CHAPTER 12
PROBLEM 12.1
Astronauts who landed on the moon during the Apollo 15, 16 and 17 missions brought back a large collection
of rocks to the earth. Knowing the rocks weighed 139 lb when they were on the moon, determine (a) the
weight of the rocks on the earth, (b) the mass of the rocks in slugs. The acceleration due to gravity on the
moon is 5.30 ft/s2.
SOLUTION
PROBLEM 12.2
The value of g at any latitude
φ
may be obtained from the formula
which takes into account the effect of the rotation of the earth, as well as the fact that the earth is not truly
spherical. Knowing that the weight of a silver bar has been officially designated as 5 lb, determine to four
significant figures (a) the mass is slugs, (b) the weight in pounds at the latitudes of 0°, 45°, and 60°.
SOLUTION
φ
= +
PROBLEM 12.3
A 400–kg satellite has been placed in a circular orbit 1500 km above the surface of the earth. The acceleration
of gravity at this elevation is 6.43 m/s2. Determine the linear momentum of the satellite, knowing that its
orbital speed is
3
25.6 10 km/h.×
SOLUTION
PROBLEM 12.4
A spring scale A and a lever scale B having equal lever arms
are fastened to the roof of an elevator, and identical packages
are attached to the scales as shown. Knowing that when the
elevator moves downward with an acceleration of
2
1 m/s
the
spring scale indicates a load of 60 N, determine (a) the weight
of the packages, (b) the load indicated by the spring scale and
the mass needed to balance the lever scale when the elevator
moves upward with an acceleration of 1 m/s2.
SOLUTION
2
PROBLEM 12.4 (Continued)
a

9.81
w
w
PROBLEM 12.5
In anticipation of a long 7° upgrade, a bus driver accelerates at a constant rate of
2
3 ft/s
while still on a level
section of the highway. Knowing that the speed of the bus is
60 mi/h
as it begins to climb the grade and that
the driver does not change the setting of his throttle or shift gears, determine the distance traveled by the bus
up the grade when its speed has decreased to
50 mi/h.
SOLUTION
upgrade
PROBLEM 12.6
A 0.2–lb model rocket is launched vertically from rest at time t = 0 with a constant thrust
of 2 lb for one second and no thrust for t > 1 s. Neglecting air resistance and the decrease
in mass of the rocket, determine (a) the maximum height h reached by the rocket, (b) the
time required to reach this maximum height.
PROBLEM 12.7
A tugboat pulls a small barge through a harbor. The
propeller thrust minus the drag produces a net thrust
that varies linearly with speed. Knowing that the
combined weight of the tug and barge is 3600 kN,
determine (a) the time required to increase the
speed from an initial value v1 = 1.0 m/s to a final
value v2 = 2.5 m/s, (b) the distance traveled during
this time interval.
PROBLEM 12.7 (Continued)
vdv
PROBLEM 12.8
Determine the maximum theoretical speed that may be achieved over a distance of 60 m by a car starting from
rest, knowing that the coefficient of static friction is 0.80 between the tires and the pavement and that 60 percent
of the weight of the car is distributed over its front wheels and 40 percent over its rear wheels. Assume
(a) four-wheel drive, (b) front–wheel drive, (c) rear–wheel drive.
SOLUTION
PROBLEM 12.8 (Continued)
PROBLEM 12.9
If an automobile’s braking distance from 90 km/h is 45 m on level pavement, determine the automobile’s
braking distance from 90 km/h when it is (a) going up a 5° incline, (b) going down a 3-percent incline.
Assume the braking force is independent of grade.
SOLUTION
Assume uniformly decelerated motion in all cases.
For braking on the level surface,
0
0
22
00
22
90 km/h 25 m/s, 0
45 m
2( )
f
f
ff
vv
xx
v v ax x
vv
= = =
−=
=+−
−
(2)( 7.79944)
040.1 m
f
PROBLEM 12.9 (Continued)
0
(2)( 6.65028)
f
0
f
PROBLEM 12.10
A mother and her child are skiing together, and the
mother is holding the end of a rope tied to the child’s
waist. They are moving at a speed of 7.2 km/h on a
gently sloping portion of the ski slope when the
mother observes that they are approaching a steep
descent. She pulls on the rope with an average force
of 7 N. Knowing the coefficient of friction between
the child and the ground is 0.1 and the angle of the
rope does not change, determine (a) the time required
for the child’s speed to be cut in half, (b) the distance
traveled in this time.
SOLUTION
PROBLEM 12.11
The coefficients of friction between the load and the flat–bed
trailer shown are
0.40
s
µ
=
and
0.30.
k
µ
=
Knowing that the
speed of the rig is 72 km/h, determine the shortest distance in
which the rig can be brought to a stop if the load is not to shift.
SOLUTION
PROBLEM 12.12
A light train made up of two cars is traveling at 90 km/h when the
brakes are applied to both cars. Knowing that car A has a mass of 25
Mg and car B a mass of 20 Mg, and that the braking force is 30 kN
on each car, determine (a) the distance traveled by the train before it
comes to a stop, (b) the force in the coupling between the cars while
the train is showing down.
SOLUTION
PROBLEM 12.13
The two blocks shown are originally at rest. Neglecting the
masses of the pulleys and the effect of friction in the pulleys
and between block A and the incline, determine (a) the
acceleration of each block, (b) the tension in the cable.
SOLUTION
1.
2
BA
Block A
200
: (200 lb)sin 30 32.2
x AA A
F ma T aΣ = − °=
(1)
Block B
350 1
: 350 lb 2
32.2 2
y BB A
F ma T a

Σ= − = 

(2)
(a) Multiply Eq. (1) by 2 and add Eq. (2) in order to eliminate T:
200 350 1
2(200)sin 30 350 2 32.2 32.2 2
AA
aa

− °+ = + 

575
150 32.2
A
a=
2
8.40 ft/s
A=a
30°
2
11
(8.40 ft/s ),
22
BA
aa= =
2
4.20 ft/s
B=a
(b) From Eq. (1),
200
(200) sin 30 (8.40)
32.2
T− °=
152.2 lbT=
PROBLEM 12.14
Solve Problem 12.13, assuming that the coefficients of
friction between block A and the incline are
0.25
s
µ
=
and
0.20.
k
µ
=
PROBLEM 12.13 The two blocks shown are originally at
rest. Neglecting the masses of the pulleys and the effect of
friction in the pulleys and between block A and the incline,
determine (a) the acceleration of each block, (b) the tension
in the cable.
SOLUTION
We first determine whether the blocks move by computing the friction force required to maintain block A in
equilibrium. T = 175 lb. When B in equilibrium,
req , blocks will move ( up and down).
m
We note that
1.
2
BA
aa=