PROBLEM 17.100 (Continued)
Principle of impulse and momentum.
1
Syst. Momenta 12
Syst. Ext. Imp. 2
Syst. Momenta
Moments about A:
2
79
16 lb 9 9 ft
32.2 12 12
0.71221 (0.11215 0.186
2
2
34 0.2795)
1.2322
Velocity of the mass center. 22
12
9ft (1.2322 rad/s)
v
PROBLEM 17.101
A 45-g bullet is fired with a velocity of 400 m/s at
30
into a 9-kg
square panel of side
200b
mm. Knowing that
150h
mm and that the
panel is initially at rest, determine (a) the velocity of the center of the panel
immediately after the bullet becomes embedded, (b) the impulsive reaction
at A, assuming that the bullet becomes embedded in 2 ms.
PROBLEM 17.101 (Continued)
(b) Linear momentum:
0
cos30 ( )
BxPG
mv A t mv
PROBLEM 17.102
A 45-g bullet is fired with a velocity of 400 m/s at
5
into a 9-kg square
panel of side
200b
mm. Knowing that the panel is initially at rest,
determine (a) the required distance h if the horizontal component of the
impulsive reaction at A is to be zero, (b) the corresponding velocity of the
center of the panel immediately after the bullet becomes embedded.
PROBLEM 17.103
The uniform rods, each of mass m, form the L-shaped rigid body
ABC which is initially at rest on the frictionless horizontal surface
when hook D of the carriage E engages a small pin at C. Knowing
that the carriage is pulled to the right with a constant velocity
v
0
,
determine immediately after the impact (a) the angular velocity of
the body, (b) the velocity of corner B. Assume that the velocity of
the carriage is unchanged and that the impact is perfectly plastic.
0
2
BC
L
v
v
0
[
B
vv
][L
]
0
[]
B
vL
v
0
() [ ]
AB x B
vvvL
()() 2
AB y B y
L
vv
2
L
Let m be the mass of each rod.
Moment of inertia of each rod.
2
1
12
ImL
(a) Principle of impulse and momentum.
Syst. Momenta
0
Syst. Ext. Imp.
0
Syst. Momenta
1
PROBLEM 17.103 (Continued)
Moments about C:
11
PROBLEM 17.104
The uniform slender rod AB of weight 5 lb and length 30 in. forms an angle
30
with the vertical as it strikes the smooth corner shown with a vertical
velocity 1
v of magnitude 8 ft/s and no angular velocity. Assuming that the impact
is perfectly plastic, determine the angular velocity of the rod immediately after the
impact.
15
212
G
L
v
Kinetics.
1
Syst. Momenta 12
Syst. Ext. Imp.
2
Syst. Momenta
moments about A: 1sin 0
22
G
LL
mv I mv
3
515 51515
(8) sin30 0 80.875 10
32.2 12 32.2 12 12
2.4 rad/s
2.40 rad/s
PROBLEM 17.105
A bullet weighing 0.08 lb is fired with a horizontal velocity of 1800 ft/s into the 15-lb
wooden rod AB of length L 30 in. The rod, which is initially at rest, is suspended by a
cord of length L 30 in. Determine the distance h for which, immediately after the
bullet becomes embedded, the instantaneous center of rotation of the rod is Point C.
PROBLEM 17.105 (Continued)
PROBLEM 17.106
A prototype of an adapted bowling device is a simple
ramp that attaches to a wheelchair. The bowling ball has
a mass moment of inertia about its center of gravity of
cmr
2
, where c is a unitless constant, r is the radius, and m
is its mass. The athlete nudges the ball slightly from a
height of h, and the ball rolls down the ramp without
sliding. It hits the bowling lane, and after slipping for a
short distance, it begins to roll again. Assuming that the
ball does not bounce as it hits the lane, determine the
angular velocity and velocity of the mass center of the
ball after it has resumed rolling.