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CHAPTER 13
PROBLEM 13.1
A 400-kg satellite is placed in a circular orbit 6394 km above the surface of the earth. At this elevation the
acceleration of gravity is
2
4.09 m/s .
Knowing that its orbital speed is 20 000 km/h, determine the kinetic
energy of the satellite.
SOLUTION
PROBLEM 13.2
A 1-lb stone is dropped down the “bottomless pit” at
Carlsbad Caverns and strikes the ground with a speed
of 95 ft/s. Neglecting air resistance, determine (a) the
kinetic energy of the stone as it strikes the ground and
the height h from which it was dropped, (b) Solve Part
a assuming that the same stone is dropped down a hole
on the moon. (Acceleration of gravity on the moon =
5.31 ft/s2.)
SOLUTION
2
lb 1 lb 0.031056 lb s /ft
W
2 (2)(5.31)
PROBLEM 13.3
A baseball player hits a 5.1-oz baseball with an initial velocity of 140 ft/s at
an angle of 40° with the horizontal as shown. Determine (a) the kinetic
energy of the ball immediately after it is hit, (b) the kinetic energy of the ball
when it reaches its maximum height, (c) the maximum height above the
ground reached by the ball.
SOLUTION
1 lb
PROBLEM 13.4
A 500-kg communications satellite is in a circular geosynchronous orbit and completes one revolution about
the earth in 23 h and 56 min at an altitude of 35800 km above the surface of the earth. Knowing that the radius
of the earth is 6370 km, determine the kinetic energy of the satellite.
PROBLEM 13.5
In an ore-mixing operation, a bucket full of ore is suspended
from a traveling crane which moves along a stationary bridge.
The bucket is to swing no more than 10 ft horizontally when
the crane is brought to a sudden stop. Determine the maximum
allowable speed v of the crane.
SOLUTION
PROBLEM 13.6
In an ore-mixing operation, a bucket full of ore is suspended
from a traveling crane which moves along a stationary bridge.
The crane is traveling at a speed of 10 ft/s when it is brought to
a sudden stop. Determine the maximum horizontal distance
through which the bucket will swing.
SOLUTION
PROBLEM 13.7
Determine the maximum theoretical speed that may be achieved over a distance of 110 m by a car starting
from rest assuming there is no slipping. The coefficient of static friction between the tires and pavement is 0.75,
and 60 percent of the weight of the car is distributed over its front wheels and 40 percent over its rear wheels.
Assume (a) front-wheel drive, (b) rear-wheel drive.
SOLUTION
PROBLEM 13.8
A 2000-kg automobile starts from rest at point A on a
o
6
incline and coasts through a distance of 150 m to point B. The
brakes are then applied, causing the automobile to come to a
stop at point C, 20 m from B. Knowing that slipping is
impending during the braking period and neglecting air
resistance and rolling resistance, determine (a) the speed of the
automobile at point B, (b) the coefficient of static friction
between the tires and the road.
SOLUTION
PROBLEM 13.9
A package is projected up a
15°
incline at A with an initial
velocity of 8 m/s. Knowing that the coefficient of kinetic
friction between the package and the incline is 0.12, determine
(a) the maximum distance d that the package will move up the
incline, (b) the velocity of the package as it returns to its
original position.
SOLUTION
A
A
PROBLEM 13.10
A 1.4 kg model rocket is launched vertically from rest with a constant thrust of 25 N until the rocket reaches
an altitude of 15 m and the thrust ends. Neglecting air resistance, determine (a) the speed of the rocket when
the thrust ends, (b) the maximum height reached by the rocket, (c) the speed of the rocket when it returns to
the ground.
SOLUTION
PROBLEM 13.11
Packages are thrown down an incline at A with a velocity of 1
m/s. The packages slide along the surface ABC to a conveyor
belt which moves with a velocity of 2 m/s. Knowing that
0.25
k
m
=
between the packages and the surface ABC,
determine the distance d if the packages are to arrive at C with
a velocity of 2 m/s.
SOLUTION
PROBLEM 13.12
Packages are thrown down an incline at A with a velocity of
1 m/s. The packages slide along the surface ABC to a conveyor
belt which moves with a velocity of 2 m/s. Knowing that
7.5 md=
and
0.25
k
m
=
between the packages and all
surfaces, determine (a) the speed of the package at C, (b) the
distance a package will slide on the conveyor belt before it
comes to rest relative to the belt.
SOLUTION
belt
PROBLEM 13.12 (Continued)
(2)(0.25)(9.81)
belt
PROBLEM 13.13
Boxes are transported by a conveyor belt with a velocity v0 to
a fixed incline at A where they slide and eventually fall off at
B. Knowing that
0.40,
k
m
=
determine the velocity of the
conveyor belt if the boxes leave the incline at B with a velocity
of 8 ft/s.
PROBLEM 13.14
Boxes are transported by a conveyor belt with a velocity v0 to
a fixed incline at A where they slide and eventually fall off at
B. Knowing that
0.40,
k
m
=
determine the velocity of the
conveyor belt if the boxes are to have zero velocity at B.
0
PROBLEM 13.15
A 1200-kg trailer is hitched to a 1400-kg car. The car and trailer are
traveling at 72 km/h when the driver applies the brakes on both the car
and the trailer. Knowing that the braking forces exerted on the car and
the trailer are 5000 N and 4000 N, respectively, determine (a) the
distance traveled by the car and trailer before they come to a stop,
(b) the horizontal component of the force exerted by the trailer hitch
on the car.
SOLUTION
PROBLEM 13.16
A trailer truck enters a 2 percent uphill grade traveling at 72 km/h 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, (b) the average force in the coupling between the cab and the trailer.
PROBLEM 13.17
The subway train shown is traveling at a speed of 30 mi/h when
the brakes are fully applied on the wheels of cars B and C,
causing them to slide on the track, but are not applied on the
wheels of 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, (b) the force in
each coupling.
SOLUTION
