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Computation. Substituting Eqs. (2)–(5) into Eq. (1), we have
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 1669
Problem 8.11
One of the basement doors is left open in the vertical position when it is given a nudge and allowed to
freely fall to the closed position. Given that the door has mass
m
and that it is modeled as a uniform thin
plate of width
w
and length
d
, determine its angular velocity when it reaches the closed position. Hint:
Assume that the door is symmetric with respect to a plane of motion in which the acceleration due to
gravity is gcos ✓rather than g.
Photo credit: © McGraw-Hill, Photo by Lucinda Dowell
Computation. Substituting Eqs. (2)–(6) into Eq. (1) and solving for !d, we have
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 1671
Problem 8.12
The L-bar consisting of two uniform bars each of length
L
is released from
rest when
✓D90ı
. Neglecting friction, determine the smallest value achieved
by
✓
.Hint: The equation
sin ✓CAcos ✓DB
admits the solution
✓D
sin1.B cos /, with Dtan1A,ifjBcos j1.
Solution
Kinematic Equations.
The system is released from rest. The minimum swing angle is achieved when the
system comes momentarily to a stop. Summarizing,
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1673
Problem 8.13
A turbine rotor with weight
WD3000 lb
, center of mass at the fixed point
G
,
and radius of gyration
kGD15 ft
is brought from rest to an angular velocity
!D1500 rpm
in 20 revolutions by applying a constant torque
M
. Neglecting
friction, determine the value of Mneeded to spin up the rotor as described.
Photo credit: NASA
Solution
We model the rotor as a rigid body in fixed axis rotation about its own center
1674 Solutions Manual
A turbine rotor with weight
WD3000 lb
, center of mass at the fixed point
G
, and radius of gyration
kGD15 ft
is spinning with an angular speed
!D
1200 rpm
when a braking system is engaged that applies a constant torque
MD3000 ftlb
. Determine the number of revolutions needed to bring the rotor
to a stop.
Photo credit: NASA
Solution
Dynamics 2e 1675
Computation. Substituting Eqs. (2)–(5) into Eq. (1), we have
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Problem 8.15
The uniform rectangular plate of length
`
, height
h
, and mass
m
lies in the vertical plane and is pinned at
one corner. If the plate is released from rest in the position shown, determine its angular velocity when the
center of mass Gis directly below the pivot O. Neglect any friction at the pin at O.
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 1677
Problem 8.16
A door
AB
weighing
80 lb
is pinned at
A
and swings in the horizontal
plane. The spring
CD
has stiffness
k
and is unstretched when
✓D0ı
. Let
LD1:5 ft and hD0:5 ft.
If the door is rotating counterclockwise and the speed of
B
is
10 ft=s
when
✓D0
, determine
k
, such that the door temporarily stops when
✓D90ı. Assume that the spring does not impinge on the mount at A.
Solution
We model the door as a thin rigid body in fixed axis rotation about point
