Explanation of Solution

Given information:

Length of the gage block $\left(L\right)$$=5”$ ; Sine bar angle $(\theta )$$=8^{\circ }17\text{'}$

Concept Used:

As it's known that A sine bar is generally used with slip gauge blocks. The sine bar forms the hypotenuse of a right triangle, while the slip gauge blocks from the opposite side. The height of the slip gauge block is found by multiplying the sine of the desired angle by the length of the sine bar: $H=L*sin\left(\theta \right).$

Calculation:

As it's known that calculating the height with use of $H=L*sin\left(\theta \right).$ and use of conversion data in degree $\{1^{\circ }(\mathrm{deg})=60\text{'}(\min )\}$

  $\begin{array}{l}H=L\times sin\left(\theta \right)\\ \Rightarrow H=5"\times sin\left(8^{\circ }17\text{'}\right)\\ \Rightarrow H=5"\times sin\left({8.283}^{\circ }\right)\\ \Rightarrow H=0.720"\end{array}$

Hence, the height $\left(H\right)$ of gage block is $H=0.720"$