Chapter 69, Problem 9A

In Exercises 9 and 10, determine the height of gage blocks required to set the angles with a 5" sine bar.
a. 40°40'
b. 7°
c. 12°10'
d. 0°30'
e. 21°57'

To determine

(a)

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

Answer to Problem 9A

Height of the gage blocks: $=3.2583\text{'}\text{'}$

Explanation of Solution

Given information:

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

Calculations:

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

  $\begin{array}{l}Height\text{ of the block}=5\text{'}\text{'}\times \sin {40}^{\circ }{40}^{\text{'}}\\ h=5\text{'}\text{'}\times \sin {40.666}^{\circ }\\ \Rightarrow h=3.2583\text{'}\text{'}\end{array}$

Conclusion:

Height of the gage blocks: $=3.2583\text{'}\text{'}$

To determine

(b)

Find the height of gage blocks required to set the angle $7^{\circ }$ on a $5\text{'}\text{'}$ sine plate.

Answer to Problem 9A

Height of the gage blocks: $=0.6093\text{'}\text{'}$

Explanation of Solution

Given information:

Angle on a $5\text{'}\text{'}$ sine plate is $7^{\circ }$.

Calculations:

The height of the gage block required to set the angle $7^{\circ }$ on a $5\text{'}\text{'}$ sine block is calculated as:

  $\begin{array}{l}Height\text{ of the block}=10\text{'}\text{'}\times \sin {13}^{\circ }{10}^{\text{'}}\\ h=5\text{'}\text{'}\times \sin 7^{\circ }\\ \Rightarrow h=0.6093\text{'}\text{'}\end{array}$

Conclusion:

Height of the gage blocks: $=0.6093\text{'}\text{'}$

To determine

(c)

Find the height of gage blocks required to set the angle ${12}^{\circ }{10}^{\text{'}}$ on a $5\text{'}\text{'}$ sine plate.

Answer to Problem 9A

Height of the gage blocks: $=1.0538\text{'}\text{'}$

Explanation of Solution

Given information:

Angle on a $5\text{'}\text{'}$ sine plate is ${12}^{\circ }{10}^{\text{'}}$.

Calculations:

The height of the gage block required to set the angle ${12}^{\circ }{10}^{\text{'}}$ on a $5\text{'}\text{'}$ sine block is calculated as:

  $\begin{array}{l}Height\text{ of the block}=5\text{'}\text{'}\times \sin {12}^{\circ }{10}^{\text{'}}\\ h=5\text{'}\text{'}\times \sin 12.1667\\ \Rightarrow h=1.0538\text{'}\text{'}\end{array}$

Conclusion:

Height of the gage blocks: $=1.0538\text{'}\text{'}$

To determine

(d)

Find the height of gage blocks required to set the angle $0^{\circ }{30}^{\text{'}}$ on a $5\text{'}\text{'}$ sine plate.

Answer to Problem 9A

Height of the gage blocks: $=0.0436\text{'}\text{'}$

Explanation of Solution

Given information:

Angle on a $5\text{'}\text{'}$ sine plate is $0^{\circ }{30}^{\text{'}}$.

Calculations:

The height of the gage block required to set the angle $0^{\circ }{30}^{\text{'}}$ on a $5\text{'}\text{'}$ sine block is calculated as:

  $\begin{array}{l}Height\text{ of the block}=5\text{'}\text{'}\times \sin 0^{\circ }{30}^{\text{'}}\\ h=5\text{'}\text{'}\times \sin 0.5\\ \Rightarrow h={0.0436}^{"}\end{array}$

Conclusion:

Height of the gage blocks: $=0.0436\text{'}\text{'}$

To determine

(e)

Find the height of gage blocks required to set the angle ${21}^{\circ }{57}^{\text{'}}$ on a $5\text{'}\text{'}$ sine plate.

Answer to Problem 9A

Height of the gage blocks: $=1.869\text{'}\text{'}$

Explanation of Solution

Given information:

Angle on a $5\text{'}\text{'}$ sine plate is ${21}^{\circ }{57}^{\text{'}}$.

Calculations:

The height of the gage block required to set the angle ${21}^{\circ }{57}^{\text{'}}$ on a $5\text{'}\text{'}$ sine block is calculated as:

  $\begin{array}{l}Height\text{ of the block}=5\text{'}\text{'}\times \sin {21}^{\circ }{57}^{\text{'}}\\ h=5\text{'}\text{'}\times \sin {21.95}^{\circ }\\ \Rightarrow h={1.869}^{"}\end{array}$

Conclusion:

Height of the gage blocks: $={1.869}^{"}$