which is a system of nine equations for the nine unknowns
Ax
,
Ay
,
Bx
,
By
,
Cx
,
Cy
,
Dx
,
Dy
, and
˛b
. Solving
this system of equations using
WrD2500 lb
,
WbD100 lb
,
LD6ft
,
hD4:5 ft
,
dD3ft
,
gD32:2 ft=s2
,
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 1627
Problem 7.105
The figure shows a weapon called a battering ram (modern large
battering rams are typically mounted on armored vehicles). The
ram has a weight
WrD2500 lb
, center of mass at
E
, and radius of
gyration
kED6:5 ft
. Also let the distance between points
A
and
B
and between points
C
and
D
be
6ft
. In addition, let
hD4:5 ft
and
dD3ft
. Finally, let the connections at points
A
,
B
,
C
, and
D
be
pin connections, and assume that the cart does not move while the
ram swings.
Assume that
AB
and
CD
are uniform thin rods weighing
100 lb
each and that the ram is at rest with
D0ı
. Assume that bar
CD
breaks suddenly, and determine the acceleration of
E
and the forces
at Aimmediately after CD breaks.
Force Laws. All forces have been accounted for on the FBD.
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.
Kinematic Equations.
Since
G
moves in a circle centered at
A
and we are interested in the response of
the system immediately after it is released from rest (i.e., all velocities are zero), 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 1629
Problem 7.106
The figure shows a weapon called a battering ram (modern large
battering rams are typically mounted on armored vehicles). The
ram has a weight
WrD2500 lb
, center of mass at
E
, and radius of
gyration
kED6:5 ft
. Also let the distance between points
A
and
B
and between points
C
and
D
be
6ft
. In addition, let
hD4:5 ft
and
dD3ft
. Finally, let the connections at points
A
,
B
,
C
, and
D
be
pin connections, and assume that the cart does not move while the
ram swings.
Assume that
AB
and
CD
are uniform thin rods weighing
100 lb
each. Assume that, at the instant shown,
D10ı
and the ram is
swinging forward with
jEvEj D 7ft=s
. At this instant, determine the
acceleration of the ram, as well as the reaction forces at points
A
and C.
Solution
The FBDs of the rod
AB
, the rod
CD
, and the ram are shown on the
right.
Balance Principles.
Based on the FBD of the ram, its Newton-Euler
equations 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.
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.
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 7.107
A spool has a weight
WD450 lb
, outer and inner radii
RD6ft
and
D4:5 ft
, respectively, radius of gyration
kGD4:0 ft
, and
mass center at
G
. The spool is being pulled to the right as shown,
and the cable wrapped around the spool is inextensible and of
negligible mass.
Assume that the spool rolls without slipping with respect
to both the cable and the ground. If the pickup truck pulls the
cable with a force
PD125 lb
, determine the acceleration of the
center of the spool and the minimum value of the static friction
coefficient between the spool and the ground that is compatible
with this motion.
gk2
Force Laws. All forces have been accounted for on the FBD.
Kinematic Equations. Since the spool rolls without slipping, 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 1633
Problem 7.108
A spool has a weight
WD450 lb
, outer and inner radii
RD6ft
and
D4:5 ft
, respectively, radius of gyration
kGD4:0 ft
, and
mass center at
G
. The spool is being pulled to the right as shown,
and the cable wrapped around the spool is inextensible and of
negligible mass.
Assume that the static friction coefficient between the spool
and the ground is
sD0:75
, and determine the maximum value
of the force that the truck could exert on the cable without causing
the spool to slip relative to the ground.
gk2
Force Laws. Since slip is impending for the spool, we have that
FDsN:
Kinematic Equations. Since the spool rolls without slipping, 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 7.109
A spool has a weight
WD450 lb
, outer and inner radii
RD6ft
and
D4:5 ft
, respectively, radius of gyration
kGD4:0 ft
, and
mass center at
G
. The spool is being pulled to the right as shown,
and the cable wrapped around the spool is inextensible and of
negligible mass.
Assume that the static and kinetic friction coefficients be-
tween the spool and the ground are
sD0:25
and
kD0:2
.
Furthermore, assume that the spool is initially at rest and that the
pickup truck pulls the spool with a force of
550 lb
. Determine
the initial acceleration of the center of the spool.
Solution
We will solve the problem under the assumption that the point on the spool in contact
with the ground slips to the left relative to the ground. The FBD corresponding to
this working assumption is shown at the right.
Balance Principles. The Newton-Euler equations corresponding to this FBD 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 1635
Before concluding that the acceleration of the center of the spool is
EaGDaGx O{
, we must verify that our
solution is consistent with the assumption that the spool slips relative to the ground. To do this, let
Q
be the
point on the spool that is in contact with the ground at this instant. The acceleration of Qis
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.