constant rate of
0.2 m/s
and the boom is being lowered at the constant rate of
0.08 rad/s. Determine (a) the velocity of Point B, (b) the acceleration of Point B.
PROBLEM 15.164 (Continued)
(b) Acceleration of Point B.
0.04926
B
PROBLEM 15.165
At the instant shown the length of the boom AB is being increased at the
constant rate of 0.2 m/s and the boom is being lowered at the constant rate of
0.08 rad/s. Determine (a) the velocity of Point B, (b) the acceleration of Point B.
SOLUTION
Velocity of coinciding Point
B′
on boom.
PROBLEM 15.165 (Continued)
(b) Acceleration of Point B.
0.017255
PROBLEM 15.166
In the automated welding setup shown, the position of the two welding
tips G and H is controlled by the hydraulic cylinder D and rod BC. The
cylinder is bolted to the vertical plate which at the instant shown rotates
counterclockwise about A with a constant angular velocity of 1.6 rad/s.
Knowing that at the same instant the length EF of the welding assembly
is increasing at the constant rate of 300 mm/s, determine (a) the velocity
of tip H, (b) the acceleration of tip H.
SOLUTION
Body ACD rotates about point A with angular velocity
1.6 rad/s
=ω
( )
1.6 rad/s=k
PROBLEM 15.167
In the automated welding setup shown, the position of the two welding
tips G and H is controlled by the hydraulic cylinder D and rod BC. The
cylinder is bolted to the vertical plate which at the instant shown rotates
counterclockwise about A with a constant angular velocity of 1.6 rad/s.
Knowing that at the same instant the length EF of the welding assembly
is increasing at the constant rate of 300 mm/s, determine (a) the velocity
of tip G, (b) the acceleration of tip G.
SOLUTION
Body ACD rotates about point A with angular velocity
1.6 rad/s
=ω
( )
1.6 rad/s=k
PROBLEM 15.167 (Continued)
PROBLEM 15.168
A chain is looped around two gears of radius 40 mm that can
rotate freely with respect to the 320–mm arm AB. The chain
moves about arm AB in a clockwise direction at the constant
rate of 80 mm/s relative to the arm. Knowing that in the
position shown arm AB rotates clockwise about A at the
constant rate
0.75
ω
=
rad/s, determine the acceleration of
each of the chain links indicated.
Links 1 and 2.
SOLUTION
Let the arm AB be a rotating frame of reference.
0.75 rad/sΩ=
(0.75 rad/s) := − k
90
2
PROBLEM 15.169
A chain is looped around two gears of radius 40 mm that can
rotate freely with respect to the 320–mm arm AB. The chain
moves about arm AB in a clockwise direction at the constant
rate 80 mm/s relative to the arm. Knowing that in the position
shown arm AB rotates clockwise about A at the constant rate
ω
0.75=
rad/s, determine the acceleration of each of the chain
links indicated.
Links 3 and 4.
SOLUTION
Let arm AB be a rotating frame of reference.
0.75 rad/s=Ω
(0.75 rad/s)= − k
PROBLEM 15.170
A basketball player shoots a free throw in such a
way that his shoulder can be considered a pin joint at
the moment of release as shown. Knowing that at the
instant shown the upper arm SE has a constant
angular velocity of 2 rad/s counterclockwise and the
forearm EW has a constant clockwise angular
velocity of 4 rad/s with respect to SE, determine the
velocity and acceleration of the wrist W.
PROBLEM 15.170 (Continued)
W=a
PROBLEM 15.171
The human leg can be crudely approximated as two rigid bars (the femur
and the tibia) connected with a pin joint. At the instant shown the veolcity
and acceleration of the ankle is zero. During a jump, the velocity of the
ankle A is zero, the tibia AK has an angular velocity of 1.5 rad/s
counterclockwise and an angular acceleration of 1 rad/s2
counterclockwise. Determine the relative angular velocity and angular
acceleration of the femur KH with respect to AK so that the velocity and
acceleration of H are both straight up at the instant shown.
SOLUTION
2
22
(1.0 ) ( 2 26 ) (1.5) ( 2 26 )
26 2 4.5 58.5
(21.5 in./s ) (60.5 in./s )
= ×−+ − −+
=− −+ −
=−−
k ij ij
ij i j
ij
PROBLEM 15.171 (Continued)
PROBLEM 15.172
The collar P slides outward at a constant relative speed u along rod
AB, which rotates counterclockwise with a constant angular velocity of
20 rpm. Knowing that
250r=
mm when
0
θ
=
and that the collar
reaches B when
90 ,
θ
= °
determine the magnitude of the acceleration
of the collar P just as it reaches B.
SOLUTION
(20)(2 ) 2
20 rpm rad/s
60 3
ππ
ω
= = =
P
P
PROBLEM 15.173
Pin P slides in a circular slot cut in the plate shown at a constant relative speed
u
90=
mm/s. Knowing that at the instant shown the plate rotates clockwise
about A at the constant rate
3 rad/s,
ω
=
determine the acceleration of the pin if
it is located at (a) Point A, (b) Point B, (c) Point C.
SOLUTION
PROBLEM 15.173 (Continued)
C
PROBLEM 15.174
Rod AD is bent in the shape of an arc of a circle of radius b = 150 mm.
The position of the rod is controlled by pin B which slides in a horizontal
slot and also slides along the rod. Knowing that at the instant shown pin
B moves to the right at a constant speed of 75 mm/s, determine (a) the
angular velocity of the rod, (b) the angular acceleration of the rod.
PROBLEM 15.174 (Continued)
sin 35
°
2
0.271 rad/s=α
PROBLEM 15.175
Solve Prob. 15.174 when
θ
= 90°.
Problem 15.174: Rod AD is bent in the shape of an arc of a circle of
radius b = 150 mm. The position of the rod is controlled by pin B which
slides in a horizontal slot and also slides along the rod. Knowing that at
the instant shown pin B moves to the right at a constant speed of
75 mm/s, determine (a) the angular velocity of the rod, (b) the angular
acceleration of the rod.
PROBLEM 15.175 (Continued)
Acceleration analysis.
/B B B AD c
′
=++aa a a
0
B=a
2
2