978-0073398242 Chapter 17 Solution Manual Part 7

subject Type Homework Help
subject Pages 9
subject Words 1333
subject Authors Brian Self, David Mazurek, E. Johnston, Ferdinand Beer, Phillip Cornwell

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page-pf1
PROBLEM 17.38
A long ladder of length l, mass m, and centroidal mass moment of inertia
I
is placed against a house at an angle
. Knowing that the ladder is
released from rest, determine the angular velocity of the ladder when
2.
Assume the ladder can slide freely on the horizontal ground and
on the vertical wall.
page-pf2
PROBLEM 17.38 (Continued)
page-pf3
PROBLEM 17.39
The ends of a 9-lb rod AB are constrained to move along slots cut in a
vertical plate as shown. A spring of constant
3k
lb/in. is attached to
end A in such a way that its tension is zero when
0.
If the rod is
released from rest when
50 ,

determine the angular velocity of the
rod and the velocity of end B when
0.
page-pf4
PROBLEM 17.39 (Continued)
page-pf5
PROBLEM 17.40
The mechanism shown is one of two identical mechanisms
attached to the two sides of a 200-lb uniform rectangular door.
Edge ABC of the door is guided by wheels of negligible mass
that roll in horizontal and vertical tracks. A spring of constant k
40 lb/ft is attached to wheel B. Knowing that the door is
released from rest in the position 30

with the spring
unstretched, determine the velocity of wheel A just as the door
reaches the vertical position.
page-pf6
PROBLEM 17.40 (Continued)
page-pf7
PROBLEM 17.41
The mechanism shown is one of two identical mechanisms
attached to the two sides of a 200-lb uniform rectangular door.
Edge ABC of the door is guided by wheels of negligible mass
that roll in horizontal and vertical tracks. A spring of constant k
is attached to wheel B in such a way that its tension is zero
when 30 .
Knowing that the door is released from rest in
the position 45
and reaches the vertical position with an
angular velocity of 0.6 rad/s, determine the spring constant k.
page-pf8
PROBLEM 17.41 (Continued)
page-pf9
PROBLEM 17.42
Each of the two rods shown is of length L 1 m and has a mass of 5 kg.
Point D is connected to a spring of constant k 20 N/m and is constrained
to move along a vertical slot. Knowing that the system is released from rest
when rod BD is horizontal and the spring connected to Point D is initially
unstretched, determine the velocity of Point D when it is directly to the
right of Point A.
page-pfa
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 17.42 (Continued)
Kinematics.
AB AB
BABBAB
vL L

v
30°
DD
vv
Locate the instantaneous center C of rod BD by drawing BC perpendicular to
vB
and DC perpendicular to
vD
.
Point C coincides with Point A in position 2.
Let
BD BD
ω
2
3
(sin60) 2
B
BD AB
EAB
GBDAB
v
L
L
v
vL L




222
2
2
22 22
22 22
111
222
11 1 1 1 3
23 212 2 2
113 7
6248 12
DBDAB
AAB BD G
AB AB AB
AB AB
vL L
TI I mv
mL mL m
mL mL










 
 




(1)
Principle of conservation of energy.
222 2
112 2 1 2
22 2 2
21
317 31
:0 2212 2 2
7331
()
12 2 2 2
AB
AB
TVT V mgL kx mL mgL kx
mL mgL k x x






(2)
Data:
2
12
5kg, 1m, 9.81m/s
20 N m, 0, 1m
mLg
kxxL


2
22 2
21
33 (0.63397)(5 kg)(9.81m/s )(1m) 31.096 J
22
11
()(20N/m)(1m)10J
22
mgL
kx x







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