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PROBLEM 13.18
The subway train shown is traveling at a speed of 30 mi/h when
the brakes are fully applied on the wheels of cars A, causing it
to slide on the track, but are not applied on the wheels of cars A
or B. Knowing that the coefficient of kinetic friction is 0.35
between the wheels and the track, determine (a) the distance
required to bring the train to a stop, (b) the force in each
coupling.
SOLUTION
BC
BC
PROBLEM 13.19
Blocks A and B weigh 25 lbs and 10 lbs, respectively, and they are both at a
height 6 ft above the ground when the system is released from rest. Just before
hitting the ground block A is moving at a speed of 9 ft/s. Determine (a) the
amount of energy dissipated in friction by the pulley, (b) the tension in each
portion of the cord during the motion.
SOLUTION
12
AB
→
PROBLEM 13.19 (Continued)
:12.10 lbB
PROBLEM 13.20
The system shown is at rest when a constant 30 lb force is
applied to collar B. (a) If the force acts through the entire
motion, determine the speed of collar B as it strikes the
support at C. (b) After what distance d should the 30 lb
force be removed if the collar is to reach support C with
zero velocity?
SOLUTION
PROBLEM 13.21
Car B is towing car A at a constant speed of 10 m/s on an uphill
grade when the brakes of car A are fully applied causing all four
wheels to skid. The driver of car B does not change the throttle
setting or change gears. The masses of the cars A and B are
1400 kg and 1200 kg, respectively, and the coefficient of
kinetic friction is 0.8. Neglecting air resistance and rolling
resistance, determine (a) the distance traveled by the cars
before they come to a stop, (b) the tension in the cable.
PROBLEM 13.22
The system shown is at rest when a constant 250-N force is applied to
block A. Neglecting the masses of the pulleys and the effect of friction
in the pulleys and between block A and the horizontal surface,
determine (a) the velocity of block B after block A has moved 2 m, (b)
the tension in the cable.
SOLUTION
B
PROBLEM 13.22 (Continued)
PROBLEM 13.23
The system shown is at rest when a constant 250-N force is applied to
block A. Neglecting the masses of the pulleys and the effect of friction
in the pulleys and assuming that the coefficients of friction between
block A and the horizontal surface are
0.25
s
m
=
and
0.20,
k
m
=
determine (a) the velocity of block B after block A has moved 2 m, (b)
the tension in the cable.
SOLUTION
Check the equilibrium position to see if the blocks move. Let F be the tension in the cable.
30
F mg
−=
30
AB
vv
+=
PROBLEM 13.23 (Continued)
PROBLEM 13.24
Two blocks A and B, of mass 4 kg and 5 kg, respectively, are connected
by a cord which passes over pulleys as shown. A 3 kg collar C is placed
on block A and the system is released from rest. After the blocks have
moved 0.9 m, collar C is removed and blocks A and B continue to move.
Determine the speed of block A just before it strikes the ground.
SOLUTION
Position to Position .
11
00vT= =
At before C is removed from the system
2 22
2 2 22
12
2
12
12
1 12 2
11
( ) (12 kg) 6
22
( ) (0.9 m)
(4 3 5)( )(0.9 m) (2 kg)(9.81 m/s )(0.9 m)
17.658 J
:
ABC
AC B
T mmmv v v
U m m mg
Ug
U
TU T
−
−
−
−
= ++ = =
= +−
= +− =
=
+=
22
22
0 17.658 6 2.943vv+= =
At Position , collar C is removed from the system.
Position to Position .
2
22
19
( ) kg (2.943) 13.244 J
22
AB
T m mv
′=+= =
22
3 33
19
( )( )
22
AB
T m mv v=+=
2
23
2 23 3
22
33
( )( )(0.7 m) ( 1 kg)(9.81 m/s )(0.7 m) 6.867 J
13.244 6.867 4.5 1.417
AB
U m mg
TU T
vv
′−
−
=−=− =−
′+=
−= =
31.190 m/s
A
vv= =
1.190 m/s
A
v=
PROBLEM 13.25
Four 3-kg packages are held in place by friction on a conveyor
which is disengaged from its drive motor. When the system is
released from rest, package 1 leaves the belt at A just as
package 4 comes onto the inclined portion of the belt at B.
Determine (a) the velocity of package 2 as it leaves the belt at
A, (b) the velocity of package 3 as it leaves the belt at A.
Neglect the mass of the belt and rollers.
SOLUTION
2
2
PROBLEM 13.25 (Continued)
(b) Package 2 falls off the belt and its energy is lost to the system, and 3 and 4 move down 2 ft.
35.60 m/sv=
PROBLEM 13.26
A 3-kg block rests on top of a 2-kg block supported by, but not attached to, a spring of
constant 40 N/m. The upper block is suddenly removed. Determine (a) the maximum
speed reached by the 2-kg block, (b) the maximum height reached by the 2-kg block.
SOLUTION
PROBLEM 13.26 (Continued)
PROBLEM 13.27
Solve Problem 13.26, assuming that the 2-kg block is attached to the spring.
PROBLEM 13.26 A 3-kg block rests on top of a 2-kg block supported by, but not
attached to, a spring of constant 40 N/m. The upper block is suddenly removed.
Determine (a) the maximum speed reached by the 2-kg block, (b) the maximum height
reached by the 2-kg block.
SOLUTION
2
dx =
PROBLEM 13.27 (Continued)
21
PROBLEM 13.28
People with mobility impairments can gain great health
and social benefits from participating in different
recreational activities. You are tasked with designing an
adaptive spring-powered shuffleboard attachment that
can be utilized by people who use wheelchairs.
Knowing that the coefficient of kinetic friction between
the 15 ounce puck A and the wooden surface is 0.3, the
maximum spring displacement you desire is 6 inches,
and that you want the puck to travel at least 30 ft/s,
determine (a) the spring constant k, (b) how far the
athlete should pull back the spring to make the puck
come to rest after 34 ft.
SOLUTION
11
1=5.13 ins
PROBLEM 13.29
A 7.5-lb collar is released from rest in the position shown, slides
down the inclined rod, and compresses the spring. The direction of
motion is reversed and the collar slides up the rod. Knowing that
the maximum deflection of the spring is 5 in., determine (a) the
coefficient of kinetic friction between the collar and the rod, (b) the
maximum speed of the collar.
SOLUTION
PROBLEM 13.30
A 10-kg block is attached to spring A and connected to spring B by a cord and
pulley. The block is held in the position shown with both springs unstretched when
the support is removed and the block is released with no initial velocity. Knowing
that the constant of each spring is 2 kN/m, determine (a) the velocity of the block
after it has moved down 50 mm, (b) the maximum velocity achieved by the block.
28
A
dx
PROBLEM 13.30 (Continued)
2000
