978-0073380292 Chapter 4 Part 6

Problem 4.79

Determine the distance between the lines of action of the

85 N

forces. See

the hint in Prob. 4.78.

Solution

From the geometry provided in the problem statement, we write the following expressions

Problem 4.80

The input shaft of a speed reducer supports a

200 Nm

moment, and the output

shafts support 300 and 500 Nm moments.

(a)

Determine the resultant moment applied by the shafts to the speed reducer.

(b)

If the speed reducer is bolted to a surface that lies in the

xy

plane,

speculate on the characteristics of the forces these bolts apply to the

speed reducer. In other words, do you expect these forces to constitute

couples only, or may they be more general? Remark: Problems such as

this are discussed in detail in Chapter 5.

Problem 4.81

Satellites and other spacecraft perform attitude positioning using thrusters that

are fired in pairs so as to produce couples. If thrusters at points

A

,

B

,

C

, and

D

each produce

3N

forces, determine the resultant moment and hence, the axis

through the center of mass about which an initially nonrotating satellite will

begin to rotate.

Problem 4.82

Forces

F

and

T

exerted by air on a rotating airplane propeller are shown. Forces

F

lie in the

xy

plane and are normal to the axis of each propeller blade, and

thrust forces

T

act in the

´

direction. Show that the forces

F

can be represented

as a couple or system of couples.

Problem 4.83

If the structure shown is subjected to couple forces applied at points

A

and

B

and the force applied at

A

is

E

FD.8 O{C10 O|40 O

k/ lb

, determine the moment

of the couple about line

a

. Line

a

has direction angles

xD72ı

,

yD36ı

,

and ´D60ı.

Problem 4.84

Determine which of the force systems shown, if any, are equivalent.

Problem 4.85

Determine which of the force systems shown, if any, are equivalent.

Problem 4.86

Determine which of the force systems shown, if any, are equivalent.

Problem 4.87

Determine values for forces

F

and

P

and moment

M

, if possible, so that the force systems shown

in Fig. P4.87(b)–(d) are equivalent to the force

system shown in Fig. P4.87(a).

Problem 4.88

Determine values for forces

F

and

P

, if possible, so that the

force systems shown in Fig. P4.88(b)–(d) are equivalent to the

force system shown in Fig. P4.88(a).

Problem 4.89

The ﬂoor of an airplane cargo bay is shown in a horizontal position.

(a) Determine an equivalent force system at point O.

(b)

Determine an equivalent force system consisting of a single force, and

specify the

x

and

´

coordinates of the point where the force’s line of

action intersects the ﬂoor.

(c)

Keeping points

A

–

D

at the locations shown, suggest a repositioning of

the forces so that the location of the force system described in Part (b) is

closer to point O.

Problem 4.90

In a vehicle collision reconstruction analysis, an engineer estimates the tire

forces shown. Determine an equivalent force system at point O.

Problem 4.91

For Prob. 4.90, determine an equivalent force system consisting of a single

force, specifying the

x

coordinate of where the force’s line of action intersects

the xaxis.

Problem 4.92

A Boeing CH-47 Chinook helicopter is shown. This heli-

copter was first produced in 1962, is still in production, and

it sees extensive military and civilian use worldwide. The

rotors counter-rotate so that a vertical stabilizing rotor is

not needed. The rotor forces

FA

and

FB

lie in the

xy

plane

where

˛A

and

˛B

are angles about the

´

axis. Forces

FC

and

FD

are due to the thrust from the engines, and they act

in the

y

direction. Forces

QA

and

QB

are lift forces from

the rotors, and they act in the

´

direction. Moments

MA

and

MB

are due to rotation of the rotors, and they act in the

˙´

direction. Points

A

–

D

lie on the lines of action of the forces

and moments (point

D

is on the opposite side of the heli-

copter and is not seen in this figure), and these points have

the coordinates given below. If the forces, moments, and

angles have the values given below, determine an equivalent

force system acting at the origin of the coordinate system,

point O.

Problem 4.93

The RMS Queen Mary II is a luxury ocean liner that has a propulsion system

consisting of four pods mounted at its stern. Each pod contains an electric

motor that is powered by a combination of diesel and gas turbine generators.

The frontmost two pods are fixed in position parallel to the

x

axis, while the

rearmost two pods can rotate 360

ı

, thus eliminating the need for a rudder. The

ship also has three bow thrusters whose net thrust is shown as

F5

; these thrusters

are used only at low speeds to provide greater maneuverability. Assuming all

forces lie in the same plane, determine an equivalent force system at point

O

that is valid for

0ı˛1360ı

and

0ı˛2360ı

. Express your answer in

terms of F1–F5,˛1, and ˛2.

Problem 4.94

If

˛D30ı

,

WD1kN

, and

QD2kN

in Fig. P4.14 on p. 217, determine an equivalent force system

consisting of a single force, and specify the distance from point

C

where the force’s line of action intersects

member CBD.