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PROBLEM 12.91 (Continued)
PROBLEM 12.92
Two 2.6-lb collars A and B can slide without friction on a frame, consisting
of the horizontal rod OE and the vertical rod CD, which is free to rotate
about CD. The two collars are connected by a cord running over a pulley
that is attached to the frame at O and a stop prevents collar B from moving.
The frame is rotating at the rate
12 rad/s
and 0.6 ftr when the stop
is removed allowing collar A to move out along rod OE. Neglecting
friction and the mass of the frame, determine, for the position 1.2 ft,r
(a) the transverse component of the velocity of collar A, (b) the tension in
the cord and the acceleration of collar A relative to the rod OE.
PROBLEM 12.93
A small ball swings in a horizontal circle at the end of a cord of length
1
l
,
which forms an angle
1
with the vertical. The cord is then slowly drawn
through the support at O until the length of the free end is
2
.l
(a) Derive a
relation among
1
,l
2
,l
1
,
and
2
.
(b) If the ball is set in motion so that
initially
1
0.8 ml
and
1
35 ,
determine the angle
2
when
2
0.6 m.l
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PROBLEM 12.94
A particle of mass m is projected from Point A with an initial velocity
0
v perpendicular to OA and moves under a central force F along an
elliptic path defined by the equation 0/(2 cos ).rr
Using Eq.
(12.35), show that F is inversely proportional to the square of the
distance r from the particle to the center of force O.
PROBLEM 12.95
A particle of mass m describes the logarithmic spiral 0b
rre
under a central force F directed toward the
center of force O. Using Eq. (12.35) show that F is inversely proportional to the cube of the distance r from
the particle to O.
PROBLEM 12.96
A particle of mass m describes the path defined by the equation
0(6 cos 5)rr
under a central force F directed away from the
center of force O. Using Eq. (12.35), show that F is inversely
proportional to the square of the distance r from the particle to O.
PROBLEM 12.97
A particle of mass m describes the parabola 2
0
4yxrunder a central
force F directed toward the center of force C. Using Eq. (12.35) and
Eq.
12.37 ' with 1,
show that F is inversely proportional to the square
of the distance r from the particle to the center of force and that the angular
momentum per unit mass 0
2.hGMr
PROBLEM 12.98
It was observed that during its second flyby of the earth, the Galileo spacecraft had a velocity of 14.1 km/s as
it reached its minimum altitude of 303 km above the surface of the earth. Determine the eccentricity of the
trajectory of the spacecraft during this portion of its flight.
PROBLEM 12.99
It was observed that during the Galileo spacecraft’s first flyby of the earth, its maximum altitude was 600 mi
above the surface of the earth. Assuming that the trajectory of the spacecraft was parabolic, determine the
maximum velocity of Galileo during its first flyby of the earth.
PROBLEM 12.100
As a space probe approaching the planet Venus on a parabolic trajectory reaches
Point A closest to the planet, its velocity is decreased to insert it into a circular
orbit. Knowing that the mass and the radius of Venus are 4.87 24
10 kg and 6052
km, respectively, determine (a) the velocity of the probe as it approaches A,
(b) the decrease in velocity required to insert it into the circular orbit.
