Mathematics for Machine Technology

John C. Peterson, Robert D. Smith

Chapter 81 Introduction to Computer Numerical Control (CNC) - all with Video Answers

Educators

Chapter Questions

Problem 1

Three views of the angular portion of a tool are shown in the figure.
a. Sketch and label a rectangular solid and the pyramid formed by the angular surface edges. Show the right triangles that contain $\angle A, \angle B$, and $\angle C$ and identify the angles.
b. Use the formula $\tan \angle C=(\tan \angle A)(\tan \angle B)$ to compute $\angle C$ to the nearest minute.
( GRAPH CAN'T COPY )

Check back soon!

Problem 2

The top, front, and right side views of a part are shown in the figure. The angular surfaces are to be machined in reference to the horizontal plunge at $\angle A$ and $\angle B$ as shown in the front and right side views.
a. Sketch and label a rectangular solid and the pyramid formed by the angular surface edges. Show the right triangle that shows $\angle C$ and the right triangles that contain $\angle A, \angle B$, and $\angle R$. Identify all four angles.
b. Compute $\angle R$ if $\tan \angle R=\frac{\tan \angle A}{\tan \angle B}$.
c. Compute $\angle C$ if $\cot \angle C=\sqrt{\cot ^2 \angle A+\cot ^2 \angle B}$.
( GRAPH CAN'T COPY )

Check back soon!

Problem 3

The top, front, and right side views of a compound-angular surface are shown in the figure. Sketch and label a rectangular solid and the pyramid formed by the surface to be cut and the extended sides of the block. Show the right triangle that contains $\angle T$ and the right triangles that contain the given angles. Identify $\angle T, \angle R$, and the given angles.
( GRAPH CAN'T COPY )

Check back soon!

03:55

Problem 4

A rectangular solid has length $L=12.6 \mathrm{~mm}$, width $W=23.8 \mathrm{~mm}$, and height $H=32.5 \mathrm{~mm}$. Find the length of a diagonal $A B$ from the upper left rear vertex to the lower right front vertex. Round the answer to 1 decimal place.

Katelyn Chen

Numerade Educator

01:03

Problem 5

Determine the length of stock required to form the "U" shown in the figure.
( GRAPH CAN'T COPY )

Maureen Foss

Numerade Educator

01:41

Problem 6

The " $U$ " in the previous exercise was made from round steel stock $7.5 \mathrm{~mm}$ in diameter.
a. What is the weight of the "U" in kilograms if steel weighs $7721 \mathrm{~kg} / \mathrm{m}^3$ ? Round the answer to 4 decimal places.
b. If a kilogram weighs approximately 2.2046 pounds, what does the "U" weigh in pounds? Round the answer to 4 decimal places.

Mitchell Riley

Numerade Educator

00:43

Problem 7

In Exercises 7 through 10, use graph paper to plot the given coordinates.
$$
\text { } \begin{aligned}
A & =(-2,5) \\
B & =(2,8) \\
C & =(-7,-2)
\end{aligned}
$$

Cory Kuzinski

Numerade Educator

01:02

Problem 8

In Exercises 7 through 10, use graph paper to plot the given coordinates.
$$
\text { } \begin{aligned}
D & =(0,3) \\
E & =(-4,0) \\
F & =(-2,-2)
\end{aligned}
$$

Ankit Gupta

Numerade Educator

02:28

Problem 9

In Exercises 7 through 10, use graph paper to plot the given coordinates.
$$
\text { } \begin{aligned}
G & =(6,-8) \\
H & =(-7,5)
\end{aligned}
$$
$$
I=(-1,0)
$$

Destin Priester

Numerade Educator

01:35

Problem 10

In Exercises 7 through 10, use graph paper to plot the given coordinates.
$$
\text { } \begin{aligned}
J & =(0,0) \\
K & =(-3,-4) \\
L & =(9,-3)
\end{aligned}
$$

Ali Soave

Numerade Educator

01:05

Problem 11

Graph the following points: $(-5,-5),(-3,-3),(0,0),(2,2),(4,4),(7,7)$. Connect these points.
a. What kind of geometric figure is formed?
b. What is the value of the angle formed in reference to the $x$-axis?

Teresa Fuston

Numerade Educator

01:08

Problem 12

Graph the following points. Connect these points in the order that they are given. What kind of a geometric figure is formed?
$$
\begin{array}{llll}
\text { Point 1: }(-9,-7) & \text { Point 5: }(4.5,1) & \text { Point 9: }(2,5) & \text { Point 13: }(-5,1) \\
\text { Point 2: }(-6,-5.3) & \text { Point 6: }(7,2.5) & \text { Point 10: }(0,6) & \text { Point 14: }(-6.5,-2) \\
\text { Point 3: }(-3,-3.5) & \text { Point 7: }(6,3) & \text { Point 11: }(-2,7) & \text { Point 15: }(-8,-5) \\
\text { Point 4: }(1,-1) & \text { Point 8: }(4,4) & \text { Point 12: }(-3,5) & \text { Point 16: }(-9,-7)
\end{array}
$$

Carson Merrill

Numerade Educator

00:58

Problem 13

Refer to the points plotted on the Cartesian coordinate plane in the following figure. Give coordinates for the following points.
A _____________
B _____________
C _____________
D _____________
E _____________
F _____________
G _____________
H _____________
( TABLE CAN'T COPY )

Erika Bustos

Numerade Educator

00:58

Problem 14

Erika Bustos

Numerade Educator

00:58

Problem 15

Refer to the points plotted on the Cartesian coordinate plane in the following figure. Give coordinates for the
following points.
A _____________
B _____________
C _____________
D _____________
E _____________
F _____________
G _____________
H _____________
( TABLE CAN'T COPY )

Erika Bustos

Numerade Educator

00:58

Problem 16

Refer to the points plotted on the Cartesian coordinate plane in the following figure. Give coordinates for the
following points.
A _____________
B _____________
C _____________
D _____________
E _____________
F _____________
G _____________
H _____________
( TABLE CAN'T COPY )

Erika Bustos

Numerade Educator

02:23

Problem 17

In Exercises 17 and 18, make sketches similar to the three-axis Cartesian coordinate system shown in Figure 81-3. For each of the given points, show the approximate locations of the points ( $x, y$, and $z$ coordinates), as shown in Figures 81-5 and 81-6. The coordinates can be considered as either inch or millimeter units with approximate distances sketched to any scale.
Point $A:(6,3,2)$
Point $B$ : $(-5,-2,2)$
Point $C:(-7,5,3)$

Linh Vu

Numerade Educator

01:07

Problem 18

In Exercises 17 and 18, make sketches similar to the three-axis Cartesian coordinate system shown in Figure 81-3. For each of the given points, show the approximate locations of the points ( $x, y$, and $z$ coordinates), as shown in Figures 81-5 and 81-6. The coordinates can be considered as either inch or millimeter units with approximate distances sketched to any scale.
Point $D$ : $(-5.5,3.6,-1.8)$
Point $E$ : $(8.3,-7.6,2.6)$
Point $F:(6.4,4.4,-3.8)$

Carson Merrill

Numerade Educator

View

Problem 19

Give the coordinates of point $A$ in the following figure with the $x$-value first, the $y$-value second, and the $z$-value third.
( GRAPH CAN'T COPY )

Alison Rodriguez

Numerade Educator

View

Problem 20

Give the coordinates of point $B$ in the following figure with the $x$-value first, the $y$-value second, and the $z$-value third.
( GRAPH CAN'T COPY )

Alison Rodriguez

Numerade Educator

02:30

Problem 21

Give the coordinates of point $C$ in the following figure with the $x$-value first, the $y$-value second, and the $z$-value third.
( GRAPH CAN'T COPY )

Teresa Fuston

Numerade Educator

View

Problem 22

Give the coordinates of point $D$ in the following figure with the $x$-value first, the $y$-value second, and the $z$-value third.
( GRAPH CAN'T COPY )

Alison Rodriguez

Numerade Educator

View

Problem 23

Give the coordinates of point $E$ in the following figure with the $x$-value first, the $y$-value second, and the $z$-value third.
( GRAPH CAN'T COPY )

Alison Rodriguez

Numerade Educator

View

Problem 24

Give the coordinates of point $F$ in the following figure with the $x$-value first, the $y$-value second, and the $z$-value third.
( GRAPH CAN'T COPY )

Alison Rodriguez

Numerade Educator