1.296. T = 11277- 14o21 (1 -.- r2/12), Al = 1/3 p.o2l3IE, where p is
the density of copper.
1.297. AV'--= (1 — 2µl FlIE = 1.6 mm3, 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 p
1.299. (a) ATI/V = —3 (1 — 20 pIE; (b) 13 = 3 (1 — 20/E.
1.300. R = 116 Eh2/pgl2 =-- 0.12 km, where p is the density of
steel.
1.301. (a) Here N is independent of x and equal to No. Integrating twice the initial equation with regard to the boundary conditions dyldx (0) = 0 and y (0) = 0, we obtain y
012E1) x2. This
is the equation of a parabola. The bending deflection is X =
=N 0/2/2E/, where I = a4/12.
(b) In this case N (x) = F (1 — x) and y = (F12EI) (1 — x13) x2;
= F1313EI, where I is of the same magnitude as in (a).
1.302. 1. = F13148EI.
1.303. (a) X = 3/2 pg141Eh2; (b) = 5/2 pg141Eh2. Here p is the
density of steel.
1.304. X, = 2/513p15/Eh2, where p is the density of steel.
1.305. (a) q =- (l/2nr3 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 ar4G(pco = 17 kW.
1.308. N = 1/2 pm (r: - r4)I(r2 2 —
1.309. U = 1/2mE82/p = 0.04 kJ, where p is the density of steel.
1.310. (a) U = 1 /onr2 /3o2g2/E; (b) U = 2/3 nr2lE (A111)2. Here p
is the density of steel.
1.311. A
1 16 n211(53E11 = 0.08 kJ.
1.312. U = 1/4 ar4Gy2// = 7 J.
1.313. u = 1/ 2 GT2r2//2.
1.314. u = 1/213 (pgh)2 = 23.5 kJ/m3, where 13 is the compressibility.
1.315. pi > p2, v1 < v2. The density of streamlines grows on
transition from point 1 to point 2.
1.316. Q = S1S2 1/ 20111 (S2 2 — Si).
1.317. Q = Si/ 2gAhp0Ip.
3 m/s, where pi and p2 are the
1.318. v= 2g (hi + hzPziPi) =
water and kerosene.
densities of
= 25 cm; lmax = 50 cm.
1.319. h
1/2 v2/g — ho = 20 cm.
1.320. h
= Po
pgh (1. — R:/r2), where R1
atmospheric pressure.
= 1 /2073 /s2t2, where p is the density of water.
1.322. A
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.
the density of copper.
1.297. AV'--= (1 — 2µl FlIE = 1.6 mm3, 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 p
1.299. (a) ATI/V = —3 (1 — 20 pIE; (b) 13 = 3 (1 — 20/E.
1.300. R = 116 Eh2/pgl2 =-- 0.12 km, where p is the density of
steel.
1.301. (a) Here N is independent of x and equal to No. Integrating twice the initial equation with regard to the boundary conditions dyldx (0) = 0 and y (0) = 0, we obtain y
012E1) x2. This
is the equation of a parabola. The bending deflection is X =
=N 0/2/2E/, where I = a4/12.
(b) In this case N (x) = F (1 — x) and y = (F12EI) (1 — x13) x2;
= F1313EI, where I is of the same magnitude as in (a).
1.302. 1. = F13148EI.
1.303. (a) X = 3/2 pg141Eh2; (b) = 5/2 pg141Eh2. Here p is the
density of steel.
1.304. X, = 2/513p15/Eh2, where p is the density of steel.
1.305. (a) q =- (l/2nr3 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 ar4G(pco = 17 kW.
1.308. N = 1/2 pm (r: - r4)I(r2 2 —
1.309. U = 1/2mE82/p = 0.04 kJ, where p is the density of steel.
1.310. (a) U = 1 /onr2 /3o2g2/E; (b) U = 2/3 nr2lE (A111)2. Here p
is the density of steel.
1.311. A
1 16 n211(53E11 = 0.08 kJ.
1.312. U = 1/4 ar4Gy2// = 7 J.
1.313. u = 1/ 2 GT2r2//2.
1.314. u = 1/213 (pgh)2 = 23.5 kJ/m3, where 13 is the compressibility.
1.315. pi > p2, v1 < v2. The density of streamlines grows on
transition from point 1 to point 2.
1.316. Q = S1S2 1/ 20111 (S2 2 — Si).
1.317. Q = Si/ 2gAhp0Ip.
3 m/s, where pi and p2 are the
1.318. v= 2g (hi + hzPziPi) =
water and kerosene.
densities of
= 25 cm; lmax = 50 cm.
1.319. h
1/2 v2/g — ho = 20 cm.
1.320. h
= Po
pgh (1. — R:/r2), where R1
atmospheric pressure.
= 1 /2073 /s2t2, where p is the density of water.
1.322. A
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.