Problem 7.22
The stationary excavator is vertically lifting the load at
A
with
acceleration
a0D2:5 m=s2
. If
`D4
m,
wD3:65
m,
dD
0:82
m, the mass of the load at
A
is
mAD8300 kg
, and the
total mass of the excavator is
mGD20;000 kg
, determine the
equivalent normal force acting on each of the two tracks and its
location relative to the rear of the track
ı
. The center of mass of
the excavator is at G.
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Dynamics 2e 1457
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Problem 7.23
The system shown lies in the vertical plane. The trolley
A
is
moving to the right with a constant acceleration
aA
. Attached
to the trolley is a rope
AB
of negligible mass. Attached to the
end of the rope is a T-bar consisting of two thin uniform bars
BC
and
DE
, each of which has length
L
and mass
m
(bar
BC
is attached at the midpoint of bar
DE
). When the trolley
A
is
accelerating at constant
aA
, the angles
and
are both constant.
Determine these two constant angles in this steady state. Note
that
cos.
2x/ Dsin x
and the mass center of the T-bar is at
G
.
Solution
The FBD of the T-bar is shown on the right, where
TAB
is the tension in the
rope AB.
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1459
which means that the moment equation becomes
3L
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Problem 7.24
The
3300 lb
front-wheel-drive car whose mass center is at
A
is pulling a
4300 lb
trailer whose mass center
is at
B
. The car and trailer start from rest and accelerate uniformly to
60 mph
in
18
s. Determine the forces
on all tires, as well as the total force acting on the car due to the trailer. In addition, determine the friction
required so that the wheels of the car do not slip. Assume that the car and trailer are laterally symmetric
and that the rotational inertia of the wheels is negligible. Note that the mass center of the trailer is directly
above the axle of the rear wheel.
fC2NrCHyWcDWc
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Dynamics 2e 1461
Force Laws. All forces are accounted for on the FBD.
Kinematic Equations.
Since the acceleration in the horizontal direction is constant, there is no acceleration
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the force on each of the rear tires of the car is
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Dynamics 2e 1463
Problem 7.25
The
3300 lb
front-wheel-drive car, which is pulling a
4300 lb
trailer, is traveling
60 mph
and applies its
brakes to come to a stop. Assuming that all four wheels of the car assist in the braking and that
sD0:85
,
determine the minimum possible stopping distance, and find the forces on all tires, as well as the total
force acting on the car due to the trailer. Assume that the car and trailer are laterally symmetric. Note that
the mass center of the trailer is directly above the axle of the rear wheel.
fC2FrDWc
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XMBWHyd4Hx.h3h2/DIB˛t;(6)
where
IB
is the mass moment of inertia of the trailer with respect to its mass center
B
,
˛t
is the angular
acceleration of the trailer, and Wtis the weight of the trailer.
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Dynamics 2e 1465
Therefore, the forces on the tires are
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