1.367. Taking into account that v = (w't/c) 2 , we getTo — yi+d(tw, (^002) In [ .± 1 + ) 2 ] = 3.5 months.
0
1.368. m/mo 1/V2 (1. --p) 70, where 13= v/c.
1.369. v (2 ri)/(1 = 0.6c, where c is the velocity
of light. The definition of density as the ratio of the rest mass of a
body to its volume is employed here.
1.370. (c — v)Ic = 1 — [1 + (m 0 c/p) 2 ] -1/ 2 = 0.44%.
1.371. v = (chi) 1 = 1/,c
1.372. A = 0.42 m (^0) c 2 instead of 0.14 m 0 c 2.
1.373. v = 1 / 2 cV 3 = 2.6.10 8 m/s.
1.374. For a < 1 the ratio is T/m^0 c 2 < 4 / 3 0.013.
1.375. p =V T (T +2m 0 c 2 )1c =1.09 GeV/c, where c is the velo-
city of light.
1.376. F = (I 1 ec) V T (T +2moc 2 ), P = T I le.
1.377. p= 2nmv 2 /(1 — v 2 /c 2 ).
1.378. v= Fct/Vm^2 oc^2 + F 2 t 2 , 1 =i 1 (moc 2 IF) 2 + c^2 t^2 — M0C^2 / F
1.379. F = m 0 c 2 1a.
1.380. (a) In two cases: F v and F v; (b) Fl = mow V-1 —13^2 ,
mow/(1 —p2) 3 / 2 , where 13= v/c•
1.382. 8' e 17(1 —13)/(1 +13), where f3 = V/c, V = 3 /oc.
1.383. E 2 — p^2 c^2 = m,;c^4 , where m 0 is the rest mass of the par-
ticle.
1.384. (a) T = 2m 0 c2 (111 +7 72moc2 — 1) = 777 MeV,
=--- 111 /2/noT = 940 MeV/c; (b) V = ci/ T/(T 2m,c^2 ) =2.12 .10^8 m/s.
1.385. M (^0) -=-112mo 2m 0 c 2 )/c, V =c1/ T 1(T +2m 0 c 2 ).
1.386. T' = 2T (T +2m 0 c 2 )1moc 2 =1.43.10 3 GeV.
1.387. Ei max = ma -Fm?— 27n(m2+ o m3)2 c 2. The particle m has the i
highest energy when the energy of the system of the remaining
two particles m 2 and m 3 is the lowest, i.e. when they move as
a single whole.
N2uc
1.388. v/c =
oninio
1+ (non'^0 dau/c , Use the momentum conservation law
(as in solving Problem 1.178) and the relativistic formula for
velocity transformation.
2.1. m = pV Ap/p 0 = 30 g, where p^0 is the standard atmospher-
ic pressure.
2.2. p = 112 (piT 2 ITi — Ap) = 0.10 atm.
2.3. ml/m 2 = (1 — alM 2 )1(alMi — 1) = 0.50, where a =
mRT/pV.
2.4.^0 RT (mPo l/M(nil-Fr%) l-1-m2/M2)^ —1.^5 g/1
) •