PROBLEM 17.137 (Continued)
PROBLEM 17.138
The gear shown has a radius R 150 mm and a radius of gyration
125 mm.k
The gear is rolling without sliding with a velocity
1
v
of magnitude 3 m/s when it strikes a step of height h 75 mm.
Because the edge of the step engages the gear teeth, no slipping
occurs between the gear and the step. Assuming perfectly plastic
impact, determine (a) the angular velocity of the gear immediately
after the impact, (b) the angular velocity of the gear after it has
rotated to the top of the step.
PROBLEM 17.138 (Continued)
Part (b) Conditions at the top of the step.
The gear pivots about the edge of the step. Use the principle of conservation of energy.
Position (2): The gear has just broken contact with the floor.
Position (3): The center of the gear is above the edge of the step.
Kinetic energy:
22
TI mv

33
3
2()
VmgRh

Principle of conservation of energy:
2233
TVTV
222 222
23
11
() () ()
22
mk R mgR mk R mgR h

 
22
160.21rad /s
3
12.66 rad/s
PROBLEM 17.139
A uniform slender rod is placed at corner B and is given a slight
clockwise motion. Assuming that the corner is sharp and becomes
slightly embedded in the end of the rod, so that the coefficient of
static friction at B is very large, determine (a) the angle

through
which the rod will have rotated when it loses contact with the corner,
(b) the corresponding velocity of end A.
PROBLEM 17.140
The motion of the slender 250-mm rod AB is guided by pins at A and B that
slide freely in slots cut in a vertical plate as shown. Knowing that the rod has
a mass of 2 kg and is released from rest when
0,
determine the reactions
at A and B when
90 .

PROBLEM 17.140 (Continued)
Position 2 90

22
2
11
22
2
(2)(9.81)(0.125 0.125cos30 )
GG
TI mv



( ) 38.1833
Cx
Cx
a

ij
For the rod AB, ,BB
v
kv j
/
//
sin30 cos30
0.125 0.21651
1
AB
GB AB
LL


rij
ij
rr
PROBLEM 17.140 (Continued)
Matching vertical components of
A
a
/
38.1833 0.125 22.0468
0.125 60.2301
B
B
GBGB
a
a



aaa
/
sin ( )
2
(2)(9.81)(0.125)sin30
GGE G
L
mg I m


kra
k
22
( 21.933 m/s ) (40.2189 m/s )
G

aij
eff
( ) ( ) : (2)( 21.932) 43.864 N
xx Gx
FF ma B
43.9 N
B
eff
GG
G
eff
( ) ( ) (0.0104667)(143.808) 1.5052 N m
GG
MI

PROBLEM 17.141
A baseball attachment that helps people with mobility
impairments play T-ball and baseball is powered by a
spring that is unstretched at position 2. The spring is
attached to a cord, which is fastened to point B on the
75-mm radius pulley. As the pulley, which is fixed at
point O, rotates backwards to the cocked position at
,
the rope wraps around the pulley and stretches the
spring of stiffness k = 2000 N/m. The combined mass
moment of inertia of all rotating components about
point O is 0.40 kg·m2. The swing is timed perfectly to
strike a 145 gram baseball travelling with a speed of
v0= 10 m/s at a distance of h = 0.7 m away from point
O. Knowing that the coefficient of restitution between
the bat and ball is 0.59, determine the velocity of the
baseball immediately after the impact. Assume that the
ball is travelling primarily in the horizontal plane and
that its spin is negligible.
Bat b
PROBLEM 17.141 (Continued)
Conservation of Momentum about point O during impact:
PROBLEM 17.142
Two panels A and B are attached with hinges to a rectangular
plate and held by a wire as shown. The plate and the panels are
made of the same material and have the same thickness. The
entire assembly is rotating with an angular velocity
0
when
the wire breaks. Determine the angular velocity of the
assembly after the panels have come to rest against the plate.
panel 0
44
12
82
12 3
tb tb

