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Problem 7.31
The uniform disk of radius
RD0:8 ft
and weight
WD20 lb
is pin-
connected to the link
AB
and is pulled on its periphery by a force
P
via a rope that is wrapped around the disk. The coefficient of kinetic
friction between the disk and the surface on which it sits is
kD0:5
.
Neglect the mass of link
AB
and assume that
s
is insufficient to
prevent slipping.
For
PD15 lb
and
D0ı
, determine the angular acceleration
of the disk
˛d
and the time it takes to achieve an angular velocity of
!dD35 rad=s, assuming that the disk starts from rest.
IBD1
2mdR2:
The Newton-Euler equations corresponding to the FBD of the link AB are:
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 1477
Force Laws. Since the disk is slipping relative to the ground, the friction law is
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 7.32
The uniform disk of radius
RD0:8 ft
and weight
WD20 lb
is pin-
connected to the link
AB
and is pulled on its periphery by a force
P
via a rope that is wrapped around the disk. The coefficient of kinetic
friction between the disk and the surface on which it sits is
kD0:5
.
Neglect the mass of link
AB
and assume that
s
is insufficient to
prevent slipping.
For
PD25 lb
and
D90ı
, determine the angular acceleration of
the disk
˛d
and the number of revolutions for it to achieve an angular
velocity of !dD45 rad=s, assuming that the disk starts from rest.
Solution
Neglecting the weight of the link
AB
, for
D90ı
, the FBD of the disk and of the link
AB
are shown below,
where
f
is the friction force between the disk and the ground and we have assumed the distance between
A
and Bis L.
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 1479
Kinematic Equations. Since the mass center of the disk does not move, 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 7.33
The uniform disk of radius
RD0:8 ft
and weight
WD20 lb
is pin-
connected to the link
AB
and is pulled on its periphery by a force
P
via a rope that is wrapped around the disk. The coefficient of kinetic
friction between the disk and the surface on which it sits is
kD0:5
.
Neglect the mass of link
AB
and assume that
s
is insufficient to
prevent slipping.
For
PD25 lb
, determine the angular acceleration of the disk
˛d
as a function of the pull angle .
IBD1
2mdR2:
The Newton-Euler equations corresponding to the FBD of the link AB are:
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 1481
Kinematic Equations. Since the mass center of the disk does not move, 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 7.34
A classic balsa wood toy airplane is powered by a rubber band that winds
up when its four-bladed propeller is rotated by hand. When released, the
rubber band unwinds and the propeller starts spinning, thus propelling
the plane around the room. Model each propeller blade as a slender rod
of length
LD6cm
and mass
mD2
g, and neglect air resistance. If we
model the rubber band as a linear elastic torsional spring with constant
ktD6107Nm=rad
, determine the angular speed of the propeller if
it is initially wound up 20 revolutions.
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 1483
f
i
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 7.35
The driveway gate is hinged at its right end and is pushed open
with a force
P
. Where should the force
P
be applied (i.e., where
should
A
be located) so that the force acting on the hinge due to the
gate always acts along a line parallel to the gate and in the plane
of the gate during the entire time the gate is opening? Neglect the
weight force acting on the gate, and model the gate as a uniform
thin bar as shown below the photo.
Photo credit: Courtesy of Amazing Gates of America
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 1485
Problem 7.36
Assuming the helicopter is on the ground, and modeling each
of its four blades as a slender rod with weight
WD400 lb
and
length
LD24 ft
, determine the constant moment that must be
applied by the engine to the mast at
O
to spin the blades from
rest to an angular speed of 289 rpm in 90 s.
Solution
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.
