Mathematics for Machine Technology
Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 67, Problem 31A

The length L of the point drill with included angle A can be calculated using the formula L = k ϕ where ϕ is the diameter of the drill and k = 1 2 tan ( ° 90 ° A 2 ) . Determine k for each of the following angles. Round your answer to three decimal places.

Chapter 67, Problem 31A, The length L of the point drill with included angle A can be calculated using the formula L=kwhere

Expert Solution
Check Mark
To determine

(a)

Find k for the given angle.

Answer to Problem 31A

  k=0.866

Explanation of Solution

Given information:

The relation:

k=12tan(90A2)

The angle A=60

Calculations:

Substituting the value A=60 in the relation given for k:

  k=12tan( 90 60 2)k=12tan( 60)=1.7322k=0.866

Conclusion:

The value of k is 0.866.

Expert Solution
Check Mark
To determine

(b)

Find k for the given angle.

Answer to Problem 31A

  k=0.575

Explanation of Solution

Given information:

The relation:

k=12tan(90A2)

The angle A=82

Calculations:

Substituting the value A=82 in the relation given for k:

  k=12tan( 90 82 2)k=12tan( 49)=1.1502k=0.575

Conclusion:

The value of k is 0.575.

Expert Solution
Check Mark
To determine

(c)

Find k for the given angle.

Answer to Problem 31A

  k=0.5

Explanation of Solution

Given information:

The relation:

k=12tan(90A2)

The angle A=90

Calculations:

Substituting the value A=90 in the relation given for k:

  k=12tan( 90 90 2)k=12tan( 45)=1.0002k=0.500

Conclusion:

The value of k is 0.500.

Expert Solution
Check Mark
To determine

(d)

Find k for the given angle.

Answer to Problem 31A

  k=0.300

Explanation of Solution

Given information:

The relation:

k=12tan(90A2)

The angle A=118

Calculations:

Substituting the value A=118 in the relation given for k:

  k=12tan( 90 118 2)k=12tan( 31)=0.6002k=0.300

Conclusion:

The value of k is 0.300.

Expert Solution
Check Mark
To determine

(e)

Find k for the given angle.

Answer to Problem 31A

  k=0.207

Explanation of Solution

Given information:

The relation:

k=12tan(90A2)

The angle A=135

Calculations:

Substituting the value A=135 in the relation given for k:

  k=12tan( 90 135 2)k=12tan( 22.5)=0.4142k=0.207

Conclusion:

The value of k is 0.207.

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