Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 29, Problem 11A
To determine

(a)

The dimension in the bilateral tolerance.

Expert Solution
Check Mark

Answer to Problem 11A

The dimension in the bilateral tolerance is 0.943±0.005.

Explanation of Solution

Given information:

The unilateral tolerance is 0.9380.000+0.010.

Write the expression for the total tolerance.

  Tt=U+L   ...........(I)

Here, the upper limit is U and the lower limit is L.

Write the expression for the mean dimension.

  Md=Bd+Tt2   ...........(II)

Here, the basic dimension is Bd.

Write the expression for the bilateral tolerance.

  Tb=Md±Tt2   ...........(III)

Calculation:

Substitute 0.010 for U and 0.000 for L in Equation (I).

  Tt=0.010+(0.000)=0.010

Substitute 0.010 for Tt and 0.938 for Bd in Equation (II).

  Md=0.938+0.0102=0.938+0.005=0.943

Substitute 0.010 for Tt and 0.943 for Md in Equation (III).

  Tb=0.943±0.0102=0.943±0.005

Conclusion:

The dimension in the bilateral tolerance is 0.943±0.005.

To determine

(b)

The dimension in the bilateral tolerance.

Expert Solution
Check Mark

Answer to Problem 11A

The dimension in the bilateral tolerance is 1.687±0.001.

Explanation of Solution

Given information:

The unilateral tolerance is 1.6860.000+0.002.

Calculation:

Substitute 0.002 for U and 0.000 for L in Equation (I).

  Tt=0.002+(0.000)=0.002

Substitute 0.002 for Tt and 1.686 for Bd in Equation (II).

  Md=1.686+0.0022=1.686+0.001=1.687

Substitute 0.002 for Tt and 1.687 for Md in Equation (III).

  Tb=1.687±0.0022=1.687±0.001

Conclusion:

The dimension in the bilateral tolerance is 1.687±0.001.

To determine

(c)

The dimension in the bilateral tolerance.

Expert Solution
Check Mark

Answer to Problem 11A

The dimension in the bilateral tolerance is 2.998±0.002.

Explanation of Solution

Given information:

The unilateral tolerance is 3.0000.004+0.000.

Calculation:

Substitute 0.000 for U and 0.004 for L in Equation (I).

  Tt=0.000+(0.004)=0.004

Substitute 0.004 for Tt and 3.000 for Bd in Equation (II).

  Md=3.000+0.0042=3.0000.002=2.998

Substitute 0.004 for Tt and 2.998 for Md in Equation (III).

  Tb=2.998±( 0.00 4 2)=2.998±0.002

Conclusion:

The dimension in the bilateral tolerance is 2.998±0.002.

To determine

(d)

The dimension in the bilateral tolerance.

Expert Solution
Check Mark

Answer to Problem 11A

The dimension in the bilateral tolerance is 0.069±0.004.

Explanation of Solution

Given information:

The unilateral tolerance is 0.0730.008+0.000.

Calculation:

Substitute 0.000 for U and 0.008 for L in Equation (I).

  Tt=0.000+(0.008)=0.008

Substitute 0.008 for Tt and 0.073 for Bd in Equation (II).

  Md=0.073+0.0082=0.0730.004=0.069

Substitute 0.008 for Tt and 0.069 for Md in Equation (III).

  Tb=0.069±( 0.00 8 2)=0.069±0.004

Conclusion:

The dimension in the bilateral tolerance is 0.069±0.004.

To determine

(e)

The dimension in the bilateral tolerance.

Expert Solution
Check Mark

Answer to Problem 11A

The dimension in the bilateral tolerance is 4.1880±0.007.

Explanation of Solution

Given information:

The unilateral tolerance is 4.18730.000+0.0014.

Calculation:

Substitute 0.0014 for U and 0.000 for L in Equation (I).

  Tt=0.0014+(0.000)=0.0014

Substitute 0.0014 for Tt and 4.1873 for Bd in Equation (II).

  Md=4.1873+0.00142=4.1873+0.007=4.1880

Substitute 0.0014 for Tt and 4.1880 for Md in Equation (III).

  Tb=4.1880±0.00142=4.1880±0.007

Conclusion:

The dimension in the bilateral tolerance is 4.1880±0.007.

To determine

(f)

The dimension in the bilateral tolerance.

Expert Solution
Check Mark

Answer to Problem 11A

The dimension in the bilateral tolerance is 0.9984±0.0037.

Explanation of Solution

Given information:

The unilateral tolerance is 1.00210.0074+0.000.

Calculation:

Substitute 0.000 for U and 0.0074 for L in Equation (I).

  Tt=0.000+(0.0074)=0.0074

Substitute 0.0074 for Tt and 1.0021 for Bd in Equation (II).

  Md=1.0021+( 0.007 4 2)=1.00210.0037=0.9984

Substitute 0.0074 for Tt and 0.9984 for Md in Equation (III).

  Tb=0.9984±0.00742=0.9984±0.0037

Conclusion:

The dimension in the bilateral tolerance is 0.9984±0.0037.

To determine

(g)

The dimension in the bilateral tolerance.

Expert Solution
Check Mark

Answer to Problem 11A

The dimension in the bilateral tolerance is 1.0006±0.0004.

Explanation of Solution

Given information:

The unilateral tolerance is 1.00100.0008+0.000.

Calculation:

Substitute 0.000 for U and 0.0008 for L in Equation (I).

  Tt=0.000+(0.0008)=0.0008

Substitute 0.0008 for Tt and 1.0010 for Bd in Equation (II).

  Md=1.0010+( 0.000 8 2)=1.00100.0004=1.0006

Substitute 0.0008 for Tt and 1.0006 for Md in Equation (III).

  Tb=1.0006±0.00082=1.0006±0.0004

Conclusion:

The dimension in the bilateral tolerance is 1.0006±0.0004.

To determine

(h)

The dimension in the bilateral tolerance.

Expert Solution
Check Mark

Answer to Problem 11A

The dimension in the bilateral tolerance is 8.4660±0.0011.

Explanation of Solution

Given information:

The unilateral tolerance is 8.46490.000+0.0022.

Calculation:

Substitute 0.0022 for U and 0.000 for L in Equation (I).

  Tt=0.0022+(0.000)=0.0022

Substitute 0.0022 for Tt and 8.4649 for Bd in Equation (II).

  Md=8.4649+0.00222=8.4649+0.0011=8.4660

Substitute 0.0022 for Tt and 8.4660 for Md in Equation (III).

  Tb=8.4660±0.00222=8.4660±0.0011

Conclusion:

The dimension in the bilateral tolerance is 8.4660±0.0011.

To determine

(i)

The dimension in the bilateral tolerance.

Expert Solution
Check Mark

Answer to Problem 11A

The dimension in the bilateral tolerance is 44.31mm±0.01mm.

Explanation of Solution

Given information:

The unilateral tolerance is 44.30mm0.00mm+0.02mm.

Calculation:

Substitute 0.02mm for U and 0.00mm for L in Equation (I).

  Tt=0.02mm+(0.00mm)=0.02mm

Substitute 0.02mm for Tt and 44.30mm for Bd in Equation (II).

  Md=44.30mm+0.02mm2=44.30mm+0.01mm=44.31mm

Substitute 0.010 for Tt and 44.31mm for Md in Equation (III).

  Tb=44.31mm±0.02mm2=44.31mm±0.01mm

Conclusion:

The dimension in the bilateral tolerance is 44.31mm±0.01mm.

To determine

(j)

The dimension in the bilateral tolerance.

Expert Solution
Check Mark

Answer to Problem 11A

The dimension in the bilateral tolerance is 10.02mm±0.04mm.

Explanation of Solution

Given information:

The unilateral tolerance is 10.06mm0.08mm+0.00mm.

Calculation:

Substitute 0.00mm for U and 0.08mm for L in Equation (I).

  Tt=0.00mm+(0.08mm)=0.08mm

Substitute 0.08mm for Tt and 10.06mm for Bd in Equation (II).

  Md=10.06mm+( 0.08mm2)=10.06mm0.04mm=10.02mm

Substitute 0.08mm for Tt and 10.02mm for Md in Equation (III).

  Tb=10.02mm±( 0.08mm2)=10.02mm±0.04mm

Conclusion:

The dimension in the bilateral tolerance is 10.02mm±0.04mm.

To determine

(k)

The dimension in the bilateral tolerance.

Expert Solution
Check Mark

Answer to Problem 11A

The dimension in the bilateral tolerance is 64.92mm±0.03mm.

Explanation of Solution

Given information:

The unilateral tolerance is 64.89mm0.00mm+0.06mm.

Calculation:

Substitute 0.06mm for U and 0.00mm for L in Equation (I).

  Tt=0.06mm+(0.00mm)=0.06mm

Substitute 0.06mm for Tt and 64.89mm for Bd in Equation (II).

  Md=64.89mm+0.06mm2=64.89mm+0.03mm=64.92mm

Substitute 0.06mm for Tt and 64.92mm for Md in Equation (III).

  Tb=64.92mm±0.06mm2=64.92mm±0.03mm

Conclusion:

The dimension in the bilateral tolerance is 64.92mm±0.03mm.

To determine

(l)

The dimension in the bilateral tolerance.

Expert Solution
Check Mark

Answer to Problem 11A

The dimension in the bilateral tolerance is 38.016mm±0.028mm.

Explanation of Solution

Given information:

The unilateral tolerance is 37.988mm0.00mm+0.056mm.

Calculation:

Substitute 0.056mm for U and 0.00mm for L in Equation (I).

  Tt=0.056mm+(0.00mm)=0.056mm

Substitute 0.056mm for Tt and 37.988mm for Bd in Equation (II).

  Md=37.988mm+0.056mm2=37.988mm+0.028mm=38.016mm

Substitute 0.056mm for Tt and 38.016mm for Md in Equation (III).

  Tb=38.016mm±0.056mm2=38.016mm±0.028mm

Conclusion:

The dimension in the bilateral tolerance is 38.016mm±0.028mm.

To determine

(m)

The dimension in the bilateral tolerance.

Expert Solution
Check Mark

Answer to Problem 11A

The dimension in the bilateral tolerance is 124.9915mm±0.085mm.

Explanation of Solution

Given information:

The unilateral tolerance is 125.00mm0.017mm+0.00mm.

Calculation:

Substitute 0.00mm for U and 0.017mm for L in Equation (I).

  Tt=0.00mm+(0.017mm)=0.017mm

Substitute 0.017mm for Tt and 125.00mm for Bd in Equation (II).

  Md=125.00mm+( 0.017mm2)=125.00mm0.085mm=124.9915mm

Substitute 0.017mm for Tt and 124.9915mm for Md in Equation (III).

  Tb=124.9915mm±( 0.017mm2)=124.9915mm±0.085mm

Conclusion:

The dimension in the bilateral tolerance is 124.9915mm±0.085mm.

To determine

(n)

The dimension in the bilateral tolerance.

Expert Solution
Check Mark

Answer to Problem 11A

The dimension in the bilateral tolerance is 43.078mm±0.013mm.

Explanation of Solution

Given information:

The unilateral tolerance is 43.091mm0.026mm+0.00mm.

Calculation:

Substitute 0.00mm for U and 0.026mm for L in Equation (I).

  Tt=0.00mm+(0.026mm)=0.026mm

Substitute 0.026mm for Tt and 43.091mm for Bd in Equation (II).

  Md=43.091mm+( 0.026mm2)=43.091mm0.013mm=43.078mm

Substitute 0.026mm for Tt and 43.078mm for Md in Equation (III).

  Tb=43.078mm±( 0.026mm2)=43.078mm±0.013mm

Conclusion:

The dimension in the bilateral tolerance is 43.078mm±0.013mm.

To determine

(o)

The dimension in the bilateral tolerance.

Expert Solution
Check Mark

Answer to Problem 11A

The dimension in the bilateral tolerance is 98.8835mm±0.0045mm.

Explanation of Solution

Given information:

The unilateral tolerance is 98.879mm0.00mm+0.009mm.

Calculation:

Substitute 0.009mm for U and 0.00mm for L in Equation (I).

  Tt=0.009mm+(0.00mm)=0.009mm

Substitute 0.009mm for Tt and 98.879mm for Bd in Equation (II).

  Md=98.879mm+0.009mm2=98.879mm+0.0045mm=98.8835mm

Substitute 0.009mm for Tt and 98.8835mm for Md in Equation (III).

  Tb=98.8835mm±0.009mm2=98.8835mm±0.0045mm

Conclusion:

The dimension in the bilateral tolerance is 98.8835mm±0.0045mm.

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