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 15, Problem 35A
To determine

(a)

The depth of cut for the given piece of round stock.

Expert Solution
Check Mark

Answer to Problem 35A

Depth of cut for the given piece of round stock should be 9.02 mm.

Explanation of Solution

Given information:

The formula for calculating the depth of round stock piece is given by -  C=D20.5×4×( D 2 )2F2

Where, C=depth of cut, D=diameter, F=length of flat

  Mathematics for Machine Technology, Chapter 15, Problem 35A , additional homework tip  1

Also, given that - D=34.80 mm, F=30.50 mm.

Calculation:

As per the problem statement, the formula for calculating the depth of round stock piece is given by -  C=D20.5×4×( D 2 )2F2

Here, we have been given D=34.80 mm, F=30.50 mm.

Putting above values in given formula for depth of cut and following order of operation as below.

  C=D20.5×4× ( D 2 )2F2C=34.8020.5×4× ( 34.80 2 )2 30.502          {Divide within parentheses}C=34.8020.5×4× ( 17.4 )2 30.502              {Square under radical sign}C=34.8020.5×4×302.76930.25              {Multiply within radical sign}             C=34.8020.5×1211.04930.25                 {Subtract within radical sign}C=34.8020.5×280.79                                 {Square root}C=34.8020.5×16.75679                                {Divide}C=17.40.5×16.75679                                   {Multiply}C=17.48.37839                                             {Subtract}C=9.02160C=9.02                                                             {Rounding off to 2 decimal places}

Hence, depth of cut for the given piece of round stock should be 9.02 mm.

To determine

(b)

To evaluate required depth of cut for the given piece of round stock.

Expert Solution
Check Mark

Answer to Problem 35A

Depth of cut for the given piece of round stock should be 8.74 mm.

Explanation of Solution

Given information:

The formula for calculating the depth of round stock piece is given by -  C=D20.5×4×( D 2 )2F2

Where, C=depth of cut, D=diameter, F=length of flat

  Mathematics for Machine Technology, Chapter 15, Problem 35A , additional homework tip  2

Also, given that - D=55.90 mm, F=40.60 mm.

Calculation:

As per the problem statement, the formula for calculating the depth of round stock piece is given by -  C=D20.5×4×( D 2 )2F2

Here, we have been given D=55.90 mm, F=40.60 mm.

Putting above values in given formula for depth of cut and following order of operation as below.

  C=D20.5×4× ( D 2 )2F2C=55.9020.5×4× ( 55.90 2 )2 40.602          {Divide within parentheses}C=34.8020.5×4× ( 27.95 )2 40.602            {Square under radical sign}C=34.8020.5×4×781.20251648.36         {Multiply within radical sign}             C=34.8020.5×3124.811648.36                {Subtract within radical sign}C=34.8020.5×1476.45                                {Square root}C=34.8020.5×16.75679                                {Divide}C=27.950.5×16.75679                                 {Multiply}C=27.9519.2123                                           {Subtract}C=8.7377C=8.74                                                             {Rounding off to 2 decimal places}

Hence, depth of cut for the given piece of round stock should be 8.74 mm.

To determine

(c)

To find out the required depth of cut for the given piece of round stock.

Expert Solution
Check Mark

Answer to Problem 35A

Depth of cut for the given piece of round stock should be 5.48 mm.

Explanation of Solution

Given information:

The formula for calculating the depth of round stock piece is given by -  C=D20.5×4×( D 2 )2F2

Where, C=depth of cut, D=diameter, F=length of flat

  Mathematics for Machine Technology, Chapter 15, Problem 35A , additional homework tip  3

Also, given that - D=91.40 mm, F=43.40 mm.

Calculation:

As per the problem statement, the formula for calculating the depth of round stock piece is given by -  C=D20.5×4×( D 2 )2F2

Here, we have been given D=91.40 mm, F=43.40 mm.

Putting above values in given formula for depth of cut and following order of operation as below.

  C=D20.5×4× ( D 2 )2F2C=91.4020.5×4× ( 91.40 2 )2 43.402          {Divide within parentheses}C=91.4020.5×4× ( 45.7 )2 43.402              {Square under radical sign}C=91.4020.5×4×2088.491883.56          {Multiply within radical sign}             C=91.4020.5×8353.961883.56                {Subtract within radical sign}C=91.4020.5×6470.4                                  {Square root}C=91.4020.5×80.4388                                   {Divide}C=45.70.5×80.4388                                      {Multiply}C=45.740.2194                                             {Subtract}C=5.48060C=5.48                                                              {Rounding off to 2 decimal places}

Hence, depth of cut for the given piece of round stock should be 5.48 mm.

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