Chapter 8 Solutions
Problem 8.1
A conveyor is moving cans at a constant speed
v0
when, to pro-
ceed to the next step in packaging, the cans are transferred onto a
stationary surface at
A
. The cans each have mass
m
, width
w
, and
height
h
. Assuming that there is friction between each can and
the stationary surface, under what conditions would we be able to
compute the stopping distance of the cans, using the work-energy
principle for a particle?
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Dynamics 2e 1659
Problem 8.2
At the instant shown, the centers of the two identical uniform disks
A
and
B
are moving to the right with the same speed
v0
. In addition,
disk
A
is rolling clockwise with an angular speed
!0
, while disk
B
has a backspin with angular speed equal to
!0
. Letting
TA
and
TB
be the kinetic energies of
A
and
B
, respectively, state which of the
following statements is true and why: (a)
TA<T
B
; (b)
TADTB
;
(c) TA>T
B.
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Problem 8.3
At the instant shown, the centers of the two identical uniform disks
A
and
B
, each with mass
m
and radius
R
, are moving to the right with the same speed
v0D4m=s
. In addition, disk
A
is rolling clockwise with
an angular speed
!0D5rad=s
, while disk
B
has a backspin with angular speed
!0D5rad=s
. Letting
mD45 kg and RD0:75 m, determine the kinetic energy of each disk.
Solution
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Dynamics 2e 1661
Problem 8.4
Two identical battering rams are mounted in two different ways on their respective frames as
shown. Bars BC and AD are identical and pinned at
B
and
C
and at
A
and
D
, respec-
tively. Bars FO and HO are rigidly attached to the ram and are pinned at
O
. At the in-
stant shown, the mass centers of rams 1 and 2, at
E
and
G
, respectively, are moving
(b) T1DT2; (c) T1>T
2.
Solution
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Problem 8.5
Two identical battering rams are mounted in two different ways on their respective frames as shown. Bars
BC and AD are identical and pinned at
B
and
C
and at
A
and
D
, respectively. Bars FO and HO are rigidly
attached to the ram and are pinned at
O
. At the instant shown, the centers of mass of rams 1 and 2, at
E
and
G
, respectively, are moving horizontally with a speed
v0D20 ft=s
. Treating the rams as slender bars
with length
LD10 ft
and weight
WD1250 lb
, and letting
HD3ft
, compute the kinetic energy of the
two rams.
Solution
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Dynamics 2e 1663
Problem 8.6
A pendulum consists of a uniform disk
A
of diameter
dD0:15
m and mass
mAD
0:35 kg
attached at the end of a uniform bar
B
of length
LD0:75
m and mass
mBD0:8 kg
. At the instant shown, the pendulum is swinging with an angular velocity
!D0:24 rad=s
clockwise. Determine the kinetic energy of the pendulum at this instant using Eq. (8.8) on p. 584.
Solution
The pendulum is undergoing a fixed axis rotation about O. Hence, the kinetic energy of the pendulum is
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Problem 8.7
A
2570 lb
car (this includes the weight of the wheels) is traveling on a horizontal flat road at
60 mph
. If
each wheel has a diameter
dD24:3 in:
and a mass moment of inertia with respect to its mass center equal
to
0:989 slugft2
, determine the kinetic energy of the car. Neglect the rotational energy of all parts except
for the wheels, which roll without slip.
Solution
Letting mdenote the mass of the car, the kinetic energy of the car is
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Dynamics 2e 1665
Problem 8.8
In Example 7.6 on p. 544, we analyzed the forces acting on a test tube in
an ultra-centrifuge. Recalling that the center of mass
G
of the test tube
was assumed to be at a distance
rD0:0918
m from the centrifuge’s spin
axis, and that the test tube had a mass
mD0:01 kg
and a mass moment
of inertia
IGD2:821⇥106kgm2
, determine the kinetic energy of the
test tube when it is spun at
!D60;000 rpm
. If you were to convert the
computed kinetic energy to gravitational potential energy, at what height,
in meters, relative to the ground could you lift a 10 kg mass?
Solution
The test tube is undergoing a fixed axis rotation about the axis of rotation of the centrifuge. Hence, the kinetic
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Problem 8.9
The uniform thin bars
AB
,
BC
, and
CD
have masses
mAB D2:3 kg
,
mBC D3:2 kg
, and
mCD D5:0 kg
, respectively. The connections at
A; B; C
, and
D
are pinned joints. Letting
RD0:75
m,
LD1:2
m, and
HD1:55
m, and
!AB D4rad=s
, compute the kinetic energy
T
of the
system at the instant shown.
Solution
The kinetic energy of the system is the sum of the kinetic energy of each individual component of the system.
Bar AB is undergoing a fixed axis rotation about A. Hence, the kinetic energy of bar AB is
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Dynamics 2e 1667
Problem 8.10
A T-bar consisting of two uniform bars, each of length
LD5ft
, is
released from rest in the position shown. Neglecting friction, determine
the angular speed of the T-bar when point Ais directly below point O.
Solution
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