1.296. T = 11277 - 14o 2 1 (1 -.- r 2 /1 2 ), Al = 1 / 3 p.o 2 l^3 IE, where p is
the density of copper.
1.297. AV'--= (1 — 2μl FlIE = 1.6 mm 3 , where p. is Poisson's
ratio for copper.
is the density, and p, is Poisson's ratio for copper.1.298. (a) Al = 1 / 2 pg/ 2 /E; (b) AVIV = (1 — 2p,) 6.111, where p1.299. (a) ATI/V = —3 (1 — 20 pIE; (b) 13 = 3 (1 — 20/E.
1.300. R = 116 Eh 2 /pgl 2 =-- 0.12 km, where p is the density of
steel.
1.301. (a) Here N is independent of x and equal to No. Integrat-
ing twice the initial equation with regard to the boundary condi-
tions dyldx (0) = 0 and y (0) = 0, we obtain y 0 12E1) x^2. This
is the equation of a parabola. The bending deflection is X =
=N 0 / 2 /2E/, where I = a^4 /12.
(b) In this case N (x) = F (1 — x) and y = (F12EI) (1 — x13) x 2 ;
= F1 3 13EI, where I is of the same magnitude as in (a).
1.302. 1. = F1^3 148EI.
1.303. (a) X = 3 / 2 pg1 4 1Eh 2 ; (b) =^5 / 2 pg1 4 1Eh 2. Here p is the
density of steel.
1.304. X, = 2 / 5 13p1 5 /Eh 2 , where p is the density of steel.
1.305. (a) q =- (l/2nr^3 ArG)- N; (b)^ (211 a-v.4G) • N.
1.306. N = n (d: — (4) G(p/32/ = 0.5 kN•m.
1.307. P = i/ 2 ar^4 G(pco = 17 kW.
1.308. N = 1/2 pm (r: - r 4 )I(r 22 —
1.309. U = 1 / 2 mE8 2 /p = 0.04 kJ, where p is the density of steel.
1.310. (a) U =^1 /onr 2 / 3 o 2 g 2 /E; (b) U = 2 /3 nr^2 lE (A111)^2. Here p
is the density of steel.
1.311. A 116 n 2 11(5 3 E11 = 0.08 kJ.
1.312. U =^1 /^4 ar^4 Gy^2 // = 7 J.
1.313. u = 1/^2 GT^2 r2//2.^
1.314. u = 1 / 213 (pgh)^2 = 23.5 kJ/m^3 , where 13 is the compressi-
bility.
1.315. pi > p 2 , v 1 < v 2. The density of streamlines grows on
transition from point 1 to point 2.
1.316. Q = S^1 S^2 1/^20111 (S^22 — Si).
1.317. Q = Si/ 2gAhp 0 Ip.
1.318. v= 2g (hi + hzPziPi) = 3 m/s, where pi and p 2 are the
densities of water and kerosene.
1.319. h = 25 cm; lmax = 50 cm.
1.320. h 1 / 2 v 2 /g — ho = 20 cm.
1.321. p = Po pgh (1. — R:/r 2 ), where R 1 <r <R (^2) , Po is the
atmospheric pressure.
1.322. A =^1 /20 73 /s 2 t^2 , where p is the density of water.
1.323. r = V2h/g S/s.
1.324. v = colt 17211h-1.
1.326. F = 2pgS c1 h = 0.50 N.
1.327. F= pgbl (2h — 1) = 5 N.