PROBLEM 13.126
The 18000-kg F-35B uses thrust vectoring to allow it
to take off vertically. In one maneuver, the pilot
reaches the top of her static hover at 200 m. The
combined thrust and lift force on the airplane applied
at the end of the static hover can be expressed as F=
(44t + 2500t2)i + (250t2 + t + 176580)j, where F and
t are expressed in newtons and seconds, respectively.
Determine (a) how long it will take the airplane to
reach a cruising speed of 1000 km/hr (cruising speed
is defined to be in the x-direction only), (b) the
altitude of the plane at this time.
SOLUTION
y,2 y,2
dt
PROBLEM 13.126 (Continued)
2
ty
PROBLEM 13.127
A truck is traveling down a road with a 4-percent 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.
SOLUTION
32.2[(0.60) cos 2.29 sin 2.29 ]
PROBLEM 13.128
In anticipation of a long
6°
upgrade, a bus driver accelerates at a constant rate from 80 km/h to 100 km/h in
8 s while still on a level section of the highway. Knowing that the speed of the bus is 100 km/h as it begins to
climb the grade at time t = 0 and that the driver does not change the setting of the throttle or shift gears,
determine (a) the speed of the bus when t = 10 s, (b) the time when the speed is 60 km/h.
SOLUTION
PROBLEM 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.
Determine (a) the time required for the train to stop after the
brakes are applied, (b) the force in the coupling between the
cars while the train is slowing down.
SOLUTION
PROBLEM 13.130
Solve Problem 13.129, assuming that a constant braking force
of 4300 lb is applied to car B, but the brakes on car A are not
applied.
PROBLEM 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. Determine (a) the time required for the train
to stop after the brakes are applied, (b) the force in the coupling
between the cars while the train is slowing down.
SOLUTION
2
(32.2 ft/s )(29.55 s)
C
C
PROBLEM 13.131
A tractor–trailer rig with a 2000–kg tractor, a 4500-kg trailer,
and a 3600-kg trailer is traveling on a level road at 90 km/h.
The brakes on the rear trailer fail and the antiskid system of the
tractor and front trailer provide the largest possible force which
will not cause the wheels to slide. Knowing that the coefficient
of static friction is 0.75, determine (a) the shortest time for the
rig to a come to a stop, (b) the force in the coupling between
the two trailers during that time. Assume that the force exerted
by the coupling on each of the two trailers is horizontal.
SOLUTION
PROBLEM 13.132
The system shown is at rest when a constant 150-N force
is applied to collar B. Neglecting the effect of friction,
determine (a) the time at which the velocity of collar B
will be 2.5 m/s to the left, (b) the corresponding tension
in the cable.
PROBLEM 13.132 (Continued)
PROBLEM 13.133
An 8-kg cylinder C rests on a 4–kg platform A supported by a cord which
passes over the pulleys D and E and is attached to a 4–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.
SOLUTION
C
PROBLEM 13.134
An estimate of the expected load on over–
the–shoulder seat belts is to be made before
designing prototype belts that will be
evalua
ted in automobile crash tests.
Assuming that an automobile traveling at 45
mi/h is brought to a stop in 110 ms,
determine (a) the average impulsive force
exerted by a 200-lb man on the belt, (b) the
maximum force
m
F
exerted on the belt if
the force–time diagram has the shape shown.
PROBLEM 13.135
A 60–g model rocket is fired vertically. The engine
applies a thrust P which varies in magnitude as shown.
Neglecting air resistance and the change in mass of the
rocket, determine (a) the maximum speed of the rocket
as it goes up, (b) the time for the rocket to reach its
maximum elevation.
SOLUTION
20.8 s.t=
PROBLEM 13.135 (Continued)
(a) Maximum speed (upward motion):
PROBLEM 13.136
A simplified model consisting of a single straight line is to be obtained for the
variation of pressure inside the 10-mm–diameter barrel of a rifle as a 20–g bullet
is fired. Knowing that it takes 1.6 ms for the bullet to travel the length of the
barrel and that the velocity of the bullet upon exit is 700 m/s, determine the value
of p0.
SOLUTION
PROBLEM 13.137
A crash test is performed between an SUV A and a 2500 lb compact car B.
The compact car is stationary before the impact and has its brakes applied. A
transducer measures the force during the impact, and the force P varies as
shown. Knowing that the coefficients of friction between the tires and road
are ms= 0.9 and mk= 0.7, determine (a) the time at which the compact car will
start moving, (b) the maximum speed of the car, (c) the time at which the car
will come to a stop.
SOLUTION
(b) Maximum Velocity will occur near the end of the impulse when:
2500 lb 77.64 slugs
s
f k kB
P F N mg
mm
= = =
PROBLEM 13.137 (Continued)
B,max 60000 150000 0
||
mm
B kB
tt
stp
PROBLEM 13.138
A crash test is performed between a 4500 lb SUV A and a compact
car B. A transducer measures the force during the impact, and the
force P varies as shown. Knowing that the SUV is travelling 30
mph when it hits the car, determine the speed of the SUV
immediately after the impact.
2
2
PROBLEM 13.139
A baseball player catching a ball can soften the impact by
pulling his hand back. Assuming that a 5-oz ball reaches his
glove at 90 mi/h and that the player pulls his hand back during
the impact at an average speed of 30 ft/s over a distance of 6
in., bringing the ball to a stop, determine the average impulsive
force exerted on the player’s hand.
av
( ) ( )
5
16
21
60
lb (132 ft/s)
(32.2 ft/s ) s
=
76.9 lb
av
F=
PROBLEM 13.140
A 1.62 ounce golf ball is hit with a golf club and leaves it with a velocity of 100 mi/h. We assume that for
0t≤≤
t0, where t0 is the duration of the impact, the magnitude F of the force exerted on the ball can be
expressed as F
0
sin ( / ).
m
F tt
π
=
Knowing that
0
0.5 ms,t=
determine the maximum value
m
F
of the force
exerted on the ball.
PROBLEM 13.141
The triple jump is a track–and–field event in which an athlete
gets a running start and tries to leap as far as he can with a hop,
step, and jump. Shown in the figure is the initial hop of the
athlete. Assuming that he approaches the takeoff line from the
left with a horizontal velocity of 10 m/s, remains in contact
with the ground for 0.18 s, and takes off at a 50° angle with a
velocity of 12 m/s, determine the vertical component of the
average impulsive force exerted by the ground on his foot. Give
your answer in terms of the weight W of the athlete.
SOLUTION