Chapter 69, Problem 10A

In Exercises 9 and 10, determine the height of gage blocks required to set the angles with a 5" sine bar.
a. 13°18'
b. 39°12'
c. 44°50'
d. 8°17'
e. 15°45'

To determine

(a)

Find the height of gage blocks required to set the angle ${13}^{\circ }{18}^{\text{'}}$ on a $5\text{'}\text{'}$ sine plate.

Answer to Problem 10A

Height of the gage blocks: $=1.1502\text{'}\text{'}$

Explanation of Solution

Given information:

Angle on a $5\text{'}\text{'}$ sine plate is ${13}^{\circ }{18}^{\text{'}}$.

Calculations:

The height of the gage block required to set the angle ${13}^{\circ }{18}^{\text{'}}$ on a $5\text{'}\text{'}$ sine block is calculated as:

  $\begin{array}{l}Height\text{ of the block}=5\text{'}\text{'}\times \sin {13}^{\circ }{18}^{\text{'}}\\ h=5\text{'}\text{'}\times \sin {13.3}^{\circ }\\ \Rightarrow h=1.1502\text{'}\text{'}\end{array}$

Conclusion:

Height of the gage blocks: $=1.1502\text{'}\text{'}$

To determine

(b)

Find the height of gage blocks required to set the angle ${39}^{\circ }{12}^{\text{'}}$ on a $5\text{'}\text{'}$ sine plate.

Answer to Problem 10A

Height of the gage blocks: $=3.16\text{'}\text{'}$

Explanation of Solution

Given information:

Angle on a $5\text{'}\text{'}$ sine plate is ${39}^{\circ }{12}^{\text{'}}$.

Calculations:

The height of the gage block required to set the angle ${39}^{\circ }{12}^{\text{'}}$ on a $5\text{'}\text{'}$ sine block is calculated as:

  $\begin{array}{l}Height\text{ of the block}=5\text{'}\text{'}\times \sin {39}^{\circ }{12}^{\text{'}}\\ h=5\text{'}\text{'}\times \sin {39.2}^{\circ }\\ \Rightarrow h=3.16\text{'}\text{'}\end{array}$

Conclusion:

Height of the gage blocks: $=3.16\text{'}\text{'}$

To determine

(c)

Find the height of gage blocks required to set the angle ${40}^{\circ }{50}^{\text{'}}$ on a $5\text{'}\text{'}$ sine plate.

Answer to Problem 10A

Height of the gage blocks: $=3.5252\text{'}\text{'}$

Explanation of Solution

Given information:

Angle on a $5\text{'}\text{'}$ sine plate is ${40}^{\circ }{50}^{\text{'}}$.

Calculations:

The height of the gage block required to set the angle ${40}^{\circ }{50}^{\text{'}}$ on a $5\text{'}\text{'}$ sine block is calculated as:

  $\begin{array}{l}Height\text{ of the block}=5\text{'}\text{'}\times \sin {40}^{\circ }{50}^{\text{'}}\\ h=5\text{'}\text{'}\times \sin {40.833}^{\circ }\\ \Rightarrow h=3.5252\text{'}\text{'}\end{array}$

Conclusion:

Height of the gage blocks: $=3.5252\text{'}\text{'}$

To determine

(d)

Find the height of gage blocks required to set the angle $8^{\circ }{17}^{\text{'}}$ on a $5\text{'}\text{'}$ sine plate.

Answer to Problem 10A

Height of the gage blocks: $=0.72\text{'}\text{'}$

Explanation of Solution

Given information:

Angle on a $5\text{'}\text{'}$ sine plate is $8^{\circ }{17}^{\text{'}}$.

Calculations:

The height of the gage block required to set the angle $8^{\circ }{17}^{\text{'}}$ on a $5\text{'}\text{'}$ sine block is calculated as:

  $\begin{array}{l}Height\text{ of the block}=5\text{'}\text{'}\times \sin 8^{\circ }{17}^{\text{'}}\\ h=5\text{'}\text{'}\times \sin {8.283}^{\circ }\\ \Rightarrow h={0.72}^{"}\end{array}$

Conclusion:

Height of the gage blocks: $={0.72}^{"}$

To determine

(e)

Find the height of gage blocks required to set the angle ${15}^{\circ }{45}^{\text{'}}$ on a $5\text{'}\text{'}$ sine plate.

Answer to Problem 10A

Height of the gage blocks: $=1.3572\text{'}\text{'}$

Explanation of Solution

Given information:

Angle on a $5\text{'}\text{'}$ sine plate is ${15}^{\circ }{45}^{\text{'}}$.

Calculations:

The height of the gage block required to set the angle ${15}^{\circ }{45}^{\text{'}}$ on a $5\text{'}\text{'}$ sine block is calculated as:

  $\begin{array}{l}Height\text{ of the block}=5\text{'}\text{'}\times \sin {15}^{\circ }{45}^{\text{'}}\\ h=5\text{'}\text{'}\times \sin {\mathrm{15..75}}^{\circ }\\ \Rightarrow h={1.3572}^{"}\end{array}$

Conclusion:

Height of the gage blocks: $={1.3572}^{"}$