viscosities of glycerin and water are equal to rh = 13.9 P and 12 =
= 0.011 P respectively.
1.338. A lead sphere is steadily sinking in glycerin whose viscosity
is equal toil = 13.9 P. What is the maximum diameter of the sphere
at which the flow around that sphere still remains laminar? It is
known that the transition to the turbulent flow corresponds to Rey-
nolds number Re = 0.5. (Here the characteristic length is taken to
be the sphere diameter.)
1.339. A steel ball of diameter d = 3.0 mm starts sinking with
zero initial velocity in olive oil whose viscosity is 1 = 0.90 P. How
soon after the beginning of motion will the velocity of the ball differ
from the steady-state velocity by n = 1.0%?
1.8. Relativistic Mechanics
1 — (v/c) 2
where / 0 is the proper length and Ato is the proper time of the moving clock.- Lorentz transformation*:
x—Vt t
1
— XVIC 2— (^) e —
(V/c)2 — (V/c)^2 •^
(1.8b)
- Interval 8 12 is an invariant:
s2 2 =c2t2 2 _1qf 2
1 -= in ,^ (I .8c)
where t 12 is the time interval between events 1 and 2, /^12 is the distance between
the points at which these events occurred. - Transformation of velocity*:
- (1.8d)
(1.8e)(1.8f)(1.8g)' vs— V^ vy "1/- 1 — (V/c)^2
voc 1 —vxV/c 2 'v,
1 —vxV/c 2- Relativistic mass and relativistic momentum:
M — mo^ p= my = MoV
y 1— (v/02^ y 1— (v/02
where mo is the rest mass, or, simply, the mass.- Relativistic equation of dynamics for a particle:
dp F
dt
where p is the relativistic momentum of the particle. - Total and kinetic energies of a relativistic particle:
E = mc2 = m0,2 + T, T -= (m — mo ) c 2.
* The reference frame K' is assumed to move with a velocity V in the posi-
tive direction of the x axis of the frame K, with the x' and x axes coinciding and
the y' and y axes parallel.- Lorentz contraction of length and slowing of a moving chick:
/ = / 0 -V 1 —(v/c) 2 , At= A to (1.8a)5* 67