978-0077687342 Chapter 16 Part 2

subject Type Homework Help
subject Pages 14
subject Words 2191
subject Authors Brian Self, 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 16.13 (Continued)
89525
F mg=
page-pf2
PROBLEM 16.14
Bars AB and BE, each of mass 4 kg, are welded together and are pin-
connected to two links AC and BD. Knowing that the assembly is
released from rest in the position shown and neglecting the masses of
the links, determine (a) the acceleration of the assembly, (b) the forces
in the links.
B
(a)
2
4.91 m/sa=
30°
page-pf3
PROBLEM 16.15
At the instant shown the tensions in the vertical ropes AB and
DE are 300 N and 200 N, respectively. Knowing that the mass
of the uniform bar BE is 5 kg, determine, at this instant, (a) the
force P, (b) the magnitude of the angular velocity of each rope,
(c) the angular acceleration of each rope.
page-pf4
PROBLEM 16.16
Three bars, each of mass 3 kg, are welded together and are pin-
connected to two links BE and CF. Neglecting the weight of the
links, determine the force in each link immediately after the system
is released from rest.
SOLUTION
page-pf5
PROBLEM 16.17
Members ACE and DCB are each 600 mm long and are connected by
a pin at C. The mass center of the 10-kg member AB is located at G.
Determine (a) the acceleration of AB immediately after the system
has been released from rest in the position shown, (b) the
corresponding force exerted by roller A on member AB. Neglect the
weight of members ACE and DCB.
page-pf6
PROBLEM 16.17 (Continued)
page-pf7
PROBLEM 16.18
A prototype rotating bicycle rack is designed to save space at a
train station. The combined weight of platform BD and the
bicycle is 40 lbs and is centered at 1 ft. above the midpoint of
the platform. The motor at A causes the support beam AB to
have an angular velocity of 10 rpm and zero angular
acceleration at θ = 30°. At this instant, determine the vertical
components of the forces exerted on platform BD by the pins
at B and D.
SOLUTION
40 lbs 1.2422 slugs
yy
page-pf8
PROBLEM 16.19
The triangular weldment ABC is guided by two pins that slide
freely in parallel curved slots of radius 6 in. cut in a vertical
plate. The weldment weighs 16 lb and its mass center is located
at Point G. Knowing that at the instant shown the velocity of
each pin is 30 in./s downward along the slots, determine (a) the
acceleration of the weldment, (b) the reactions at A and B.
SOLUTION
page-pf9
PROBLEM 16.19 (Continued)
page-pfa
PROBLEM 16.20
The coefficients of friction between the 30-lb block and the 5-lb platform
BD are
0.50
s
µ
=
and
0.40.
k
µ
=
Determine the accelerations of the block
and of the platform immediately after wire AB has been cut.
SOLUTION
Assume that the block does not slide relative to the platform. Draw the free body diagram of the platform and
block.
eff
yy
30 7.5 22.5 lbN=−=
page-pfb
PROBLEM 16.20 (Continued)
page-pfc
PROBLEM 16.20 (Continued)
Note: Since
0,N>
we check that contact between block and platform is maintained.
page-pfd
PROBLEM 16.21
Draw the shear and bending-moment diagrams for the vertical rod
AB of Problem 16.16.
PROBLEM 16.16 Three bars, each of mass 3 kg, are welded
together and are pin-connected to two links BE and CF. Neglecting
the weight of the links, determine the force in each link immediately
after the system is released from rest.
SOLUTION
From the solution of Problem 16.16, the acceleration of all points of vertical rod AB is
2
page-pfe
PROBLEM 16.21 (Continued)
( ) : 32.203
FF V xΣ=Σ =
max (16.101 N/m)(0.450 m)M=
max
page-pff
PROBLEM 16.22
Draw the shear and bending-moment diagrams for each of the bars
AB and BE of Prob. 16.14.
PROBLEM 16.14
Bars AB and BE, each of mass 4 kg, are welded together and are pin-
connected to two links AC and BD. Knowing that the assembly is
released from rest in the position shown and neglecting the masses of
the links, determine (a) the acceleration of the assembly, (b) the
forces in the links.
SOLUTION
43
23
0.5 2 2
n
g
ma u gu


 
= =


 

 



0;
nn
F V maΣ= −=
33.983 , at 0.5 m 16.99 NVu uV−= = =
2
n
u
M M ma 
Σ= = 

22
33.983 16.991
2
u
Mu= =
at
0.5 m, 4.25 N muM= = ⋅
page-pf10
PROBLEM 16.22 (Continued)
page-pf11
PROBLEM 16.23
For a rigid body in translation, show that the system of the inertial terms consists of
vectors
()
i
ma
attached to the various particles of the body, where
a
is the
acceleration of the mass center G of the body. Further show, by computing their
sum and the sum of their moments about G, that the inertial terms reduce to a
single vector
ma
attached at G.
page-pf12
PROBLEM 16.24
For a rigid body in centroidal rotation, show that the system of the inertial terms
consists of vectors
2
()
ii
m'−∆ rω
and
( )( )
ii
m'∆×ra
attached to the various particles
i
P
of the body, where
ω
and
a
are the angular velocity and angular acceleration of the
body, and where
i
'r
denotes the position vector of the particle
i
P
relative to the mass
center G of the body. Further show, by computing their sum and the sum of their
moments about G, that the inertial terms reduce to a couple
.Ιa
i
page-pf13
PROBLEM 16.25
It takes 10 min for a 2.4-Mg flywheel to coast to rest from an angular velocity of 300 rpm. Knowing that the
radius of gyration of the flywheel is 1 m, determine the average magnitude of the couple due to kinetic
friction in the bearing.
page-pf14
PROBLEM 16.26
The rotor of an electric motor has an angular velocity of 3600 rpm when the load and power are cut off. The
120-lb rotor, which has a centroidal radius of gyration of 9 in., then coasts to rest. Knowing that kinetic
friction results in a couple of magnitude
2.5 lb ft
exerted on the rotor, determine the number of revolutions
that the rotor executes before coming to rest.
SOLUTION
2
22
2
120 lb 9 in. 2.0963 lb ft s
12
32.2 ft/s
I mk  
= = =
 
 
( )
2
; 2.5 lb ft 2.0963 lb ft sMI
aa
= = ⋅
( )
2
1.1926 rad/s deceleration
a
=
0
2
3600 rpm 120 rad/s
60
π
ωπ

= =


22
02;
ω ω
= +
( )
2
2
rad
0 120 2 1.1926 rad/s
s
πθ

= +−


1 rev
59,585.07 rad 9, 483.26 rev
2 rad
θπ

= =


or 9480 rev
θ
=

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.