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PROBLEM 12.121
Show that the angular momentum per unit mass h of a satellite describing an elliptic orbit of semimajor axis a
and eccentricity about a planet of mass M can be expressed as
2
(1 )hGMa
PROBLEM 12.122
In the braking test of a sports car its velocity is reduced from 70 mi/h to zero in a distance of 170 ft with
slipping impending. Knowing that the coefficient of kinetic friction is 80 percent of the coefficient of static
friction, determine (a) the coefficient of static friction, (b) the stopping distance for the same initial velocity if
the car skids. Ignore air resistance and rolling resistance.
PROBLEM 12.123
A bucket is attached to a rope of length L 1.2 m and is made to revolve in a
horizontal circle. Drops of water leaking from the bucket fall and strike the floor
along the perimeter of a circle of radius a. Determine the radius a when
30 .
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 12.123 (Continued)
Projection on horizontal floor (uniform motion)
00
() sin30 0, 0.6 m
z
xx vtL x
PROBLEM 12.124
A 12-lb block B rests as shown on the upper surface of a 30-lb wedge A.
Neglecting friction, determine immediately after the system is released from
rest (a) the acceleration of A, (b) the acceleration of B relative to A.
PROBLEM 12.125
A 500-lb crate B is suspended from a cable attached to a 40-lb trolley A
which rides on an inclined I-beam as shown. Knowing that at the instant
shown the trolley has an acceleration of 1.2 ft/s
2
up and to the right,
determine (a) the acceleration of B relative to A, (b) the tension in cable CD.
or
For trolley A
or
or
g
2
2
(1.2 ft/s )sin 25
(500 lb) 1 32.2 ft/s
507.87 lb
AB
T
:sin25sin25
A
x
AA CD AB A A
W
Fma T T W a
g
2
2
1.2 ft/s
(507.87 lb)sin 25 (40 lb) sin 25 32.2 ft/s
CD
T
233 lb
CD
T
PROBLEM 12.126
The roller-coaster track shown is contained in a vertical plane.
The portion of track between A and B is straight and
horizontal, while the portions to the left of A and to the right
of B have radii of curvature as indicated. A car is traveling at a
speed of 72 km/h when the brakes are suddenly applied,
causing the wheels of the car to slide on the track
Determine the initial deceleration of the car if the brakes are
applied as the car (a) has almost reached A, (b) is traveling
between A and B, (c) has just passed B.
(0.25).
k
PROBLEM 12.126 (Continued)
or
()
RF n
NNmga
PROBLEM 12.127
The parasailing system shown uses a
winch to pull the rider in towards the
boat,
whichistravellingwitha
constantvelocity.
During the interval
when
is between 20º and 40º, (where t
= 0 at
= 20º) the angle increases at the
constant rate of 2 º/s. During this time,
the length of the rope is defined by the
relationship
3/2
1
125 3
rt
, where r
and t are expressed in meters and
seconds, respectively. At the instant
when the rope makes a 30 degree angle
with the water, the tension in the rope is
18 kN. At this instant, what is the
magnitude and direction of the force of
the parasail on the 75 kg parasailor?
P
P
PROBLEM 12.127 (Continued)
P
P
