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PROBLEM 12.128
A small 200-g collar C can slide on a semicircular rod which is made to rotate about
the vertical AB at the constant rate of 6 rad/s. Determine the minimum required value
of the coefficient of static friction between the collar and the rod if the collar is not to
slide when (a) (b) (c) Indicate in each case the direction
of the impending motion.
90 ,
75 ,
45 .
PROBLEM 12.128 (Continued)
PROBLEM 12.128 (Continued)
s
PROBLEM 12.129
Telemetry technology is used to quantify kinematic values of a
200-kg roller coaster cart as it passes overhead. According to
the system,
At this instant, determine
(a) the normal force between the cart and the track, (b) the
radius of curvature of the track.
25 m, 10 m/s,rr
2
2 m/s , 90 ,r
0.4 rad/s,
2
0.32 rad/s .
PROBLEM 12.130
The radius of the orbit of a moon of a given planet is equal to twice the radius of that planet. Denoting
by
the mean density of the planet, show that the time required by the moon to complete one full revolution
about the planet is where G is the constant of gravitation.
1/2
(24 / ) ,G
PROBLEM 12.131
At engine burnout on a mission, a shuttle had reached Point A at an
altitude of 40 mi above the surface of the earth and had a horizontal
velocity v0. Knowing that its first orbit was elliptic and that the shuttle
was transferred to a circular orbit as it passed through Point B at an
altitude of 170 mi, determine (a) the time needed for the shuttle to travel
from A to B on its original elliptic orbit, (b) the periodic time of the
shuttle on its final circular orbit.
AB
AB
PROBLEM 12.131 (Continued)
circ 1.498 h
PROBLEM 12.132
A space probe in a low earth orbit is inserted into an elliptic
transfer orbit to the planet Venus. Knowing that the mass of the
sun is times the mass of the earth and assuming that
the probe is subjected only to the gravitational attraction of the
sun, determine the value of which defines the relative position
of Venus with respect to the earth at the time the probe is inserted
into the transfer orbit.
3
332.8 10
,
PROBLEM 12.132 (Continued)
PROBLEM 12.133*
Disk A rotates in a horizontal plane about a vertical axis at the
constant rate rad/s. Slider B has mass 1 kg and moves in a
frictionless slot cut in the disk. The slider is attached to a spring of
constant k, which is undeformed when Knowing that the slider
is released with no radial velocity in the position
determine the position of the slider and the horizontal force exerted
on it by the disk at for (a) (b)
010
0.r
500 mm,r
0.1 st
100 N/m,k
200 N/m.k
