Bukhovtsev-et-al-Problems-in-Elementary-Physics

248 ANSWERS AND SOLUTIONS
1-9. The Law of Gravitation
220. According to Newton's second law, mig==F, where m, is the inertial
mass-a quantity that characterizes the ability of bodies to acquire an acceleration
under the influence of a definite force.
mM
On the other hand, according to the law of gravitation F='V ~2 g, where
y is the gravity constant and m g and Mg are the gravitational masses of
the interacting bodies. The gravitational mass determines the force of gravity
and, in this sense, can be referred to as a gravitational charge.
It is not obvious in advance that mi=m g • If this equation (proportionality
is sufficient) is satisfied, however, the gravity acceleration is the same for all
bodies since, when the gravity force is introduced into Newton's second law,
the masses mj and m g can be cancelled, and g will be equal to y ; .
Identical accelerations are imparted to all bodies irrespective of their
masses, only by the force of gravity.
221. The gravitational acceleration g=y ~ (see Problem 220). Assuming
that g=982 em/s, we find that y=6.68X 10- 8 ems,-1 S-2.
222. The bodies inside the spaceship will cease to exert any pressure on
the walls of the cabin if they have the same acceleration as the spaceship.
Only the force of gravity can impart an identical acceleration in this space
to all the bodies irrespective of their mass. Consequently, it is essential that
the engine of the spaceship be shut off and there be no resistance of the
external medium. The spaceship may move in any direction with respect to
that of the force of gravity.
223. The force of gravity imparts the same acceleration to the pendulum
and the block. Gravity does not cause any deformations in the system during
free falling. For this reason the pendulum will so move with respect to the
block as if there is no gravitation (see the solution to Problem 222). The
pendulum will move with a constant angular velocity as long as the block
falls.
224. On section Be A (Fig. 371) the force of gravity performs positive work
(the angle 9 1 is acute) and the velocity of the planet will increase, reaching
its maximum at point A.
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Fig. 311 Fig. 372