Chapter 27, Problem 10A

To determine

(a)

The maximum limit.

The minimum limit.

Answer to Problem 10A

The maximum limit is $2.818^{″}$.

The minimum limit is $2.806^{″}$.

Explanation of Solution

Given information:

The bilateral tolerance is $2.812^{″}\pm 0.006^{″}$.

Write the expression for the maximum limit.

  $L_{\max }=B_d+0.006^{″}$   ...........(I)

Here, the basic dimension is $B_d$.

Write the expression for the minimum limit.

  $L_{\min }=B_d-0.006^{″}$   ...........(II)

Calculation:

Substitute $2.812^{″}$ for $B_d$ in Equation (I).

  $\begin{array}{c}{L}_{\max }=2.812^{″}+0.006^{″}\\ =2.818^{″}\end{array}$

Substitute $2.812^{″}$ for $B_d$ in Equation (II).

  $\begin{array}{c}{L}_{\min }=2.812^{″}-0.006^{″}\\ =2.806^{″}\end{array}$

Conclusion:

The maximum limit is $2.818^{″}$.

The minimum limit is $2.806^{″}$.

To determine

(b)

The maximum limit.

The minimum limit.

Answer to Problem 10A

The maximum limit is $3.007^{″}$.

The minimum limit is $2.999^{″}$.

Explanation of Solution

Given information:

The bilateral tolerance is $3.003^{″}\pm 0.004^{″}$.

Write the expression for the maximum limit.

  $L_{\max }=B_d+0.004^{″}$   ...........(III)

Here, the basic dimension is $B_d$.

Write the expression for the minimum limit.

  $L_{\min }=B_d-0.004^{″}$   ...........(IV)

Calculation:

Substitute $3.003^{″}$ for $B_d$ in Equation (III).

  $\begin{array}{c}{L}_{\max }=3.003^{″}+0.004^{″}\\ =3.007^{″}\end{array}$

Substitute $3.003^{″}$ for $B_d$ in Equation (IV).

  $\begin{array}{c}{L}_{\min }=3.003^{″}-0.004^{″}\\ =2.999^{″}\end{array}$

Conclusion:

The maximum limit is $3.007^{″}$.

The minimum limit is $2.999^{″}$.

To determine

(c)

The maximum limit.

The minimum limit.

Answer to Problem 10A

The maximum limit is $3.981^{″}$.

The minimum limit is $3.961^{″}$.

Explanation of Solution

Given information:

The bilateral tolerance is $3.971^{″}\pm 0.010^{″}$.

Write the expression for the maximum limit.

  $L_{\max }=B_d+0.010^{″}$   ...........(V)

Here, the basic dimension is $B_d$.

Write the expression for the minimum limit.

  $L_{\min }=B_d-0.010^{″}$   ...........(VI)

Calculation:

Substitute $3.971^{″}$ for $B_d$ in Equation (V).

  $\begin{array}{c}{L}_{\max }=3.971^{″}+0.010^{″}\\ =3.981^{″}\end{array}$

Substitute $3.971^{″}$ for $B_d$ in Equation (VI).

  $\begin{array}{c}{L}_{\min }=3.971^{″}-0.010^{″}\\ =3.961^{″}\end{array}$

Conclusion:

The maximum limit is $3.981^{″}$.

The minimum limit is $3.961^{″}$.

To determine

(d)

The maximum limit.

The minimum limit.

Answer to Problem 10A

The maximum limit is $4.0574^{″}$.

The minimum limit is $4.0550^{″}$.

Explanation of Solution

Given information:

The bilateral tolerance is $4.0562^{″}\pm 0.0012^{″}$.

Write the expression for the maximum limit.

  $L_{\max }=B_d+0.0012^{″}$   ...........(VII)

Here, the basic dimension is $B_d$.

Write the expression for the minimum limit.

  $L_{\min }=B_d-0.0012^{″}$   ...........(VIII)

Calculation:

Substitute $4.0562^{″}$ for $B_d$ in Equation (VII).

  $\begin{array}{c}{L}_{\max }=4.0562^{″}+0.0012^{″}\\ =4.0574^{″}\end{array}$

Substitute $4.0562^{″}$ for $B_d$ in Equation (VIII).

  $\begin{array}{c}{L}_{\min }=4.0562^{″}-0.0012^{″}\\ =4.0550^{″}\end{array}$

Conclusion:

The maximum limit is $4.0574^{″}$.

The minimum limit is $4.0550^{″}$.

To determine

(e)

The maximum limit.

The minimum limit.

Answer to Problem 10A

The maximum limit is $1.3808^{″}$.

The minimum limit is $1.3790^{″}$.

Explanation of Solution

Given information:

The bilateral tolerance is $1.3799^{″}\pm 0.0009^{″}$.

Write the expression for the maximum limit.

  $L_{\max }=B_d+0.0009^{″}$   ...........(IX)

Here, the basic dimension is $B_d$.

Write the expression for the minimum limit.

  $L_{\min }=B_d-0.0009^{″}$   ...........(X)

Calculation:

Substitute $1.3799^{″}$ for $B_d$ in Equation (IX).

  $\begin{array}{c}{L}_{\max }=1.3799^{″}+0.0009^{″}\\ =1.3808^{″}\end{array}$

Substitute $1.3799^{″}$ for $B_d$ in Equation (X).

  $\begin{array}{c}{L}_{\min }=1.3799^{″}-0.0009^{″}\\ =1.3790^{″}\end{array}$

Conclusion:

The maximum limit is $1.3808^{″}$.

The minimum limit is $1.3790^{″}$.

To determine

(f)

The maximum limit.

The minimum limit.

Answer to Problem 10A

The maximum limit is $2.0007^{″}$.

The minimum limit is $1.9993^{″}$.

Explanation of Solution

Given information:

The bilateral tolerance is $2.0000^{″}\pm 0.0007^{″}$.

Write the expression for the maximum limit.

  $L_{\max }=B_d+0.0007^{″}$   ...........(XI)

Here, the basic dimension is $B_d$.

Write the expression for the minimum limit.

  $L_{\min }=B_d-0.0007^{″}$   ...........(XII)

Calculation:

Substitute $2.0000^{″}$ for $B_d$ in Equation (XI).

  $\begin{array}{c}{L}_{\max }=2.0000^{″}+0.0007^{″}\\ =2.0007^{″}\end{array}$

Substitute $2.0000^{″}$ for $B_d$ in Equation (XII).

  $\begin{array}{c}{L}_{\min }=2.0000^{″}-0.0007^{″}\\ =1.9993^{″}\end{array}$

Conclusion:

The maximum limit is $2.0007^{″}$.

The minimum limit is $1.9993^{″}$.

To determine

(g)

The maximum limit.

The minimum limit.

Answer to Problem 10A

The maximum limit is $43.51\text{mm}$.

The minimum limit is $43.41\text{mm}$.

Explanation of Solution

Given information:

The bilateral tolerance is $43.46\text{mm}\pm 0.05\text{mm}$.

Write the expression for the maximum limit.

  $L_{\max }=B_d+0.05\text{mm}$   ...........(XIII)

Here, the basic dimension is $B_d$.

Write the expression for the minimum limit.

  $L_{\min }=B_d-0.05\text{mm}$   ...........(XIV)

Calculation:

Substitute $43.46\text{mm}$ for $B_d$ in Equation (XIII).

  $\begin{array}{c}{L}_{\max }=43.46\text{mm}+0.05\text{mm}\\ =43.51\text{mm}\end{array}$

Substitute $43.46\text{mm}$ for $B_d$ in Equation (XIV).

  $\begin{array}{c}{L}_{\min }=43.46\text{mm}-0.05\text{mm}\\ =43.41\text{mm}\end{array}$

Conclusion:

The maximum limit is $43.51\text{mm}$.

The minimum limit is $43.41\text{mm}$.

To determine

(h)

The maximum limit.

The minimum limit.

Answer to Problem 10A

The maximum limit is $107.15\text{mm}$.

The minimum limit is $106.99\text{mm}$.

Explanation of Solution

Given information:

The bilateral tolerance is $107.07\text{mm}\pm 0.08\text{mm}$.

Write the expression for the maximum limit.

  $L_{\max }=B_d+0.08\text{mm}$   ...........(XV)

Here, the basic dimension is $B_d$.

Write the expression for the minimum limit.

  $L_{\min }=B_d-0.08\text{mm}$   ...........(XVI)

Calculation:

Substitute $107.07\text{mm}$ for $B_d$ in Equation (XV).

  $\begin{array}{c}{L}_{\max }=107.07\text{mm}+0.08\text{mm}\\ =107.15\text{mm}\end{array}$

Substitute $107.07\text{mm}$ for $B_d$ in Equation (XVI).

  $\begin{array}{c}{L}_{\min }=107.07\text{mm}-0.08\text{mm}\\ =106.99\text{mm}\end{array}$

Conclusion:

The maximum limit is $107.15\text{mm}$.

The minimum limit is $106.99\text{mm}$.

To determine

(i)

The maximum limit.

The minimum limit.

Answer to Problem 10A

The maximum limit is $62.14\text{mm}$.

The minimum limit is $61.94\text{mm}$.

Explanation of Solution

Given information:

The bilateral tolerance is $62.04\text{mm}\pm 0.10\text{mm}$.

Write the expression for the maximum limit.

  $L_{\max }=B_d+0.10\text{mm}$   ...........(XVII)

Here, the basic dimension is $B_d$.

Write the expression for the minimum limit.

  $L_{\min }=B_d-0.10\text{mm}$   ...........(XVIII)

Calculation:

Substitute $62.04\text{mm}$ for $B_d$ in Equation (XVII).

  $\begin{array}{c}{L}_{\max }=62.04\text{mm}+0.10\text{mm}\\ =62.14\text{mm}\end{array}$

Substitute $62.04\text{mm}$ for $B_d$ in Equation (XVIII).

  $\begin{array}{c}{L}_{\min }=62.04\text{mm}-0.10\text{mm}\\ =61.94\text{mm}\end{array}$

Conclusion:

The maximum limit is $62.14\text{mm}$.

The minimum limit is $61.94\text{mm}$.

To determine

(j)

The maximum limit.

The minimum limit.

Answer to Problem 10A

The maximum limit is $10.227\text{mm}$.

The minimum limit is $10.179\text{mm}$.

Explanation of Solution

Given information:

The bilateral tolerance is $10.203\text{mm}\pm 0.024\text{mm}$.

Write the expression for the maximum limit.

  $L_{\max }=B_d+0.024\text{mm}$   ...........(XIX)

Here, the basic dimension is $B_d$.

Write the expression for the minimum limit.

  $L_{\min }=B_d-0.024\text{mm}$   ...........(XX)

Calculation:

Substitute $10.203\text{mm}$ for $B_d$ in Equation (XIX).

  $\begin{array}{c}{L}_{\max }=10.203\text{mm}+0.024\text{mm}\\ =10.227\text{mm}\end{array}$

Substitute $10.203\text{mm}$ for $B_d$ in Equation (XX).

  $\begin{array}{c}{L}_{\min }=10.203\text{mm}-0.024\text{mm}\\ =10.179\text{mm}\end{array}$

Conclusion:

The maximum limit is $10.227\text{mm}$.

The minimum limit is $10.179\text{mm}$.

To determine

(k)

The maximum limit.

The minimum limit.

Answer to Problem 10A

The maximum limit is $289.012\text{mm}$.

The minimum limit is $288.998\text{mm}$.

Explanation of Solution

Given information:

The bilateral tolerance is $289.005\text{mm}\pm 0.007\text{mm}$.

Write the expression for the maximum limit.

  $L_{\max }=B_d+0.007\text{mm}$   ...........(XXI)

Here, the basic dimension is $B_d$.

Write the expression for the minimum limit.

  $L_{\min }=B_d-0.007\text{mm}$   ...........(XXII)

Calculation:

Substitute $289.005\text{mm}$ for $B_d$ in Equation (XXI).

  $\begin{array}{c}{L}_{\max }=289.005\text{mm}+0.007\text{mm}\\ =289.012\text{mm}\end{array}$

Substitute $289.005\text{mm}$ for $B_d$ in Equation (XXII).

  $\begin{array}{c}{L}_{\min }=289.005\text{mm}-0.007\text{mm}\\ =288.998\text{mm}\end{array}$

Conclusion:

The maximum limit is $289.012\text{mm}$.

The minimum limit is $288.998\text{mm}$.

To determine

(l)

The maximum limit.

The minimum limit.

Answer to Problem 10A

The maximum limit is $66.776\text{mm}$.

The minimum limit is $66.746\text{mm}$.

Explanation of Solution

Given information:

The bilateral tolerance is $66.761\text{mm}\pm 0.015\text{mm}$.

Write the expression for the maximum limit.

  $L_{\max }=B_d+0.015\text{mm}$   ...........(XXIII)

Here, the basic dimension is $B_d$.

Write the expression for the minimum limit.

  $L_{\min }=B_d-0.015\text{mm}$   ...........(XXIV)

Calculation:

Substitute $66.761\text{mm}$ for $B_d$ in Equation (XXIII).

  $\begin{array}{c}{L}_{\max }=66.761\text{mm}+0.015\text{mm}\\ =66.776\text{mm}\end{array}$

Substitute $66.761\text{mm}$ for $B_d$ in Equation (XXIV).

  $\begin{array}{c}{L}_{\min }=66.761\text{mm}-0.015\text{mm}\\ =66.746\text{mm}\end{array}$

Conclusion:

The maximum limit is $66.776\text{mm}$.

The minimum limit is $66.746\text{mm}$.