978-0073398242 Chapter 15 Solution Manual Part 34

subject Type Homework Help
subject Pages 9
subject Words 1564
subject Authors Brian Self, David Mazurek, E. Johnston, Ferdinand Beer, Phillip Cornwell

Unlock document.

This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
page-pf1
PROBLEM 15.234
The 400-mm bar AB is made to rotate at the constant rate
2
ω
=
/
d dt
θ
= 8 rad/s
with respect to the frame CD which itself rotates at the constant rate
1
ω
= 12 rad/s about the Y axis. Knowing that
θ
=
60°
at the instant shown,
determine the velocity and acceleration of point A.
page-pf2
PROBLEM 15.234 (Continued)
page-pf3
PROBLEM 15.235
The 400-mm bar AB is made to rotate at the rate
2
ω
=
/d dt
θ
with respect
to the frame CD which itself rotates at the rate
1
ω
about the Y axis. At the
instant shown
1
ω
= 12 rad/s,
1/
d dt
ω
=
16
2
rad/s ,
2
ω
= 8 rad/s,
2
/d dt
ω
= 10
2
rad/s ,
and
θ
=
60 .°
Determine the velocity and
acceleration of point A at this instant.
page-pf4
PROBLEM 15.235 (Continued)
Coriolis acceleration:
( )( )
( ) ( )
2
/
2 2 12 0.8 3 0.8 19.2 3 m/s
AF
× = ×− + =v j ij k
Acceleration of point A:
//
2
A A AF AF
=+ aaa v
( ) ( ) ( )
20.8 3 6.4 3 1.0 19.2 3 1.2
A
=−+ + +a ij k
( ) ( ) ( )
2 22
22.5 m/s 10.09 m/s 34.9 m/s
A
=−− +a i jk
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
page-pf5
PROBLEM 15.236
The arm AB of length 16 ft is used to provide an elevated
platform for construction workers. In the position shown, arm
AB is being raised at the constant rate
/ 0.25d dt
θ
=
rad/s;
simultaneously, the unit is being rotated about the Y axis at the
constant rate
ω
1 = 0.15 rad/s. Knowing that
θ
= 20°, determine
the velocity and acceleration of Point B.
page-pf6
PROBLEM 15.236 (Continued)
Motion of Point B relative to the frame.
2
/ 2/
/ 2/
22
(0.25 rad/s)
(1.36808 ft/s) (3.7588 ft/s)
( 0.25 ) (1.36808 3.7588 )
(0.93969 ft/s ) (0.34202 ft/s )
BF BA
BF BF
d
dt
θ
=
=
= ×
= +
= ×
=−× +
=
k
k
vr
ij
av
k ij
ij
ω
ω
ω
.Velocity of Point B
/B B BF
= +vvv
(1.37 ft/s) (3.76 ft/s) (1.88 ft/s)
B
=−+ +v i jk
.
Coriolis acceleration
/
2
2 (2)(0.15 ) (1.36808 3.7588 )
(0.41042 ft/s )
BF
×= × +
=
Ωv j i j
k
.Acceleration of Point B
//
2
B B BF BF
=+ aaa Ωv
222
(1.22 ft/s ) (0.342 ft/s ) (0.410 ft/s )
B
=−−aijk
page-pf7
PROBLEM 15.237
The remote manipulator system (RMS) shown is used
to deploy payloads from the cargo bay of space
shuttles. At the instant shown, the whole RMS is
rotating at the constant rate
10.03 rad/s
ω
=
about the
axis AB. At the same time, portion BCD rotates as a
rigid body at the constant rate
2
/ 0.04 rad/sd dt
ωβ
= =
about an axis through B
parallel to the X axis. Knowing that
30 ,
β
= °
determine (a) the angular acceleration of BCD, (b) the
velocity of D, (c) the acceleration of D.
page-pf8
PROBLEM 15.237 (Continued)
Motion of D relative to the frame: This motion is a rotation about B with angular velocity.
2
/frame 2 /
/frame 2 /frame
22
(0.04 rad/s)
(0.04 ) (5.75 5.6292 )
(0.04 ) (0.22517 0.23 )
(0.0092 m/s ) (0.009007 m/s )
D DB
DD
r
=
= ×
= ×−
= ×
=×+
=−+
i
vr
ij k
a
i jk
jk
ω
ω
ω
(b) Velocity of D.
/frameDDD
= +vvv
(0.169 m/s) (0.225 m/s) (0.230 m/s)
D=−++v ijk
:Coriolis acceleration
/frame
2
D
×Ωv
page-pf9
PROBLEM 15.238
A disk of radius 120 mm rotates at the constant rate
2
5
ω
=
rad/s
with respect to the arm AB, which itself rotates at the constant
rate
1
3
ω
=
rad/s. For the position shown, determine the velocity
and acceleration of Point C.
page-pfa
PROBLEM 15.239
The crane shown rotates at the constant rate
1
0.25
ω
=
rad/s;
simultaneously, the telescoping boom is being lowered at the
constant rate
2
0.40
ω
=
rad/s. Knowing that at the instant
shown the length of the boom is 20 ft and is increasing at the
constant rate
1.5 ft/s,u=
determine the velocity and
acceleration of Point B.

Trusted by Thousands of
Students

Here are what students say about us.

Copyright ©2022 All rights reserved. | CoursePaper is not sponsored or endorsed by any college or university.