Earth's surface. What additional velocity has to be imparted to the
spaceship to overcome the gravitational pull?
1.231. At what distance from the centre of the Moon is the point
at which the strength of the resultant of the Earth's and Moon's
gravitational fields is equal to zero? The Earth's mass is assumed to
be 1 1 = 81 times that of the Moon, and the distance between the cen-
tres of these planets n = 60 times greater than the radius of the Earth
R.
1.232. What is the minimum work that has to be performed to
bring a spaceship of mass m = 2.0.10 3 kg from the surface of the Earth
to the Moon?
1.233. Find approximately the third cosmic velocity v 3 , i.e. the
minimum velocity that has to be imparted to a body relative to the
Earth's surface to drive it out of the Solar system. The rotation of
the Earth about its own axis is to be neglected.
1.5. Dynamics of a Solid Body
- Equation of dynamics of a solid bOdy rotating about a stationary axis z:
Ipz = N (1.5a)
where N , is the algebraic sum of the moments of external forces relative to the
z axis. - According to Steiner's theorem:
/ = /c ma 2. (1.5b) - Kinetic energy of a solid body rotating about a stationary axis:
T= —^1 2 - 10.
(1.5c)- Work performed by external forces during the rotation of a solid body
about a stationary axis:
A = J Nz dcp. - Kinetic energy of a solid body in plane motion:
T — /CO nwb
2 2- Relationship between the angular velocity w' of gyroscope precession,
its angular momentum M equal to Ro, and the moment N of the external forces:
[w' M] = N. (^) (1.51)
1.234. A thin uniform rod AB of mass m = 1.0 kg moves transla-
tionally with acceleration w = 2.0 m/s 2 due to two antiparallel forces
F 1 and F (^2) (Fig. 1.52). The distance between the points at which these
forces are applied is equal to a = 20 cm. Besides, it is known that
F2 = 5.0 N. Find the length of the rod.
1.235. A force F = Ai + Bj is applied to a point whose radius
vector relative to the origin of coordinates (^0) is equal to r = ai
bj, where a, b, A, B are constants, and i, j are the unit vectors of
(1.5d)
(1.5e)
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