EBK MATHEMATICS FOR MACHINE TECHNOLOGY
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
8th Edition
ISBN: 9781337798396
Author: SMITH
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Chapter 16, 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

  EBK MATHEMATICS FOR MACHINE TECHNOLOGY, Chapter 16, 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

  EBK MATHEMATICS FOR MACHINE TECHNOLOGY, Chapter 16, 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

  EBK MATHEMATICS FOR MACHINE TECHNOLOGY, Chapter 16, 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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For the Big-M tableau (of a maximization LP and row0 at bottom and M=1000), Z Ꮖ 1 x2 x3 81 82 83 e4 a4 RHS 0 7 0 0 1 0 4 3 -3 20 0 -4.5 0 0 0 1 -8 -2.5 2.5 6 0 7 0 1 0 0 8 3 -3 4 0 -1 50 1 0 0 0-2 -1 1 4 0000 0 30 970 200 If the original value of c₁ is increased by 60, what is the updated value of c₁ (meaning keeping the same set for BV. -10? Having made that change, what is the new optimal value for ž?
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