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PROBLEM 12.75 (Continued)
PROBLEM 12.76
A particle of mass m is projected from Point A with an initial velocity v0
perpendicular to line OA and moves under a central force F along a
semicircular path of diameter OA. Observing that 0cosrr
and using
Eq. (12.25), show that the speed of the particle is 2
0/cos .vv
PROBLEM 12.77
For the particle of Problem 12.76, determine the tangential component t
F
of the central force F along the tangent to the path of the particle for
(a) 0,
(b) 45 .
PROBLEM 12.76 A particle of mass m is projected from Point A with an
initial velocity v0 perpendicular to line OA and moves under a central force
F along a semicircular path of diameter OA. Observing that 0cosrr
and using Eq. (12.25), show that the speed of the particle is 2
0/cos .vv
PROBLEM 12.78
Determine the mass of the earth knowing that the mean radius of the moon’s orbit about the earth is 238,910 mi
and that the moon requires 27.32 days to complete one full revolution about the earth.
PROBLEM 12.79
Show that the radius r of the moon’s orbit can be determined from the radius R of the earth, the acceleration of
gravity g at the surface of the earth, and the time
required for the moon to complete one full revolution about
the earth. Compute r knowing that 27.3
days, giving the answer in both SI and U.S. customary units.
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 12.80
Communication satellites are placed in a geosynchronous orbit, i.e., in a circular orbit such that they complete
one full revolution about the earth in one sidereal day (23.934 h), and thus appear stationary with respect to
the ground. Determine (a) the altitude of these satellites above the surface of the earth, (b) the velocity with
which they describe their orbit. Give the answers in both SI and U.S. customary units.
PROBLEM 12.80 (Continued)
PROBLEM 12.81
Show that the radius r of the orbit of a moon of a given planet can be determined from the radius R of the
planet, the acceleration of gravity at the surface of the planet, and the time
required by the moon to complete
one full revolution about the planet. Determine the acceleration of gravity at the surface of the planet Jupiter
knowing that R 71,492 km and that
3.551 days and r 670.9 103 km for its moon Europa.
PROBLEM 12.82
The orbit of the planet Venus is nearly circular with an orbital velocity of 126.5 3
10 km/h. Knowing that
the mean distance from the center of the sun to the center of Venus is 108 6
10 km and that the radius of the
sun is 3
695 10 km, determine (a) the mass of the sun, (b) the acceleration of gravity at the surface of the
sun.
PROBLEM 12.83
A satellite is placed into a circular orbit about the planet Saturn at an altitude of 2100 mi. The satellite
describes its orbit with a velocity of 3
54.7 10 mi/h. Knowing that the radius of the orbit about Saturn and the
periodic time of Atlas, one of Saturn’s moons, are 3
85.54 10 mi and 0.6017 days, respectively, determine
(a) the radius of Saturn, (b) the mass of Saturn. (The periodic time of a satellite is the time it requires to
complete one full revolution about the planet.)
