PROBLEM 12.14 (Continued)
32.2
PROBLEM 12.15
Each of the systems shown is initially at rest.
Neglecting axle friction and the masses of the pulleys,
determine for each system (a) the acceleration of
block A, (b) the velocity of block A after it has
moved through 10 ft, (c) the time required for block
A to reach a velocity of 20 ft/s.
SOLUTION
Let y be positive downward for both blocks.
Constraint of cable:
constant
AB
yy+=
A
PROBLEM 12.15 (Continued)
2
A
3
A
3
A
(c) Time at
20 ft/s. Use formula (3).
A
v=
20
PROBLEM 12.16
Boxes A and B are at rest on a conveyor belt that is initially at
rest. The belt is suddenly started in an upward direction so
that slipping occurs between the belt and the boxes. Knowing
that the coefficients of kinetic friction between the belt and
the boxes are
( ) 0.30
kA
µ
=
and
( ) 0.32,
kB
µ
=
determine the
initial acceleration of each box.
SOLUTION
Assume that
BA
aa>
so that the normal force NAB between the boxes is zero.
PROBLEM 12.16 (Continued)
Note: If it is assumed that the boxes remain in contact
( 0),
AB
N≠
then assuming NAB to be compression,
AB
PROBLEM 12.17
A 5000-lb truck is being used to lift a 1000 lb boulder B that
is on a 200 lb pallet A. Knowing the acceleration of the truck
is
1 ft/s2, determine (a) the horizontal force between the tires
and the ground, (b) the force between the boulder and the
pallet.
SOLUTION
2
PROBLEM 12.17 (Continued)
Horizontal components :
TT
F T ma−=
(a) Horizontal friction force between tires and ground.
AB
PROBLEM 12.18
Block A has a mass of 40 kg, and block B has a mass of 8 kg.
The coefficients of friction between all surfaces of contact are
0.20
s
µ
=
and
0.15.
k
µ
=
If P
0,=
determine (a) the
acceleration of block B, (b) the tension in the cord.
SOLUTION
From the constraint of the cord:
PROBLEM 12.18 (Continued)
0.15 cos 25 ( )
[ sin 25 0.15( 2 )cos 25 ]
9.81[40 sin 25 0.15(40 2 8)cos 25 ] 40
91.15202 40 (N)
A AB
B AB
A A B AB
B
B
mg m a
gm m m ma
a
a
− °− −
= °− + ° +
= °− + × ° +
= +
Equating the two expressions for T
PROBLEM 12.19
Block A has a mass of 40 kg, and block B has a mass of 8 kg.
The coefficients of friction between all surfaces of contact are
0.20
s
µ
=
and
0.15.
k
µ
=
If
40 NP=
, determine (a) the
acceleration of block B, (b) the tension in the cord.
SOLUTION
A AB
PROBLEM 12.19 (Continued)
PROBLEM 12.19 (Continued)
PROBLEM 12.20
The flat–bed trailer carries two 1500–kg beams with the upper
beam secured by a cable. The coefficients of static friction
between the two beams and between the lower beam and the
bed of the trailer are 0.25 and 0.30, respectively. Knowing that
the load does not shift, determine (a) the maximum acceleration
of the trailer and the corresponding tension in the cable, (b) the
maximum deceleration of the trailer.
SOLUTION
(a) Maximum acceleration. The cable secures the upper beam to the cab; the lower beam has impending slip.
(b) Maximum deceleration of trailer.
PROBLEM 12.20 (Continued)
PROBLEM 12.21
A baggage conveyor is used to unload luggage from an airplane.
The 10–kg duffel bag A is sitting on top of the 20-kg suitcase B.
The conveyor is moving the bags down at a constant speed of
0.5 m/s when the belt suddenly stops. Knowing that the
coefficient of friction between the belt and B is 0.3 and that bag A
does not slip on suitcase B, determine the smallest allowable
coefficient of static friction between the bags.
SOLUTION
PROBLEM 12.21 (Continued)
: cos 20 0
F ma N m g
Σ = − °=
PROBLEM 12.22
To unload a bound stack of plywood from a truck, the driver first tilts the
bed of the truck and then accelerates from rest. Knowing that the
coefficients of friction between the bottom sheet of plywood and the bed
are
0.40
s
µ
=
and
0.30,
k
µ
=
determine (a) the smallest acceleration of
the truck which will cause the stack of plywood to slide, (b) the
acceleration of the truck which causes corner A of the stack to reach the
end of the bed in 0.9 s.
SOLUTION
Let
P
a
be the acceleration of the plywood,
T
a
be the acceleration of the truck, and
/PT
a
be the acceleration
of the plywood relative to the truck.
2
2
( cos 20 sin 20 )
y P y P PT
PT
N mg a
= °− °
PROBLEM 12.22 (Continued)
T
PROBLEM 12.23
To transport a series of bundles of shingles A
to a roof, a contractor uses a motor-driven lift
consisting of a horizontal platform BC which
rides on rails attached to the sides of a ladder.
The lift starts from rest and initially moves
with a constant acceleration a1 as shown. The
lift then decelerates at a constant rate a2 and
comes to rest at D, near the top of the ladder.
Knowing that the coefficient of static friction
between a bundle of shingles and the
horizontal platform is 0.30, determine the
largest allowable acceleration a1 and the
largest allowable deceleration a2 if the bundle
is not to slide on the platform.
SOLUTION
PROBLEM 12.23 (Continued)
2