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PROBLEM 16.145 (Continued)
Rod
LL
PROBLEM 16.146
The uniform slender 2-kg bar BD is attached to the uniform 6-kg
uniform disk by a pin at B and released from rest in the position
shown. Assuming that the disk rolls without slipping, determine
(a) the initial reaction at the contact point A, (b) the corresponding
smallest allowable value of the coefficient of static friction.
PROBLEM 16.147*
The 6-lb cylinder B and the 4-lb wedge A are held at rest in the
position shown by cord C. Assuming that the cylinder rolls without
sliding on the wedge and neglecting friction between the wedge and
the ground, determine, immediately after cord C has been cut, (a) the
acceleration of the wedge, (b) the angular acceleration of the cylinder.
SOLUTION
Kinematics: We resolve
B
a
into
A
a
and a component parallel to the incline
/
BA
Kinetics: Cylinder and wedge
n
Cylinder
22
1 1 6 lb (0.25 ft)
22
3
16
W
gg
Ig
=
PROBLEM 16.147* (Continued)
(b) Angular acceleration of the cylinder.
A
A
PROBLEM 16.148*
The 6-lb cylinder B and the 4-lb wedge A are held at rest in the
position shown by cord C. Assuming that the cylinder rolls without
sliding on the wedge and neglecting friction between the wedge and
the ground, determine, immediately after cord C has been cut, (a) the
acceleration of the wedge, (b) the angular acceleration of the
cylinder.
SOLUTION
Kinematics: We resolve
B
a
into
A
a
and a horizontal component
/BA
a
/
BA
Kinetics: Cylinder and wedge:
A
PROBLEM 16.148* (Continued)
(a) Acceleration of the wedge.
PROBLEM 16.149*
Each of the 3-kg bars AB and BC is of length L = 500 mm. A horizontal force P of
magnitude 20 N is applied to bar BC as shown. Knowing that b = L (P is applied at C),
determine the angular acceleration each bar.
SOLUTION
2
x AB BC
PROBLEM 16.149* (Continued)
Bar AB:
L
PROBLEM 16.150*
Each of the 3-kg bars AB and BC is of length
500 mm.L=
A horizontal force P of
magnitude 20 N is applied to bar BC. For the position shown, determine (a) the distance
b for which the bars move as if they formed a single rigid body, (b) the corresponding
angular acceleration of the bars.
3
PROBLEM 16.150* (Continued)
Bar BC:
L
11 11 (3 kg)(0.5 m)
mL
PROBLEM 16.151*
(a) Determine the magnitude and the location of the maximum bending moment in the rod of Problem 16.78.
(b) Show that the answer to Part a is independent of the weight of the rod.
SOLUTION
L
3
PROBLEM 16.151* (Continued)
Substituting into (2)
3
max 2
1 1 12
() 2 2 23
3 33
() 33
J
PL P L PL
ML
PL
M
=−=
=
PROBLEM 16.152*
Draw the shear and bending-moment diagrams for the beam of Problem 16.84 immediately after the cable
at B breaks.
SOLUTION
From answers to Problem 16.84:
3
1
2
4 3 4 3 12
LL
PROBLEM 16.152* (Continued)
2
3
mg mg mg
27 3
PROBLEM 16.153
A cyclist is riding a bicycle at a speed of 20 mph on a horizontal road. The distance between the axles is
42 in., and the mass center of the cyclist and the bicycle is located 26 in. behind the front axle and 40 in.
above the ground. If the cyclist applies the brakes only on the front wheel, determine the shortest distance in
which he can stop without being thrown over the front wheel.
SOLUTION
0
20 mphv=
When cyclist is about to be thrown over the front wheel,
0
A
N=
eff
( ) : (26 in.) (40in.)
BB
M M mg maΣ=Σ =
22
26 26 (32.2 ft/s ) 20.93 ft/s
40 40
ag= = =
Uniformly accelerated motion:
0
22 2 2
0
20 mph 29.333 ft/s
2 : 0 (29.333 ft/s) 2( 20.93 ft/s )
20.555 ft
v
v v as s
s
= =
−= − =−
=
20.6 fts=
PROBLEM 16.154
The forklift truck shown weighs 2250 lb and is
used to lift a crate of weight
2500 lb.W=
The
truck is moving to the left at a speed of 10 ft/s
when the brakes are applied on all four wheels.
Knowing that the coefficient of static friction
between the crate and the fork lift is 0.30,
determine the smallest distance in which the truck
can be brought to a stop if the crate is not to slide
and if the truck is not to tip forward.
SOLUTION
req 0.09 0.30.
PROBLEM 16.155
The total mass of the baja car and driver, including the
wheels, is 250 kg. Each pair of 58-cm radius wheels and
axle has a total mass of 20 kg and a mass moment of
inertia of 2.9 kg-m2. The center of gravity of the driver
and baja body (not including the wheels) is located x= 0.70
m from the rear axle A and y = 0.55 m from the ground,
and the wheelbase is L= 1.60 m. If the engine exerts a
torque of 500 N-m on the rear axle, what is the car’s
acceleration?
SOLUTION
x ww x w
PROBLEM 16.155 (Continued)
Free Body Diagram of Car Body:
Kinetics:
Set up System of Linear Equations (1)→(10):
x cx
F ma
=
∑
xy xy
1 0 0 0 1 0 0 0 20 0 0
0 1 0 0 0 1 0 0 0 0 196
0 0 0 0 0.58 0 0 0 0 2.9
0 0 1 0 0 0 1 1 20 0
0001000000
x
y
x
y
A
A
B
B
f
−−
−
−
− −−
−
.2
500
0
196.2
x
PROBLEM 16.156
Identical cylinders of mass m and radius r are pushed by a series of moving arms. Assuming the coefficient of
friction between all surfaces to be
1
µ
<
and denoting by a the magnitude of the acceleration of the arms,
derive an expression for (a) the maximum allowable value of a if each cylinder is to roll without sliding,
(b) the minimum allowable value of a if each cylinder is to move to the right without rotating.
SOLUTION
a
r
P is horizontal component of force that the arm exerts on cylinder.
eff
( ): ( ) ( )
AA k
M M Pr P r I m a r
µa
Σ=Σ − =+
2
1
(1 ) ( )
2
3
2 (1 )
a
P r mr ma r
r
ma
P
µ
µ
−= +
=−
(1)
0:
y
FΣ=
0N P mg
µ
−−=
(2)
eff
( ):
xx
FFΣ=Σ
P N ma
µ
−=
(3)
Solve (2) for N and substitute for N into (3).
2
P P mg ma
µµ
−− =
Substitute P from (1):
23
(1 ) 2 (1 )
ma mg ma
µµ
µ
− −=
−
3(1 ) 2 2
(1 3 ) 2 0
a ga
ag
µµ
µµ
+− =
+− =
2
13
ag
µ
µ
=+
PROBLEM 16.156 (Continued)
