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Problem 8.29
A
14 lb
bowling ball is thrown onto a lane with a backspin angular speed
!0D10 rad=s
and forward velocity
v0D17 mph
. After a few seconds, the
ball starts rolling without slip and moving forward with a speed
v
fD17:2 ft=s
.
Let
rD4:25 in:
be the radius of the ball, and let
kGD2:6 in:
be its radius of
gyration.
Determine the work done by friction on the ball from the initial time until
the time that the ball starts rolling without slip.
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.
Dynamics 2e 1699
Problem 8.30
A
14 lb
bowling ball is thrown onto a lane with a backspin angular speed
!0D10 rad=s
and forward velocity
v0D17 mph
. After a few seconds, the
ball starts rolling without slip and moving forward with a speed
v
fD17:2 ft=s
.
Let
rD4:25 in:
be the radius of the ball, and let
kGD2:6 in:
be its radius of
gyration.
Knowing that the coefficient of kinetic friction between the lane and the
ball is
kD0:1
, determine the length
L
f
over which the friction force acts
in order to slow down the ball from
v0
to
v
f
. Does
L
f
also represent the
distance traveled by the center of the ball? Explain.
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.
Dynamics 2e 1701
Problem 8.31
A bowling ball is thrown onto a lane with a forward velocity
v0
and no angular
velocity (
!0D0
). Because of friction between the lane and the ball, after a
short time, the ball starts rolling without slip and moving forward with speed
v
f
. Let
LG
be the distance traveled by the center of the ball while slowing
down from v0to v
f. In addition, let L
fbe the length over which the friction
force had to act in order to slow down the ball from
v0
to
v
f
. State which
of the following relations is true and why: (a)
LG<L
f
; (b)
LGDL
f
; (c)
LG>L
f.
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.
1702 Solutions Manual
The uniform sphere
B
, of radius
rD6cm
and mass
mBD5kg
, is
rigidly attached to the uniform thin bar
AB
, which is pinned at
A
and
has a mass
mAB D8kg
. The system rotates in the vertical plane. The
spring
CD
has stiffness
kD2000 N=m
and is designed so that the
system is in static equilibrium when
✓D0ı
. Let
LD18:2 cm
and
hD24:6 cm.
If the system is released from rest when
✓D30ı
, determine the
angular speed of the arm for ✓D0.
Solution
Dynamics 2e 1703
Kinematic Equations. The system is released from rest, 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 8.33
The uniform sphere
B
, of radius
rD6cm
and mass
mBD5kg
, is
rigidly attached to the uniform thin bar
AB
, which is pinned at
A
and
has a mass
mAB D8kg
. The system rotates in the vertical plane. The
spring
CD
has stiffness
kD2000 N=m
and is designed so that the
system is in static equilibrium when
✓D0ı
. Let
LD18:2 cm
and
hD24:6 cm.
If the system is released from rest when
✓D30ı
, determine the
maximum angle ✓reached by the arm AB.
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 1705
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.
1706 Solutions Manual
A
500 lb
spool with inner and outer radii
⇢D4ft
and
RD6ft
, respectively,
is released from rest on an incline with
✓D30ı
. The center of the spool
G
coincides with its center of mass, and the radius of gyration of the spool is
kGD5ft
. Assume that the only forces acting on the spool after its release are
the spool’s weight, the tension in the cord, and the contact force between the
spool and the incline.
If the angular speed of the spool is
!s2 D1:2 rad=s
after
G
has displaced
a distance
dD10 ft
from the release position, determine the work done by
friction from the instant of release to when !s2 is achieved.
Solution
We model the disk as a rigid body subject to its own weight
mg
, the
Dynamics 2e 1707
Problem 8.35
A
500 lb
spool with inner and outer radii
⇢D4ft
and
RD6ft
, respectively,
is released from rest on an incline with
✓D30ı
. The center of the spool
G
coincides with its center of mass, and the radius of gyration of the spool is
kGD5ft
. Assume that the only forces acting on the spool after its release are
the spool’s weight, the tension in the cord, and the contact force between the
spool and the incline.
If the spool starts moving immediately after release and the coefficient of
kinetic friction between the spool and the incline is
kD0:25
, determine the
speed of Gafter Ghas displaced a distance dD10 ft down the incline.
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.
