the wheel to come to rest when a force of
is
applied to the handle. The coefficient of kinetic friction
between the belt and the wheel rim is
. (
Hint
:
Recall from the statics text that the relation of the tension
in the belt is given by
, where
is the angle of
contact in radians.)
•19–13.
The 200-lb flywheel has a radius of gyration about
its center of gravity
O
of
.
If it rotates
counterclockwise with a constant angular velocity of
before the brake is applied, determine the
required force
P
that must be applied to the handle to stop
the wheel in 2 s. The coefficient of kinetic friction between
the belt and the wheel rim is
. (
Hint
: Recall from the
statics text that the relation of the tension in the belt is given
by
, where
is the angle of contact in radians.)
b
T
B
=
T
C
e
mb
m
k
=
0.3
1200 rev
>
min
k
O
=
0.75 ft
b
T
B
=
T
C
e
mb
m
k
=
0.3
P
=
200 lb
1200 rev
>
min
k
O
=
0.75 ft
19–11.
A motor transmits a torque of
to
the center of gear
A
. Determine the angular velocity of each
of the three (equal) smaller gears in 2 s starting from rest.
The smaller gears (
B
) are pinned at their centers, and the
masses and centroidal radii of gyration of the gears are
given in the figure.
M
=
0.05 N
#
m
•19–9.
If the cord is subjected to a horizontal force of
, and the gear rack is fixed to the horizontal plane,
determine the angular velocity of the gear in 4 s,starting from
rest. The mass of the gear is 50 kg, and it has a radius of
gyration about its center of mass
O
of
.
19–10.
If the cord is subjected to a horizontal force of
, and gear is supported by a fixed pin at
O
,
determine the angular velocity of the gear and the velocity
of the 20-kg gear rack in 4 s, starting from rest. The mass of
the gear is 50 kg and it has a radius of gyration of
. Assume that the contact surface between
the gear rack and the horizontal plane is smooth.
k
O
=
125 mm
P
=
150 N
k
O
=
125 mm
P
=
150 N
2.5 ft
1.25 ft
1 ft
P
O
A
B
v
C
Probs. 19–12/13
200 mm
C
500 mm
500 mm
400 mm
P
(N)
5
2
A
P
B
t
(s)
Prob. 19–14
19–14.
The 12-kg disk has an angular velocity of
. If the brake
ABC
is applied such that the
magnitude of force
P
varies with time as shown, determine
the time needed to stop the disk. The coefficient of kinetic
friction at
B
is
. Neglect the thickness of the brake.
m
k
=
0.4
v
=
20
rad
>
s

19.2
P
RINCIPLE OF
I
MPULSE AND
M
OMENTUM
513
19
•19–17.
The 5-kg ball is cast on the alley with a backspin
of
, and the velocity of its center of mass
O
is
. Determine the time for the ball to stop back
spinning, and the velocity of its center of mass at this
instant.
The coefficient of kinetic friction between the ball
and the alley is
.
m
k
=
0.08
v
0
=
5 m
>
s
v
0
=
10 rad
>
s
*19–16.
If the boxer hits the 75-kg punching bag with an
impulse of
, determine the angular velocity of
the bag immediately after it has been hit. Also, find the
location
d
of point
B
, about which the bag appears to rotate.
Treat the bag as a uniform cylinder.