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Unformatted text preview: 3 Article 3/4 Problems 157 Representative Problems 3/18 The threewheel truck is used to carry the 100kg box as shown. Calculate the changes in the normal
force reactions at the three wheels due to the weight
of the box. Problem 3/78 3/79 The square steel plate has a mass of 1800 kg with mass center at its center G. Calculate the tension in
each of the three cables with which the plate is
lifted while remaining horizontal. Problem 3/79 3/80 The two uniform rectangular plates each weighing 800 lb are freely hinged about their common edge
and suspended by the central cable and four sym
metrical corner cables. Calculate the tension T in
each of the corner cables and the tension To in the
center cable. Problem 3/80 3/81 The smooth homogeneous sphere rests in the 120°
groove and bears against the end plate, which is
normal to the direction of the groove. Determine the
angle 0, measured from the horizontal, for which
the reaction on each side of the groove equals the
force supported by the end plate. / I End view
of Vgroove  — — —  ~— — Horizontal Problem 3/81 158 Chapter 3 Equilibrium 3/ 82 Because of a combination of soil support conditions 3/84 A smooth homogeneous sphere of mass m and ra and the tension in the single power cable, the utility
pole has developed the indicated 5° lean. The 9m
uniform pole has a mass per unit length of 25 kg/m,
and the tension in the power cable is 900 N. Deter
mine the reactions at the base 0. Note that the
power cable lies in a vertical plane parallel to the xz
plane. Problem 3/82 3/83 As part of a check on its design, a lower Aarm (part of an automobile suspension) is supported by bear
ings at A and B and subjected to the pair of 900N
forces at C and D. The suspension spring, not shown
for clarity, exerts a force FS at E as shown, where E
is in plane ABCD. Determine the magnitude FS of
the spring force and the magnitudes FA and FE of
the bearing forces at A and B which are perpendicu
lar to the hinge axis AB. Problem 3/83 3/85 37” dius r is suspended by a wire AB of length 2r from
point B on the line of intersection of the two smooth
vertical walls at right angles to one another. Deter
mine the reaction R of each wall against the sphere. Problem 3/84 A rider holds her bicycle at the 10° angle shown by
exerting a force perpendicular to the plane of the bi
cycle frame. If friction at A and B is sufﬁcient to
prevent lateral slippage, determine the force exerted
by the rider on the seat, the upward normal forces
at A and B, and the lateral friction forces at A and
B. Even though the bicycle is free to roll, assume
that it does not. The bicycle weighs 29 lb with cen
ter of gravity at G. Problem 3/85 are. 1 by
a bi
t to
rted
rces
and
Lime
cen vertical 3/56 The 100lb uniform square plate is supported by a
ballandsocket joint at O, a cable at E, a ﬁxture at A
which can support vertical force only, and a linear
Spring at C. If the unstretched length of the spring
is 6 in., determine the spring constant k required for
equilibrium in the position shown. Problem 3l86 13:] 87 During a test, the left engine of the twinengine air
plane is revved up and a 2kN thrust is generated.
The main wheels at B and C are braked in order to
prevent motion. Determine the change (compared
with the nominal values with both engines off) in
the normal reaction forces at A, B, and C. Problem 3/87 3/88 The uniform 15kg plate is welded to the vertical
shaft, which is supported by bearings A and B.
Calculate the magnitude of the force supported by
bearing B during application of the 120N  m couple
to the shaft. The cable from C to D prevents the
plate and shaft from turning, and the weight of the
assembly is carried entirely by bearing A. Article 3/4 Problems 159 400 mm Problem 3] 88 3I89 The uniform panel door weighs 60 lb and is pre vented from opening by the strut C, which is a light
twoforce member whose upper end is secured
under the door knob and whose lower end is at
tached to a rubber cup which does not slip on the
ﬂoor. Of the door hinges A and B, only B can sup—
port force in the vertical zdirection. Calculate the
compression C in the strut and the horizontal com
ponents of the forces supported by hinges A and B
when a horizontal force P = 50 lb is applied normal
to the plane of the door as shown. “x. ___—~'. I J
_.,,_s_.—~ \
"EX
\
\ 3’ Problem 3189 Article 5/7 Problems 289  \ .— 5,145 The angle strut is welded to the end 0 of the 5] 148 Repeat Prob. 5/147, where the 1500N load has 9am
lent Ibeam and supports the 1.6kN vertical force. been replaced by the 4.2kNm couple.
Determine the bending moment at B and the dis
tance x to the left of C at which the bending mo
ment is zero. Also construct the moment diagram
for the beam.
1.6 kN ,. 200
“ Problem 5114B
5] 149 The adjusting screw of the specialpurpose offset
clamp supports a compression of 500 N. Calculate
the shear force V, the tension T, and the bending
moment M at section A of the clamp bar for x =
and _ 250 mm. Which of these three quantities changes
l and with x?
Problem 5] 145
5I'l46 The Ibeam supports the 1000lb force and the
2000lbft couple applied to the 2ft strut welded to
the end of the beam. Calculate the shear V and mo
ment M at the section midway between A and B.
1000 lb 2000 lbtt
Problem 51149 5I150 Draw the shear and moment diagrams for the
I. the ' _ _ loaded beam and specify the shear V and moment 5;
Strut M at a section 3 m to the left of the support at A.
riding 4.— 3' 44.53 .}.:_3*_,. E
i
Problem 5]]46 :
5] 147 Plot the shear and moment diagrams for the beam ' . _ !
loaded with both the distributed and point loads.  What are the values of the shear and moment ""
at x = 6 m? Determine the maximum bending 4:1
moment Mmﬂx. " 6 m ' ' 3 m
1500 N Problem 5,150
800 N/m
‘— — x
Problem 5] 147 352 Chapter 6 Friction 6/34 Determine the range of weights W of the uniform
slender bar for which the system will be in equilib
rium. Neglect friction at all bearings. Problem 6l34 6/35 The uniform rod with center of mass at G is sup
ported by the pegs A and B, which are ﬁxed in the
wheel. If the coefﬁcient of friction between the rod
and pegs is [.L, determine the angle 0 through which
the wheel may be slowly turned about its horizontal
axis through 0, starting from the position shown,
before the rod begins to slip. Neglect the diameter of
the rod compared with the other dimensions. Problem 6/35 6/36 The solid semicylinder of mass m and radius r is
rolled through an angle 0 by the horizontal force P.
If the coefﬁcient of static friction is us, determine
the angle 0 at which the cylinder begins to slip on
the horizontal surface as P is gradually increased.
What value of us would permit 0 to reach 90°? Problem 6136 6/37 The 10kg solid cylinder is resting in the inclined
Vblock. If the coefﬁcient of static friction between
the cylinder and the block is 0.50, determine (a) the
friction force F acting on the cylinder at each side
before force P is applied and (b) the value of P
required to start sliding the cylinder up the incline. l____ Horiz. — — — Problem 6I37 6/38 The three identical rollers are stacked on a horizon
tal surface as shown. If the coefﬁcient of static
friction its is the same for all pairs of contacting sur
faces, ﬁnd the minimum value of us for which the
rollers will not slip. Problem 6/38 Article 6/3 Problems 353 ined 6139 The movable lefthand jaw of the bar clamp can be
veen slid along the frame to increase the capacity of
)the the clamp. To prevent slipping of the jaw on the
side frame when the clamp is under load, the dimension
of p x must exceed a certain minimum value. For given
ine. values of a and b and a static friction coefﬁcient as,
specify this design minimum value of x to prevent
slipping of the jaw.
Problem 6/4'I 6/42 A uniform block of mass m is at rest on an incline 6. Determine the maximum force P which can be ap plied to the block in the direction shown before P slipping begins. The coefﬁcient of static friction between the block and the incline is us. Also deter mine the angle B between the horizontal direction of P and the direction of initial movement of the block. Problem 6I39
izon itatic 6I40 The uniform slender bar of length l is placed in the
_ sup opening of width d at the 30° angle shown. For what
'1 the range of l/d will the bar remain in static equilib rium? The coefﬁcient of static friction at A and B is
as = 0.40. Problem 6I42 6/43 The singlelever block brake prevents rotation of
the ﬂywheel under a counterclockwise torque M.
Find the force P required to prevent rotation if the
coefﬁcient of static friction is as. Explain what would
happen if the geometry permitted b to equal use. Problem 6/40 6I41 Determine the maximum value of the angle 0 for
which the uniform slender rod will remain in equi
librium. The coefﬁcient of static friction at A is
“A = 0.80, and friction associated with the small
roller at B may be neglected. Problem 6143 ...
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This note was uploaded on 12/15/2011 for the course EM 306 taught by Professor Rodin during the Fall '07 term at University of Texas.
 Fall '07
 Rodin
 Statics

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