978-0077687342 Chapter 16 Part 6

subject Type Homework Help
subject Pages 14
subject Words 2415
subject Authors Brian Self, E. Johnston, Ferdinand Beer, Phillip Cornwell

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page-pf1
PROBLEM 16.66
A thin plate of the shape indicated and of mass m is suspended from two
springs as shown. If spring 2 breaks, determine the acceleration at that
instant (a) of Point A, (b) of Point B.
A square plate of side b.
page-pf2
PROBLEM 16.66 (Continued)
(a)
/A G AG
=+=aaa a
2
b
a
+
g
bg
3

g
1
page-pf3
PROBLEM 16.67
A thin plate of the shape indicated and of mass m is suspended from two
springs as shown. If spring 2 breaks, determine the acceleration at that
instant (a) of point A, (b) of point B.
A thin hoop of diameter b.
/B G BG
2g=
b

;
B
page-pf4
PROBLEM 16.68
A thin plate of the shape indicated and of mass m is suspended
from two springs as shown. If spring 2 breaks, determine the
acceleration at that instant (a) of Point A, (b) of Point B.
A rectangular plate of height b and width a.
2mg
2mg
page-pf5
PROBLEM 16.68 (Continued)
:[m mg+Σ =Fa
]
1
2mg
+
1
2mg
+
m=a
1
2g
1
2g
eff
11
( ):2 22 2
GG
ab
M M mg mg I
a
 
Σ=Σ + =
 
 
22
11
() ( )
4 12
mg a b m a b
a
+= +
22
3( )ga b
ab
+
=+
α
In vector notation,
22
1()
2
3( )
g
ga b
ab
= −
+
= − +
a ij
αk
2
2
22
1 3( ) 1
()
22
A
ga b
ga
ab
+
 
= − +− ×−


+
 
a ij k i
1 3( )
()
ga ba
gab
+
= −+ +
a ij j
page-pf6
PROBLEM 16.69
A sphere of radius r and mass m is projected along a rough horizontal surface with the
initial velocities indicated. If the final velocity of the sphere is to be zero, express, in
terms of v0, r, and
,
k
µ
(a) the required magnitude of
0,
ω
(b) the time t1 required for the
sphere to come to rest, (c) the distance the sphere will move before coming to rest.
10 1
22
k
kk k
gg g
µµ µ
 
page-pf7
PROBLEM 16.69 (Continued)
For a solid sphere
22
2
5
kr=
0
5
v
rvr
0
5
v
1
2
k
µ
page-pf8
PROBLEM 16.70
PROBLEM 16.69 A sphere of radius r and mass m is projected along a rough
horizontal surface with the initial velocities indicated. If the final velocity of
the sphere is to be zero, express, in terms of v0, r, and
,
k
µ
(a) the required magnitude of
0,
ω
(b) the time t1 required for the sphere to come to rest, (c) the distance the sphere
will move before coming to rest.
10 1
22
k
kk k
gg g
µµ µ
 
page-pf9
PROBLEM 16.70 (Continued)
For a hoop,
kr=
(a) Eq. (3):
0
00
2
v
rrr
r
ω
= =
0
0
v
r
=
ω
0
v
1
2
k
µ
page-pfa
PROBLEM 16.71
A bowler projects an 8-in.-diameter ball weighing 12 lb along an alley with a forward
velocity v0 of 15 ft/s and a backspin
ω
0 of 9 rad/s. Knowing that the coefficient of
kinetic friction between the ball and the alley is 0.10, determine (a) the time t1 at which
the ball will start rolling without sliding, (b) the speed of the ball at time t1, (c) the
distance the ball will have traveled at time t1.
2
00
1
()
2
k
vr
tgg
ω
µ
+
=
(3)
1
page-pfb
PROBLEM 16.71 (Continued)
page-pfc
PROBLEM 16.72
Solve Problem 16.71, assuming that the bowler projects the ball with the same forward
velocity but with a backspin of 18 rad/s.
PROBLEM 16.71 A bowler projects an 8-in.-diameter ball weighing 12 lb along an
alley with a forward velocity v0 of 15 ft/s and a backspin
ω
0 of 9 rad/s. Knowing that
the coefficient of kinetic friction between the ball and the alley is 0.10, determine
(a) the time t1 at which the ball will start rolling without sliding, (b) the speed of the
ball at time t1, (c) the distance the ball will have traveled at time t1.
2
00
1
()
2
7
k
vr
tg
ω
µ
+
=
(3)
1
page-pfd
PROBLEM 16.72 (Continued)
( )
1
3
15 (18)
21.8634 s
1
page-pfe
PROBLEM 16.73
A uniform sphere of radius r and mass m is placed with no initial velocity on
a belt that moves to the right with a constant velocity v1. Denoting by
µ
k the
coefficient of kinetic friction between the sphere and the belt, determine
(a) the time t1 at which the sphere will start rolling without sliding, (b) the
linear and angular velocities of the sphere at time t1.
k
5
2
k
g
tt
r
µ
ωa
= =
(2)
Point C is the point of contact with belt.
5
k
g
µ

27
k
rg



7
r
page-pff
PROBLEM 16.74
A sphere of radius r and m has a linear velocity v0 directed to the left and no
angular velocity as it is placed on a belt moving to the right with a constant
velocity v1. If after first sliding on the belt the sphere is to have no linear
velocity relative to the ground as it starts rolling on the belt without sliding,
determine in terms of v1 and the coefficient of kinetic friction
k
µ
between
the sphere and the belt (a) the required value of v0, (b) time t1 at which the
sphere will start rolling on the belt, (c) the distance the sphere will have
moved relative to the ground at time t1.
SOLUTION
1
k
g

5
page-pf10
PROBLEM 16.74 (Continued)
2
1
page-pf11
PROBLEM 16.75
Show that the couple
Iα
of Figure 16.15 can be eliminated by attaching the vectors
t
ma
and
n
ma
at a Point P called the center of percussion, located on line OG at a distance
2/GP k r=
from the mass center of the body.
page-pf12
PROBLEM 16.76
A uniform slender rod of length L = 900 mm and mass m = 4 kg is suspended from a
hinge at C. A horizontal force P of magnitude 75 N is applied at end B. Knowing that
225 mm,r=
determine (a) the angular acceleration of the rod, (b) the components
of the reaction at C.
page-pf13
PROBLEM 16.77
In Problem 16.76, determine (a) the distance
r
for which the horizontal component of the reaction at C is
zero, (b) the corresponding angular acceleration of the rod.
page-pf14
PROBLEM 16.78
A uniform slender rod of length L = 36 in. and weight W = 4 lb hangs freely from a hinge
at A. If a force P of magnitude 1.5 lb is applied at B horizontally to the left (h = L),
determine (a) the angular acceleration of the rod, (b) the components of the reaction at A.
SOLUTION
2
11
22

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