Problem 8.84
A uniform disk of mass
mD20 kg
and radius
RD0:75
m is being pulled
to the left with a constant horizontal force
P
by the cord wrapped around it.
Assume that the disk starts from rest and that it rolls without slip.
Apply the impulse-momentum principles to determine
P
if the center of
the disk achieves a speed vGD5m=s after 3s.
4.t2t1/:(7)
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Dynamics 2e 1799
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Problem 8.85
Moving on a straight and horizontal stretch of road, the rear-wheel-
drive car shown can go from rest to
60 mph
in
tD8
s. The
car weighs
2570 lb
(the weight includes the wheels). Each wheel
has diameter dD24:3 in:, mass moment of inertia relative to its
own center of mass
IGD0:989 slugft2
, and the center of mass
of each wheel coincides with its geometric center. Determine
the average friction force
Favg
acting on the car during
t
. In
addition, if the wheels roll without slip, for each wheel, determine
the average moment
Mavg
, computed relative to the wheel’s center,
that is applied to the wheel during t.
Solution
Average force acting on the car.
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Dynamics 2e 1801
Determination of the average moment acting on each wheel.
The four wheels are identical to one another. We consider one of the four wheels
and model it as a rigid body with center of mass at
G
coinciding with the center
1802 Solutions Manual
A spool with radius
RD3ft
is released from rest on an incline with
✓D30ı
, and its
center, which coincides with its center of mass, is observed to reach a speed of
8ft=s
two seconds after release. If the spool rolls without slip, use the impulse-momentum
principles to determine the radius of gyration of the spool kG.
Solution
Dynamics 2e 1803
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Problem 8.87
An eccentric wheel
B
weighing
150 lb
has its mass center
G
at a distance
dD4in:
from the wheel’s center
O
. The wheel is in the horizontal plane and is spun from rest by
applying a constant torque
MD32 ftlb
. Determine the wheel’s radius of gyration
kG
if
it takes 2s to spin up the wheel to 140 rpm. Neglect all possible sources of friction.
t1
where, denoting by
IO
the mass moment of inertia of the wheel about
O
and by
E!wD!wO
k
the angular
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Dynamics 2e 1805
Problem 8.88
The uniform thin pin-connected bars AB,BC, and CD have masses
mAB D
2:3 kg
,
mBC D3:2 kg
, and
mCD D5:0 kg
, respectively. Letting
RD0:75
m,
LD1:2
m, and
HD1:55
m, and knowing that bar
AB
rotates at a constant
angular velocity
!AB D4rad=s
, compute the angular momentum of bar
AB
about A, of bar BC about A, and bar CD about Dat the instant shown.
Solution
Angular momentum of bar AB about A.
Using the component system
shown, since
AB
is in a fixed axis rotation about
A
, using Eq. (8.44) on p. 620
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Problem 8.89
The weights of the uniform thin pin-connected bars
AB
,BC,
and CD are
WAB D4lb
,
WBC D6:5 lb
, and
WCD D10 lb
,
respectively. Letting
D47ı
,
RD2ft
,
LD3:5 ft
,
and
HD4:5 ft
, and knowing that bar
AB
rotates at a constant
angular velocity
!AB D4rad=s
, compute the magnitude of the
linear momentum of the system at the instant shown.
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Dynamics 2e 1807
Equation (8) is a vector equation corresponding to two scalar equations in the two unknowns
!BC
and
!CD
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