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Unformatted text preview: eaches 13.15 The subway train shown is traveling at a speed of 30 mi/h when
coefﬁ. the brakes are fully applied on the wheels of cars B and C, causing
line is them to slide on the track, but are not applied on the wheels of
(b) the car A. 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, (17) the force in each
coupling. 30 mi/h Fig. 913.15 .>locity 13.16 Solve Prob. 13.15 assuming that the brakes are applied only on the
tween wheels of car A. 1mum VelOC 13.17 A trailer truck enters a 2 percent downhill grade traveling at 108 km/h and must slow down to 72 km/h in 300 m. The cab has
a mass of 1800 kg and the trailer 5400 kg. Determine (a) the aver— 0 to 3 age braking force that must be applied, (19) the average force
at B. exerted on the coupling between cab and trailer if 70 percent
l"eyor of the braking force is supplied by the trailer and 30 percent by
Us. the cab. 108 km/h _ H W I *
WA... 1. '.".',"i. _ L——300m————’l Fig. P13.l7 to a
at B' 13.18 A trailer truck enters a 2 percent uphill grade traveling at 72 km/h
veyor and reaches a speed of 108 km/h in 300 m. The cab has a mass
of 1800 kg and the trailer 5400 kg. Determine (a) the average force
at the wheels of the cab, (17) the average force in the coupling
Ill/5' between the cab and the trailer.
lthh
ween
.f the 108 km/h
72 km'h
m/s. 2% up grade
rhich
0.25 Fig. mars Problems 773 the cable. 13.21 The system shown is at rest when a constant 150N force is applied
to collar B. {a} If the force acts through the entire motion, deter
mine the speed of collar B as it strikes the support at C. (b) After
what distance d should the 150N force be removed if the collar
is to reach support C with zero velocity? Fig. P13.2'l 13.22 Blocks A and B have masses of 11 kg and 5 kg, respectively, and
they are both at a height h = 2 m above the ground when the
system is released from rest. Just before hitting the ground blockA
is moving at a speed of 3 m/s. Determine (a) the amount of energy
dissipated in friction by the pulley, (b) the tension in each portion Fig. P1332 of the cord during the motion.  Kine'i“ °f POF'iC'W EnergY and Momemum 13.19 Two identical blocks are released from rest. Neglecting the mags Melh°d5 of the pulleys and the effect of friction, determine (a) the velocity
{ of block B after it has moved 2 m, (b) the tension in the cable.
Fig. "3.19 and "3.20
13.20 Two identical blocks are released from rest. Neglecting the mass
of the pulleys and knowing that the coefficients of static and
kinetic friction are 1.1.5 = 0.30 and M = 0.20, determine (a) the
velocity of block B after it has moved 2 m, (b) the tension in 13.39 The sphere at A is given a downward velocity v0 and swings in a
vertical circle of radius l and center 0. Determine the smallest
velocity v0 for which the sphere will reach point B as it swings
about point 0 (a) if A0 is a rope, { ) if A0 is a slender rod of
negligible mass. The sphere at A is given a downward velocity v0 of magnitude
5 m/s and swings in a vertical plane at the end of a rope of length
l = 2 m attached to a support at 0. Determine the angle 0 at
which the rope will break, knowing that it can withstand a maxi—
mum tension equal to twice the weight of the sphere. A section of track for a roller coaster consists of two circular arcs AB and CD joined by a straight portion BC. The radius of AB is 90 ft and the radius of CD is 240 ft. The car and its occupants, of total weight 560 lb reach point A with ractically no velocity and . then drop freely along the track. DetErmine the normal force ﬁg. “3'39 and "3.40
exerted by the track on the car as the car reaches point B. Ignore air resistance and rolling resistance. « ; ‘mmmk‘ human Fig. P13.“ and P'l3.42 13.42 A section of track for a roller coaster consists of two circular arcs
AB and CD joined by a straight portion BC. The radius of AB is
90 ft and the radius of CD is 240 ft. The car and its occupants, of
total weight 560 lb, reach point A with practically no velocity and
then drop freely along the track. Determine the maximum and
minimum values of the normal force exerted by the track on the
car as the car travels from A to D. Ignore air resistance and rolling
resistance. A small sphere B of mass m is released from rest in the position
shown and swings freely in a vertical plane, first about 0 and then
about the peg A after the cord comes in contact with the peg.
Determine the tension in the cord (0) just before the sphere
comes in contact with the peg, (19) just after it comes in contact
with the peg. Fig. Pl3.43 Kinetics 0‘ POF’iC'eSI Energy and Momen’um 13.63 It is shown in mechanics of materials that when an elastic beam I
Methods AB supports a block of weight W at a given point B, the deﬂection ‘1 . ys, (called the static deflection) is proportional to W. Show that if. the same block is dropped from a height h onto the end B of a T cantilever beam AB and does not bounce off, the maximum deflec tion y," in the ensuing motion can be expressed as y," = g“ h
B [1 + V1 + 2h/yst)_ Note that this formula is approximate, since
A ’:‘.::M_U_._"" _ “mun—M“— mm."— __ ; ____ _._ _J ym it is based on the assumption that there is no energy dissipated in
T the impact and that the weight of the beam is small compared to
the weight of the block. 13.64 A thin circular rod is supported in a vertical plane by a bracket at
A. Attached to the bracket and loosely wound around the rod is a
spring of constant k = 3 lb/ft and undeformed length equal to the
arc of circle AB. An 8oz collar C, not attached to the spring, can
slide without friction along the rod. Knowing that the collar is
released from rest when 2 30°, determine (a) the maximum
height above point B reached by the collar, (19) the maximum speed
of the collar. 13.65 A thin circular rod is supported in a vertical plane by a bracket at
A. Attached to the bracket and loosely wound around the rod is a
spring of constant k t 3 lb/ft and undeformed length equal to the
arc of circle AB. An 8—oz collar C, not attached to the spring, can 134 Fig. Pl3.64 and P‘l3.65 (a) the smallest value of 0 for which the collar will pass through
D and reach point A, (b) the velocity of the collar as it reaches
point A. 13.66 A 2.7lb collar can slide along the rod shown. It is attached to an 13"
elastic cord anchored at F, which has an undeformed length of 0.9 ft
and spring constant of 5 lb/ft. Knowing that the collar is released '3 I
from rest at A and neglecting friction, determine the speed of the " collar {(1} at B, (b) at E. 13.1 13.1 13.67 The system shown is in equilibrium when 45 = 0. Knowing that
initially <15 = 90° and that block C is given a slight nudge when
the system is in that position, determine the speed of the block as
it passes through the equilibrium position 4) = 0. Neglect the
weight of the rod. \9 Fig. P13.67 A spring is used to stop a 50kg package which is moving down a
20° incline. The spring has a constant k = 30 kN/m and is held by
cables so that it is initially compressed 50 mm. Knowing that the
velocity of the package is 2 m/s when it is 8 m from the spring and
neglecting friction, determine the maximum additional deforma
tion of the spring in bringing the package to rest. Solve Prob. 13.68 assuming the kinetic coefficient of friction
between the package and the incline is 0.2. _
Flg. P'I3.68
A 300g pellet is released from rest at A and slides with friction along the surface shown. Determine the force exerted on the pel let by the surface {a) just before the pellet reaches B, (b) immedi ately after it has passed through B. Fig. "3.70 and P13.7I A BOOg pellet is released from rest at A and slides without friction
along the surface shown. Determine the force exerted on the pel
let by the surface (a) just before the pellet reaches C, (b) imme
diately after it has passed through C. A 1.2lb collar can slide without friction along the semicircular rod
BCD. The spring is of constant 1.8 lb/in and its undeformed length
is 8 in. Knowing that the collar is released from rest at B, deter—
mine {a} the speed of the collar as it passes through C, (b) the
force exerted by the rod on the collar at C. Fig. "3.72 PROBLEMS Fig. 1:13.121 Fig. P13.123 814 13.119 A 1200kg automobile is moving at a speed of 90 km/h when the brakes are fully applied, causing all four wheels to skid. Determine
the time required to stop the automobile (a) on dry pavement (m. = 0.75), (b) on an icy road (/14. = 0.10). 13.120 A 40,000ton ocean liner has an initial velocity of 2.5 mi/h. 13.121 Neglecting the frictional resistance of the water, determine the
time required to bring the liner to rest by using a single tugboat
which exerts a constant force of 35 kips. The initial velocity of the block in position A is 30 ft/s. Knowing
that the coefficient of kinetic friction between the block and the
plane is M = 0.30, determine the time it takes for the block to
reach B with zero velocity, if (a) 0 = O, (b) 0 = 20°. 13.122 A 2kg particle is acted upon by the force, expressed in newtons, 13.123 13.124 13.125 F = (8 — 6t)i + (4 — t2)j + (4 + t)k. Knowing that the velocity
of the particle is v = (150 m/s)i + (100 m/s)j  (250 m/s)k at
t = 0, determine (a) the time at which the velocity of the particle
is parallel to the yz plane, (19} the corresponding velocity of the
particle. Skid marks on a drag race track indicate that the rear (drive)
wheels of a car slip for the first 60 ft of the 1320ft track.
(a) Knowing that the coefficient of kinetic friction is 0.60, deter
mine the shortest possible time for the car to travel the initial
60ft portion of the track if it starts from rest with its front
wheels just off the ground. (1)} Determine the minimum time for
the car to run the whole race if, after skidding for 60 ft, the wheels
roll without sliding for the remainder of the race. Assume for the
rolling portion of the race that 60 percent of the weight is on the
rear wheels and that the coefficient of static friction is 0.85.
Ignore air resistance and rolling resistance. A truck is traveling on a level road at a speed of 90 km/h when its
brakes are applied to slow it down to 30 km/h. An antiskid braking
system limits the braking force to a value at which the wheels of
the truck are just about to slide. Knowing that the coefficient of
static friction between the road and the wheels is 0.65, determine
the shortest time needed for the truck to slow down. A truck is traveling down a road with a 4percent grade at a speed
of 60 mi/h when its brakes are applied to slow it down to 20 mi/h.
An antiskid braking system limits the braking force to a value
at which the wheels of the truck are just about to slide. Knowing
that the coefficient of static friction between the road and the wheels is 0.60, determine the shortest time needed for the truck
to slow down. 13.12! 13.121 13. 121 13.12' 13.13 13.11 13.11 13.1 n the
“mine
*ment mi/h.
9 the
gboat wing
i the
:k to ﬁve)
ack.
ter
itial
‘ont
 for
eels
the
the
85. its ing
: of ine 13.126 Baggage on the ﬂoor of the baggage car of a highspeed train is
not prevented from moving other than by friction. Determine the
smallest allowable value of the coefficient of static friction between
a trunk and the floor of the car if the trunk is not to slide when
the train decreases its speed at a constant rate from 200 km/h to
90 km/h in a time interval of 12 5. 13.127 Solve Prob. 13.126, assuming that the train is going down a
5percent grade. 13.128 A sailboat weighing 980 lb with its occupants is running down
wind at 8 mi/h when its spinnaker is raised to increase its speed.
Determine the net force provided by the spinnaker over the 10s
interval that it takes for the boat to reach a speed of 12 mi/h. 13.129 A light train made of two cars travels at 45 mi/h. Car A weighs
18 tons, and car B weighs 13 tons. When the brakes are applied,
a constant braking force of 4300 lb is applied to each car. Deter
mine {a} the time required for the train to stop after the brakes
are applied, [bl the force in the coupling between the cars while the train is slowing down. 13.130 Solve Prob. 13.129, assuming that a constant braking force of
4300 lb is applied to car B but that the brakes on car A are not applied. 13.131 A trailer truck with a 2000—kg cab and an 8000—kg trailer is travel
ing on a level road at 90 km/h. The brakes on the trailer fail and
the antiskid system of the cab provides the largest possible force
which will not cause the wheels of the cab to slide. Knowing that
the coefficient of static friction is 0.65, determine {a} the shortest
time for the rig to come to a stop, (b) the force in the coupling
during that time. ' 13.132 An 8kg cylinder C rests on a 4kg platform A supported by a cord
which passes over the pulleys D and E and is attached to a4—kg
block B. Knowing that the system is released from rest, determine
(a) the velocity of block B after 0.8 s, (b) the force exerted by the cylinder on the platform. Fig. 1:13.132 13.133 The system shown is released from rest. Determine the time it
takes for the velocity of A to reach 1 m/s. Neglect friction and the mass of the pulleys. Problems Fig. P13.128 45 mi/h <——
A 18 tons 815 Fig. P13.129 Fig. P13.13'I Fig. 913.133 13.141 The last segment of the triple jump track—and—field event is the
jump, in which the athlete makes a final leap, landing in a sand
filled pit. Assuming that the velocity of a 185lb athlete just before \
landing is 30 ft/s at an angle of 35° with the horizontal and that
the athlete comes to a complete stop in 0.22 s after landing, deter—
mine the horizontal component of the average impulsive force exerted on his feet during landing. 13.142 An estimate of the expected load on overtheshoulder seat belts
is to be made before designing prototype belts that will be evalu— _
ated in automobile crash tests. Assuming that an automobile travel M    '   ing at 45 mi/h is brought to a stop in 110 ms, determine
(a) the average impulsive force exerted by a ZOOlb man on the
belt, {12) the maximum force Fm exerted on the belt if the force time diagram has the shape shown. Landing pit
Fig. P13.'l4'l Fig. 913.142 13.143 A 46g golf ball is hit with a golf club and leaves it witha veloc
ity of 50 m/s. We assume that for 0 S t S to, where to is the
duration of the impact, the magnitude F of the force exerted on
the ball can be expressed as F = Fm sin (wt/t0). Knowing that
to = 0.5 ms, determine the maximum value Fm of the force exerted on the ball. 13.144 The design for a new cementless hip implant is to be studied using
an instrumented implant and a fixed simulated femur. Assuming
the punch applies an average force of 2 kN over a time of 2 ms to
the 200 g implant, determine (a) the velocity of the implant imme
diately after impact, (19) the average resistance of the implant to
penetration if the implant moves 1 mm before coming to rest. Fig. 913.144 13.145 A 20Mg railroad car moving at 4 km/h is to be coupled to a 40—Mg
car which is at rest with locked wheels {,uk : 0.30). Determine
{a} the velocity of both cars after the coupling is completed,
(19} the time it takes for both cars to come to rest. 4 km/h Fig. P13.145 Problems 8 'l 7 818 Kine'ics 0f PGY'iC'ESI EWSY 0nd MOmenfum 13.146 At an intersection car B was traveling south and car A was traveljn I
Me'hods 30° north of east when they slammed into each other. Upon inves~ ' tigation it was found that after the crash the two cars got stuck and skidded off at an angle of 10° north of east. Each driver claimed that he was going at the speed limit of 50 km/h and that he tried to slow down but couldn’t avoid the crash because the other driver was going a lot faster. Knowing that the masses of cars A and B were 1500 kg and 1200 kg, respectively, determine {a} which car was going faster, (b) the speed of the faster of the two cars if the slower car was traveling at the speed limit. 13.147 A mother and her child are skiing together, with the mother hold.
ing the end of a rope tied to the child’s waist. They are moving at
a speed of 7.2 km/h on a flat portion of the ski trail when the
mother observes that they are approaching a steep descent. She
decides to pull on the rope to decrease the child’s speed. Knowing
that this maneuver causes the child’s speed to be cut in half in
3 s and neglecting friction, determine (a) the mother’s speed at the
end of the 35 interval, (1)) the average value of the tension in the
rope during that time interval. Fig. Pl3.‘l46 Fig. P'l3.'l47 13.148 Bullet B weighs 0.5 oz and blocks A and C both weigh 3 lb. The
coefﬁcient of friction between the blocks and the plane is Mk = 0.25.
Initially the bullet is moving at 00 and blocks A and C are at rest
(Fig. 1). After the bullet passes through A it becomes embedded in
block C and all three objects come to stop in the positions shown
(Fig. 2). Determine the initial speed of the bullet on. Fig. "3.148 ...
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