1.232. A
ym (M1/R1 M 2/R2) = 1.3.108 kJ, where M and
R are the mass and the radius of the Earth and the Moon.
1.233. v3 V 2v: +
- 1)2 V;, x 17 km/s.
Here i4
TME IR, ME and R are the mass and the radius of the Earth;
Vi = yMslr, Ms is the mass of the Sun, r is the radius of the
Earth's orbit.
1.234. 1 = 2aF2/mw = 1.0 m.
1.235. N = (aB—bA)k, where k is the unit vector of the z
axis; l= I aB — bA
+ B2.
1.236. 1= I aA—bB
A2+ B2.
1.237. F„ = 2F. This force is parallel to the diagonal AC and
is applied at the midpoint of the side BC.
1.238. (a) I = 1/3m12; (b) I = 'ism (a2
b2).
1.239. (a) I = iJ2 rtpbR4 = 2.8 g•m2; (b) I = 8/10 mR2.
1.240. I = il4mR2.
1.241. I = (37/72) mR2 = 0.15 kg•m2.
1.242. I = 213 mR2.
1.243. (a) co = gt1R (1 + M/2m); (b) T = mg2t2/2(1
M12m).
1.244. T = 112mg, Ivo = gmr21I.
1.245. co =176F sin (/ml.
1.246. R
1,712 — rni lg
Ti
—
(m+4m2)
(mi - I- m2
m/2) R '
T2
MI (M+ 41711)
(7712 — kini) kntig2t 2
1.247. Arad/s2;
m+2(mi-Fm2) •
1.248. n = (1 + k2) co:R/8ak (k
1) g.
1.249. t = 314coRlkg.
1.250. (w) = 1/3ceo •
1.251. 13 = 2mgx1R1(M + 2m).
1.252. (a) k > 2/7 tan a; (b) T = 5114 mg2t2 sins a.
1.253. (a) T = 116 mg = 13 N, t3 = 2/3 g/R = 5.102
(b) P = 213 mg2t.
1.254. w' = 2/3 (g — w0), F = 1/3 m (g — wo).
1.255. w= g sin a/(1
I/mr2) = 1.6 m/s2.
1.256. Finax = 3kmg1(2 — 3k); wmax = 2kg1(2 — 3k).
F (cos cc — r I R)
F2t2 (cos a, — r/R)2
1.257. (a) wx — m (1+7)
(b) A —
2m (1+7)
1.258. T = 1110 mg.
1.259. w = 3g (M + 3m)1(M + 9m ± I1R2).
1.260. (a) w =
F (3m1-1-2m2)F 2t 2 (3m2-1-2m2)
m1
(b)
(m1M2)
2m1(m1+ ms)
1.261. w
1
F/(m1
217m2); w2
2/7
1.262. (a) t =
co0R1kg; (b) A = —1/ontw:R2.
1.263. a) =1710g (R+r)/17r2.
1.264. vo = V 113gR (7 cos a — 4) =1.0 m/s.
1.265. v
°
=1/ 8gR.
1.266. T = mv2.
1.267. T = 7110 mv2 (1 + 217r21R2).
19•
ym (M1/R1 M 2/R2) = 1.3.108 kJ, where M and
R are the mass and the radius of the Earth and the Moon.
1.233. v3 V 2v: +
- 1)2 V;, x 17 km/s.
Here i4
TME IR, ME and R are the mass and the radius of the Earth;
Vi = yMslr, Ms is the mass of the Sun, r is the radius of the
Earth's orbit.
1.234. 1 = 2aF2/mw = 1.0 m.
1.235. N = (aB—bA)k, where k is the unit vector of the z
axis; l= I aB — bA
+ B2.
1.236. 1= I aA—bB
A2+ B2.
1.237. F„ = 2F. This force is parallel to the diagonal AC and
is applied at the midpoint of the side BC.
1.238. (a) I = 1/3m12; (b) I = 'ism (a2
b2).
1.239. (a) I = iJ2 rtpbR4 = 2.8 g•m2; (b) I = 8/10 mR2.
1.240. I = il4mR2.
1.241. I = (37/72) mR2 = 0.15 kg•m2.
1.242. I = 213 mR2.
1.243. (a) co = gt1R (1 + M/2m); (b) T = mg2t2/2(1
M12m).
1.244. T = 112mg, Ivo = gmr21I.
1.245. co =176F sin (/ml.
1.246. R
1,712 — rni lg
Ti
—
(m+4m2)
(mi - I- m2
m/2) R '
T2
MI (M+ 41711)
(7712 — kini) kntig2t 2
1.247. Arad/s2;
m+2(mi-Fm2) •
1.248. n = (1 + k2) co:R/8ak (k
1) g.
1.249. t = 314coRlkg.
1.250. (w) = 1/3ceo •
1.251. 13 = 2mgx1R1(M + 2m).
1.252. (a) k > 2/7 tan a; (b) T = 5114 mg2t2 sins a.
1.253. (a) T = 116 mg = 13 N, t3 = 2/3 g/R = 5.102
(b) P = 213 mg2t.
1.254. w' = 2/3 (g — w0), F = 1/3 m (g — wo).
1.255. w= g sin a/(1
I/mr2) = 1.6 m/s2.
1.256. Finax = 3kmg1(2 — 3k); wmax = 2kg1(2 — 3k).
F (cos cc — r I R)
F2t2 (cos a, — r/R)2
1.257. (a) wx — m (1+7)
(b) A —
2m (1+7)
1.258. T = 1110 mg.
1.259. w = 3g (M + 3m)1(M + 9m ± I1R2).
1.260. (a) w =
F (3m1-1-2m2)F 2t 2 (3m2-1-2m2)
m1
(b)
(m1M2)
2m1(m1+ ms)
1.261. w
1
F/(m1
217m2); w2
2/7
1.262. (a) t =
co0R1kg; (b) A = —1/ontw:R2.
1.263. a) =1710g (R+r)/17r2.
1.264. vo = V 113gR (7 cos a — 4) =1.0 m/s.
1.265. v
°
=1/ 8gR.
1.266. T = mv2.
1.267. T = 7110 mv2 (1 + 217r21R2).
19•