978-0133915426 Chapter 5 Part 1

subject Type Homework Help
subject Pages 14
subject Words 1369
subject Authors Russell C. Hibbeler

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5–10.
Determine the components of the support reactions at the
fixed support Aon the cantilevered beam.
1.5 m
30
30
6 kN
SOLUTION
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© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
Ans:
NA=750 N
B
y
=600 N
Bx=450 N
SOLUTION
5–11.
Determine the reactions at the supports.
400 N/m
3 m
3
4
5
3 m
A
B
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*5–12.
AB
4 kN
30
Determine the horizontal and vertical components of
reaction at the pin Aand the reaction of the rocker Bon
the beam.
SOLUTION
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*5–16.
Determine the tension in the cable and the horizontal and
vertical components of reaction of the pin A.The pulley at
Dis frictionless and the cylinder weighs 80 lb.
BA
D
C
2
1
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404
5–17.
The man attempts to support the load of boards having a
weight Wand a center of gravity at G. If he is standing on a
smooth floor,determine the smallest angle at which he can
hold them up in the position shown. Neglect his weight.
u
SOLUTION
G
4ft
4ft
u
Ans:
u=41.4°
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5–18.
Determine the components of reaction at the supports Aand
Bon the rod.
A
B
P
L
––
2
L
––
2
SOLUTION
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406
5–19.
The man has a weight Wand stands at the center of the
plank. If the planes at Aand Bare smooth, determine the
tension in the cord in terms of Wand u.
SOLUTION
B
Lu
f
2
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*5–20.
Auniform glass rod having a length Lis placed in the smooth
hemispherical
bowl having a radius r.Determine the angle of
inclination
for equilibrium.u
SOLUTION
By observation
.
Equilibrium:
a
T
ake the positive root
Ans.u=cos-1
¢
L+2L2+128r2
16r
cos u=L+2L2+128r2
16r
cos u=L;2L2+128r2
16r
2 cos2u-L
4rcos u-1=0
(1 -cos2u)-cos2u+L
4rcos u=0
sin2u-cos2u+L
4rcos u=0
+a©Fy=0; (Wtan u) sin u+WL
4r-Wcos u=0
+Q©Fx=0; NAcos u-Wsin u=0NA=Wtan u
MA=0; NB(2rcos u)-WaL
2cos ub=0NB=WL
4r
f=u
B
r
A
u
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© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
Ans:
TBC =113 N
SOLUTION
5–21.
The uniform rod AB has a mass of 40 kg. Determine the
force in the cable when the rod is in the position shown.
There is a smooth collar at A.A
60
3 m
C
B
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*5–24.
The relay regulates voltage and current. Determine the force
in the spring CD,which has a stiffness of k120 Nm, so
that it will allow the armature to make contact at Ain figure
(a) with a vertical force of 0.4 N. Also,determine the force
in the spring when the coil is energized and attracts the
armature to E,figure (b), thereby breaking contact at A.
50 mm 50 mm 30 mm
10°
D
D
k
k
C
CB
BEA
A
SOLUTION
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5–25.
Determine the reactions on the bent rod which is supported
byasmooth surface at Band by a collar at A, which is fixed
to the rod and is free to slide over the fixed inclined rod.
3ft3ft
3
4
5
100 lb
200lbft
2ft
B
12
5
13
A
SOLUTION
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5–26.
The mobile crane is symmetrically supported by two
outriggers at Aand two at Bin order to relieve the
suspension of the truck upon which it rests and to provide
greater stability. If the crane and truck have a mass of
18 Mg and center of mass at ,and the boom has a mass
of 1.8 Mg and a center of mass at ,determine the vertical
reactions at each of the four outriggers as a function of the
boom angle when the boom is supporting a load having a
mass of 1.2 Mg.Plot the results measured from to
the critical angle where tipping starts to occur.
u=
u
G2
G1
G
2
6.25 m
6m
SOLUTION
MB=0; -NA(4) +18
A
103
B
(9.81)(1) +1.8
A
103
B
(9.81) (2 -6 sin u)
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*5–28.
A linear torsional spring deforms such that an applied couple
moment M is related to the spring’s rotation
u
in radians by
the equation M = (20
u
)
N#m
. If such a spring is attached to
the end of a pin-connected uniform 10-kg rod, determine
the angle
u
for equilibrium. The spring is undeformed
when
u
= 0°.
SOLUTION
A
0.5 m
u
M (20 u) N m
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