Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
PROBLEM 15.97
At the instant shown, the velocity of collar A is 0.4 m/s to the
right and the velocity of collar B is 1 m/s to the left. Determine
(a) the angular velocity of bar AD, (b) the angular velocity of
bar BD, (c) the velocity of point D.
SOLUTION
Method 1
Assume
D
v
has the direction indicated by the angle
β
as shown.
Draw
CDI perpendicular to
.
D
v
Then, point C is the instantaneous
center of rod
AD and point I is the instantaneous center of rod BD.
.Geometry
( ) ( )
22
0.27 0.36 0.45 mAD = +=
( ) ( )
22
0.18 0.135 0.225 mBD =+=
cos cos
ββ
PROBLEM 15.97 (C
ontinued)
( )
cos 0.135 0.375 m
BC CD
θ
= +=
/
1.4 3.73 rad/s
0.375
BA
BD
v
CB
ω
= = =
( ) ( )( )
/
0.3 3.73 1.120 m/s
D A BD
v CD
ω
= = =
()a
/
1.120
0.45
DA
AD
v
AD
ω
= =
2.49 rad/s
AD
=ω
()b
3.73 rad/s
BD
=ω
()c
[
/
0.4 m/s
D A DA
=+=v vv
[
1.120+
]
θ
0.835 m/s=
53.6°
0.835 m/s
D
=v
53.6 °
PROBLEM 15.98
Two rods AB and DE are connected as shown. Knowing that
Point D moves to the left with a velocity of 40 in./s, determine
(a) the angular velocity of each rod, (b) the velocity of Point A.
B=
PROBLEM 15.98 (Continued)
A
A=v
PROBLEM 15.99
Describe the space centrode and the body centrode of rod ABD of Problem
15.83. (Hint: The body centrode need not lie on a physical portion of the
rod.)
PROBLEM 15.83 Rod ABD is guided by wheels at A and B that roll in
horizontal and vertical tracks. Knowing that at the instant shown
60
β
= °
and the velocity of wheel B is 40 in./s downward, determine (a) the
angular velocity of the rod, (b) the velocity of Point D.
PROBLEM 15.100
Describe the space centrode and the body centrode of the gear of
Sample Problem 15.6 as the gear rolls on the stationary horizontal
rack.
PROBLEM 15.101
Using the method of Section 15.3, solve Problem 15.60.
PROBLEM 15.60 In the eccentric shown, a disk of 2-in.-radius
revolves about shaft O that is located 0.5 in. from the center A of the
disk. The distance between the center A of the disk and the pin at B is
8 in. Knowing that the angular velocity of the disk is 900 rpm
clockwise, determine the velocity of the block when
30 .
θ
= °
SOLUTION
9.2331
AC
B
PROBLEM 15.102
Using the method of Section 15.3, solve Problem 15.64.
PROBLEM 15.64 In the position shown, bar AB has an angular velocity
of 4 rad/s clockwise. Determine the angular velocity of bars BD and DE.
SOLUTION
PROBLEM 15.102 (Continued)
700 mm/s 0.95455 rad/s
733.33 mm
B
BD
v
CB
ω
= = =
DE
PROBLEM 15.103
Using the method of Section 15.3, solve
Problem 15.65.
PROBLEM 15.65 Linkage DBEF is part
of a windshield wiper mechanism, where
points O, F and D are fixed pinned
connections. At the position shown,
θ
=
60° and link EB is horizontal. Knowing
that link EF has a counterclockwise angular
velocity of 4 rad/s at the instant shown,
determine the angular velocity of links EB
and DB.
BD
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 15.104
Using the method of section 15.3, solve Problem 15.38.
PROBLEM 15.38 An automobile travels to the right at a
constant speed of 48 mi/h. If the diameter of a wheel is 22 in.,
determine the velocities of Points B, C, D, and E on the rim of
the wheel.
SOLUTION
E
PROBLEM 15.105
A 5-m steel beam is lowered by means of two cables
unwinding at the same speed from overhead cranes. As the
beam approaches the ground, the crane operators apply brakes
to slow the unwinding motion. At the instant considered the
deceleration of the cable attached at B is
2
2.5 m/s ,
while that
of the cable attached at D is
2
1.5 m/s .
Determine (a) the
angular acceleration of the beam, (b) the acceleration of points
A and E.
SOLUTION
α
=α
/
, 0, 2 m
DB
≈=rω
PROBLEM 15.106
For a 5-m steel beam AE the acceleration of point A is
2
2 m/s
downward and the angular acceleration of the beam is
2
1.2 rad/s
counterclockwise. Knowing that at the instant
considered the angular velocity of the beam is zero, determine
the acceleration (a) of cable B, (b) of cable D.
SOLUTION
2
2 m/s
A
=a
2
, 1.2 rad/s=α
PROBLEM 15.107
A 900-mm rod rests on a horizontal table. A force P applied as
shown produces the following accelerations:
2
3.6 m/s
A=a
to
the right,
2
6 rad/s
α
=
counterclockwise as viewed from above.
Determine the acceleration (a) of Point G, (b) of Point B.
SOLUTION
B=a
PROBLEM 15.108
In Problem 15.107, determine the point of the rod that (a) has
no acceleration, (b) has an acceleration of
2
2.4 m/s
to the right.
SOLUTION
(a)
For 0:
Q
a=
PROBLEM 15.109
Knowing that at the instant shown crank BC has a constant angular
velocity of 45 rpm clockwise, determine the acceleration (a) of Point A,
(b) of Point D.
SOLUTION
A=a
PROBLEM 15.109 (Continued)
D
PROBLEM 15.110
End A of rod AB moves to the right with a constant velocity of 6 ft/s. For the
position shown, determine (a) the angular acceleration of rod AB, (b) the
acceleration of the midpoint G of rod AB.
AB
AB
PROBLEM 15.110 (Continued)
2
G=+=a ij
PROBLEM 15.111
An automobile travels to the left at a constant speed of 72 km/h.
Knowing that the diameter of the wheel is 560 mm, determine
the acceleration (a) of Point B, (b) of Point C, (c) of Point D.
SOLUTION
h 1000 m
Acceleration.
Plane motion = Trans. with A + Rotation about A
2 22
/// (0.280 m)(71.429 rad/s) 1428.6 m/s
BA CA DA
(a)
2
/
0 1428.6 m/s
B A BA
=+=+aaa
2
1430 m/s
B
=a
(b)
2
/
0 1428.6 m/s
C A CA
=+=+aaa
2
1430 m/s
C=a
(c)
2
/0 1428.6 m/s
D A DA
=+=+a aa
60°
2
1430 m/s
D
=a
60°
