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Force Laws. Due to the choice of datum,
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 1749
Problem 8.57
The figure shows the cross section of a garage door with length
LD9ft
and weight
WD175 lb
. At
A
and
B
, there are rollers of negligible
mass constrained to move in the guide whose horizontal portion is at
a distance
HD11 ft
from the floor. The door’s motion is assisted by
two springs, each with constant
k
(only one spring is shown). The door
is released from rest when
dD26 in:
and the spring is stretched
4in:
Neglecting friction, knowing that, when
A
touches the floor,
B
is in
the vertical portion of the guide, and modeling the door as a uniform
thin plate, determine the minimum value of
k
so that
A
will strike the
ground with a speed no greater than 1ft=s.
Solution
We model the door as a thin rigid body subject to its own weight
W
, the
Problem 8.58
The figure shows the cross section of a garage door with length
LD2:5
m and mass
mD90 kg
. At the ends
A
and
B
, there are
rollers of negligible mass constrained to move in the guide whose
horizontal portion is at a distance
HD3
m from the floor. The door’s
motion is assisted by two counterweights
C
, each of mass
mC
(only
one counterweight is shown). If the door is released from rest when
dD53 cm
, neglecting friction and modeling the door as a uniform
thin plate, determine the minimum value of
mC
so that
A
will strike
the ground with a speed no greater than 0:25 m=s.
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 1751
Computation. Substituting Eqs. (2)–(4) 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 8.59
The uniform thin rod
AB
is pin-connected to the slider
S
, which moves along
the frictionless guide, and to the disk
D
, which rolls without slip over the
horizontal surface. The pins at
A
and
B
are frictionless, and the system is
released from rest. Neglect the vertical dimension of S.
Letting
LD1:75
m and
RD0:6
m, assuming that
S
and
D
are of neg-
ligible mass, that the mass of rod
AB
is
mAB D7kg
, and that the system is
released from the angle
✓0D65ı
, determine the speed of the slider
S
when it
strikes the ground.
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 1753
where we have used the expression for !AB in Eq. (5). Next, we now observe that, in ¡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 8.60
The uniform thin rod
AB
is pin-connected to the slider
S
, which moves along
the frictionless guide, and to the disk
D
, which rolls without slip over the
horizontal surface. The pins at
A
and
B
are frictionless, and the system is
released from rest. Neglect the vertical dimension of S.
Letting
LD4:5 ft
and
RD1:2 ft
, assuming that AB is of negligible mass,
the weight of
S
is
WSD3lb
,
D
is a uniform disk of weight
WDD9lb
, and
the system is released from the angle
✓0D67ı
, determine the speed of the
slider Swhen it strikes the ground.
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 1755
Kinematic Equations. We observing that Smoves only in the vertical direction, so
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 8.61
The uniform thin rod
AB
is pin-connected to the slider
S
, which moves along
the frictionless guide, and to the disk
D
, which rolls without slip over the
horizontal surface. The pins at
A
and
B
are frictionless, and the system is
released from rest. Neglect the vertical dimension of S.
Letting
LD1:75
m and
RD0:6
m, assuming that the mass of
S
is
mSD4:2 kg
,
D
is a uniform disk of mass
mDD12 kg
, the mass of AB is
mAB D7kg
, and that the system is released from the angle
✓D69ı
, determine
the speed and the direction of motion of point
B
when the slider
S
strikes the
ground.
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 1757
Force Laws.
Due to the choice of datum, and recalling that the size of the slider is being ignored, 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.
